[Journal of Astrophysics and Astronomy] Multimessenger Astrophysics (Volume 39, Issue 4, August 2018)

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J. Astrophys. Astr. (2018) 39:44 DOI 10.1007/s12036-018-9541-6

© Indian Academy of Sciences

Editorial Recent discoveries in astrophysics and cosmology have generated tremendous excitement in the scientific world. The first high-energy neutrinos of cosmic origin were recorded by the IceCube, a gigantic cubickilometre-sized detector in the Antarctic ice at the South Pole. The prize catch of gravitational waves (GW) from merging black holes in LIGO detectors for the first time in 2015 opens a new window to the Universe. The discovery of gravitational waves from the merging binary neutron star in August last year followed by its detection across the electromagnetic (EM) spectrum is an outstanding event in the history of mankind. The detection of light from first stars just 180 million years after the Big Bang, hailed as another great breakthrough, was reported recently by a group of radio astronomers. This observation also hinted at the presence of dark matter. All these observations mark a new era of multimessenger astronomy: the exploration of the Universe through combining information from a multitude of cosmic messengers: electromagnetic radiation, gravitational waves, neutrinos and cosmic rays. The questions that can be explored through multimessenger observations concern the dynamics of exploding stars, the formation and evolution of black holes, the origin of cosmic rays, relativistic jets, supermassive black holes in the hearts of galaxies, colliding black holes and neutron stars and many others. Multimessenger astronomy also allows us to address the question of why we are here in the first place, by shedding light on the origin of heavy elements and the evolution of galaxies and the Universe. In the next decade, multimessenger astronomy will probe the rich physics of transient phenomena in the sky, such as the merger of neutron stars and/or black holes, gamma-ray bursts, active galactic nuclei and core-collapse supernovae. India is making a steady progress in multimessenger astronomy with the Giant Metre-Wave Radio Telescope (GMRT) near Pune, a marvel created by Professor Govind Swarup; AstroSat, Published online 11 August 2018

the first Indian observatory in space and gravitational observatory LIGO, India which is in the making. Furthermore, India is participating and taking lead in building the Square Kilometre Array (SKA), the next generation radio telescope to be co-located in South Africa and Australia, Thirty Metre optical Telescope (TMT) and has strong co-operation with the members of the next generation imaging atmospheric Cerenkov detector consortium, Cerenkov Telescope Array (CTA) with generous support from the Department of Atomic Energy and Department of Science and Technology. Saha Institute of Nuclear Physics (SINP) has been involved in PICASSO/PICO Dark Matter search experiment in SNOLab, Canada since 2009 as well as study of very high energy gammaray sources observed with the Major Atmospheric Gamma Imaging Cerenkov (MAGIC) telescope experiment since 2015. Furthermore, SINP along with other institutions is spearheading the Dark Matter search experiment in the underground laboratory to be set up in Jaduguda. Multimessenger astronomy hence requires a coordination of a global network of multimessenger instruments, to develop multimessenger observational strategies and data analysis and an interdisciplinary effort to interpret observations and constrain theoretical models. All this requires tight collaborations between the different GW/EM and neutrino/cosmic-rays communities. The Astroparticle and Cosmology Division of SINP thus aims to bring together these communities together in order to start a discussion on how to coordinate these diverse astrophysical activities under the umbrella of multimessenger astrophysics. This is our tribute to Professor Meghnad Saha on his 125th birth anniversary. Guest Editors Debades Bandyopadhyay Pratik Majumdar

J. Astrophys. Astr. (2018) 39:40 https://doi.org/10.1007/s12036-018-9533-6

© Indian Academy of Sciences

Calculation of the transport coefficients of the nuclear pasta phase RANA NANDI1,∗

and STEFAN SCHRAMM2

1

Tata Institute of Fundamental Research, Mumbai 400 005, India. Institute for Advanced Studies, 60438 Frankfurt am Main, Germany. ∗ Corresponding author. E-mail: [email protected] 2 Frankfurt

MS received 31 May 2018; accepted 11 June 2018; published online 11 July 2018 Abstract. We calculate the transport coefficients of low-density nuclear matter, especially the nuclear pasta phase, using quantum molecular dynamics simulations. The shear viscosity as well as the thermal and electrical conductivities are determined by calculating the static structure factor of protons for all relevant density, temperature and proton fractions, using simulation data. It is found that all the transport coefficients have similar orders of magnitude as found earlier without considering the pasta phase. Our results are thus in contrast to the common belief that the pasta layer is highly resistive and therefore have important astrophysical consequences. Keywords. Neutron stars—transport properties—molecular dynamics.

1. Introduction Based on the composition a neutron star (NS) can be divided into several parts. At the surface there is a thin envelope containing mostly H and He ions and Fe atoms. The outer crust starts at ∼ 104 g cm−3 when atoms get fully ionized and form a Coulomb lattice embedded in an electron gas. With increasing density the nucleus become increasingly neutron-rich due to electron capture process. At ∼4 × 1011 g cm−3 , the nucleus become so neutron rich that neutrons begin to drip out of the nuclei (Baym et al. 1971; Rüster et al. 2006; Nandi & Bandyopadhyay 2011). This marks the end of the outer crust and the beginning of the inner crust. In the inner crust nuclei are immersed in both an electron gas and a neutron gas (Haensel 2001; Nandi et al. 2011). With further increase in density, nuclei come closer and at ∼1014 g cm−3 they merge together to form uniform matter of neutrons, protons, electrons and muons. Just before the transition to uniform matter, nuclei take various complicated shapes due to the competition between Coulomb energy and surface energy. These exotic shapes are collectively known as nuclear ‘pasta phase’ (Ravenhall et al. 1983). The study of pasta phase is crucial to understand various astrophysical phenomena. For example, the scattering of neutrinos from the pasta phase in corecollapse supervovae can significantly affect the neutrino transport, that plays a critical role in the eventual

supernova explosion (Horowitz et al. 2004). On the other hand, the electron-pasta scattering is supposed to greatly influence the transport properties like shear viscosity and thermal and electrical coductivities of NS crust and therefore, can play a crucial role in understanding the phenomena of cooling (Horowitz et al. 2015), magnetic field decay (Pons et al. 2013), crustal oscillations (Chugunov & Yakovlev 2005), etc. of NS. The pasta phase was initially studied by static methods using few specific shapes (Ravenhall et al. 1983; Lorenz et al. 1993; Oyamatsu 1993; Newton & Stone 2009). However, since the shapes are not known a priori it is important to adopt dynamical approach that allows arbitrary nuclear shapes. After the first work of Maruyama et al. (1998), several authors have studied the characteristics of pasta phase using molecular dynamics simulation of different types (Horowitz et al. 2004; Schneider et al. 2013; Dorso et al. 2012; Watanabe et al. 2003; Nandi & Schramm 2016, 2017; Schramm & Nandi 2017a, b). In this article, we study the transport properties of the nuclear pasta phase using quantum molecular dynamics (QMD) simulation.

2. Formalism In QMD, the wave function of a nucleon is represented by a Gaussian wave packet with time-independent width. The interaction between nucleons is described by

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a Skyrme-like Hamiltonian (Nandi & Schramm 2018; Chikazumi et al. 2001)

90

H = T +VPauli +VSkyrme +Vsym +VMD +VSurface +VCoul , (1)

70

where ρp (q, t) is the Fourier transform of proton number density, which is calculated using positions of the nucleons at time t. The average is taken over simulation time as well as all the directions of momentum transfer q = 2π L (l, m, n), where l, m, n are integers and L is the length of the cubic simulation box determined from the number of nucleons used in the simulation and the density as L = (N /ρ)1/3 . To incorporate long-range (small q) correlations among protons one needs to have enough number of particles. We take 4096 nucleons at ρ = 0.1ρ0 (ρ0 = 0.168 fm−3 is the nuclear saturation density), and increase it with density keeping L fixed at 62.47 fm. Therefore, for the highest density (0.6ρ0 ) considered here we have 24,576 particles. To keep the simulation runtime within reasonable limit, we perform simulation using GPU platform.

3. Results We calculate Sp (q) and subsequently transport coefficients for various density, temperatures and proton fraction (Yp ) relevant for various astrophysical scenarios. In Fig. 1, we plot Sp (q) as a function of q for symmetric nuclear matter at ρ = 0.1ρ0 and temperatures T = 1−5 MeV. The Sp (q = qpeak ) is proportional to the size of the clusters but get corrected by the nuclear

Sp(q)

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Figure 1. Static structure factor versus momentum transfer for protons at ρ = 0.1ρ0 , Yp = 0.5 and different temperatures (T = 1–5) MeV. 350

T=1 T=2 T=3 T=4 T=5

300 250 Sp(q)

where T is the kinetic energy, VPauli is the phenomenological Pauli potential, VSkyrme is the Skyrme-like interaction between nucleons, VMD denotes the momentum-dependent part, Vsym is the isospindependent part, VSurface is the potential that depends on the density gradient and VCoul is the Coulomb interaction. The explicit expressions for all the potentials can be found in Nandi and Schramm (2018). The dominant contribution to transport properties like shear viscosity (η) and thermal and electrical conductivities (κ, σ ) of pasta phase comes from electronion scattering as electrons are the most important carriers of charge and momentum in this condition. All these transport coefficients can easily be calculated when the static structure factor (Sp (q)) that describes correlation between protons is known. We calculate Sp (q) from the autocorrelation function (Nandi & Schramm 2018) 1 ρp (q, t)∗ ρp (q, t), (2) Sp (q) = Np

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Figure 2. Same as in Fig. 1, but for Yp = 0.3 and ρ = 0.4ρ0 .

form factor and the screening effects of other ions. At ρ = 0.1ρ0 , nucleons form spherical clusters. With increasing T more and more nucleons evaporate from clusters making the system increasingly uniform and hence lead to smaller Sp (qpeak ). An interesting behavior of Sp (q) is seen in the pasta phase region (ρ  0.2ρ0 ). In Fig. 2, we plot Sp (q) for asymmetric nuclear matter (Yp = 0.3) at ρ = 0.4ρ0 . From the figure, we see that Sp (q) increases very sharply at T = 2 MeV. This is because cylindrical structures found at this density at low T merge together to form almost perfect equidistant slabs at T = 2, as can be seen from the snapshot shown in Fig. 3. With further increase in T , these slabs gradually merge to form bubble phase and Sp (q) decreases, as a consequence. In Fig. 4, we plot Sp (q) for all density and temperatures considered here. A careful observation shows that at low-density Sp (q) decreases with temperature for all three values of Yp . However in the pasta phase region (ρ  0.2ρ0 ), the

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Figure 3. Simulation snapshot for neutron (green) and proton (red) distributions at ρ = 0.4ρ0 , Yp = 0.3 and T = 2 MeV.

Yp=0.5

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Sp(q)

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T=0 T=1 T=2 T=3 T=4 T=5 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6

ρ/ρ0

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Figure 4. Sp (q) as a function of density for Yp and T .

Sp (q) rises at intermediate temperatures as discussed before in connection to Fig. 2. Using the calculated structure factors we finally calculate the transport coefficients. In Fig. 5 and Fig. 6, we display the results of shear viscosity and thermal conductivity for asymmetric nuclear matter with Yp = 0.3 and Yp = 0.1, which are typical values for supernova matter and neutron star inner crust, respectively. It is observed that although there are irregularities in the pasta phase region both the transport coefficients generally increase with density and temperature. Most importantly, the order of magnitude of both the coefficients are same as found earlier without considering the pasta phase (Flowers & Itoh 1976; Nandkumar & Pethick 1983). Similar behavior is also found for electrical conductivity.

4. Conclusion We have calculated the transport coefficients namely shear viscosity and thermal and electrical conductivities of low-density nuclear matter at various astrophysical conditions, using quantum molecular dynamics simulations. Under these conditions the electrons are most important carriers and their transport is limited mainly by electron–ion scattering, which we calculate by determining the static structure for protons (Sp (q)) using our simulation data. Although Sp (q) shows some irregularities in the pasta region, all the transport coefficients are found to have similar orders of magnitude as found without considering the pasta phase. Our results therefore contradict the speculation that the pasta layer is highly resistive and bear important astrophysical

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J. Astrophys. Astr. (2018) 39:40 14.5

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Figure 5. Shear viscosity and thermal conductivity of nuclear matter as a function of density and temperature at Yp = 0.3. 15.5

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Figure 6. Same as in figure 5, but with Yp = 0.1.

consequences. However, longer and larger simulations are required to confirm these findings. References Baym G., Pethick C., Sutherland P. 1971, Astrophys. J., 45, 429 Chikazumi S., Maruyama T., Chiba S., Niita K., Iwamoto A. 2001, Phys. Rev. C, 63, 024602 Chugunov A. I., Yakovlev D. G., 2005, Astron. Rep., 49, 724

Dorso C. O., Giménez Molinelli P. A., López J. A. 2012, Phys. Rev. C, 86, 055805 Flowers, E., Itoh, N. 1976, Astrophys. J., 206, 218 Haensel P. 2001, Physics of Neutron Star Interiors, Lecture Notes in Physics 578, Springer, Berlin, p. 127 Horowitz C. J., Pérez-García M. A., Piekarewicz J. 2004, Phys. Rev. C, 69, 045804 Horowitz C. J., Berry D. K., Briggs C. M., Caplan M. E., Cumming A., Schneider A. S. 2015, Phys. Rev. Lett., 114, 031102

J. Astrophys. Astr. (2018) 39:40 Lorenz C. P., Ravenhall D. G., Pethick C. J. 1993, Phys. Rev. Lett., 70, 379 Maruyama T., Niita K., Oyamatsu K., Maruyama T., Chiba S., Iwamoto A. 1998, Phys. Rev. C, 57, 655 Nandkumar R., Pethick C. J. 1983, Mon. Not. R. Astron. Soc., 209, 511 Nandi R., Bandyopadhyay D., Mishustin I., Greiner W. 2011, Astrophys. J., 736, 156 Nandi R., Bandyopadhyay D. 2011, J. Phys. Conf. Ser., 312, 042016 Nandi R., Schramm S. 2016, Phys. Rev. C, 94, 025806 Nandi R., Schramm S. 2017, Phys. Rev. C, 95, 065801 Nandi R., Schramm S. 2018, Astrophys. J., 857, 12 Newton W. G., Stone J. R. 2009, Phys. Rev. C, 79, 055801

Page 5 of 5 40 Oyamatsu K. 1993, Nucl. Phys., A561, 431 Pons J. A., Viganò D., Rea N. 2013, Nat. Phys., 9, 431 Ravenhall D. G., Pethick C. J., Wilson J. R. 1983, Phys. Rev. Lett., 50, 2066 Rüster S. B., Hempel M., Schaffner-Bielich J. 2006, Phys. Rev. C, 73, 035804 Schneider A. S., Horowitz C. J., Hughto J., Berry D. K. 2013, Phys. Rev. C, 88, 065807 Schramm S., Nandi R. 2017a, J. Phys. Conf. Ser., 861, 012021 Schramm S., Nandi R. 2017b, Int. J. Mod. Phys. Conf. Ser., 45, 1760027 Watanabe G., Sato K., Yasuoka K., Ebisuzaki T. 2003, Phys. Rev. C, 68, 035806

J. Astrophys. Astr. (2018) 39:41 https://doi.org/10.1007/s12036-018-9532-7

© Indian Academy of Sciences

Review

Entering the cosmic ray precision era PASQUALE DARIO SERPICO USMB, CNRS, LAPTh, Univ. Grenoble Alpes, 74940 Annecy, France. E-mail: [email protected] MS received 5 April 2018; accepted 18 May 2018; published online 11 July 2018 Abstract. Here we outline some recent activities in the theory and phenomenology of Galactic cosmic rays, in the light of the great precision of direct cosmic ray measurements reached in the last decade. In the energy domain of interest, ranging from a few GeV/nucleon to tens of TeV/nucleon, data have revealed some novel features requiring an explanation. We shall emphasize the importance of a more refined modeling, of achieving a better assessment of theoretical uncertainties associated to the models, and of testing key predictions specific of different models against the rich datasets available nowadays. Despite the still shaky theoretical situation, several hints have accumulated suggesting the need to go beyond the approximation of a homogeneous and non-dynamical diffusion coefficient in the Galaxy. Keywords. Cosmic rays—astroparticle physics—interstellar medium.

1. Introduction The evolution of cosmic ray (CR) astrophysics has been relatively slow, when compared with other branches of astronomy and astrophysics. This is not surprising, given the lack of positional information and the complicated propagation that make the source identification and the interstellar transport characterization such difficult inversion problems. About a decade ago, a few main questions in CR physics and the consensual answers to them had crystallized into a ‘standard framework’: • How is CR acceleration taking place? Primarily via ‘diffusive shock acceleration’. • In what type of objects? Predominantly (Galactic) supernova remnants. • Where are they located? When did the events happen? Randomly in the Galaxy, well approximated by a continuum injection term, with a size much smaller than typical source–Earth distance. • How do CRs get to us, after leaving their acceleration sites? Diffusing into an externally assigned, roughly scale-invariant turbulent magnetized interstellar medium (ISM). Obviously, this does not mean that alternative scenarios had not been occasionally considered. And, certainly, some of the above-listed topics have been developed

into a remarkable detail. For instance, the study of non-linear effects and their impact on some expectations of diffusive shock acceleration models is now a mature sub-field of theoretical research of its own. But it is fair to say that no stringent test of either the standard or more exotic models had been possible via charged CR measurements till recently, when a wealth of 21st century experiments has significantly improved the precision of the observations, while extending their dynamical range. Take the following list of statements: • We only have access to cosmic ray fluxes ‘modulated’ by heliosphere. • The positron flux is dominated by secondaries, with propagation parameters (as opposed to assumptions on the source and model framework) constituting the dominant source of theoretical uncertainty. • Primary cosmic ray fluxes have power-law spectra. • Primary spectra have universal (species independent) spectral indices. The first item has been disproven by the unique exploit of the Voyager Interstellar mission1 (see, Stone et al. 2013, Cummings et al. 2016). The second item, usually taken for granted in most phenomenological studies 1 https://voyager.jpl.nasa.gov/mission/interstellar-mission/.

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over the past 30 years, has not only been shaken by new data, notably—but not exclusively—the celebrated ‘PAMELA positron fraction rise’ (Adriani et al. 2009) but appears nowadays very doubtful (see, for instance, the mini-review of Serpico 2012). The last two items have become unsteady nearly 7– 8 years ago by the more precise measurements available (Ahn et al. 2010, Yoon et al. 2011, Adriani et al. 2011), with a trend still continuing today, notably thanks to AMS-02 (Aguilar et al. 2015a, b). Also in the light of the importance of some of these issues for other astroparticle physics applications—notably, indirect dark matter searches—a new scrutiny of the simplest theoretical scenarios is ongoing. Ideally, theorists would like to match theoretical uncertainties with experimental ones, refining the level of predictions and improving our understanding of these high-energy phenomena. At the same time, they face the challenge to come up with a sufficiently predictive framework, not plagued by a proliferation of parameters, which in this field are often too hard or impossible to fix otherwise than by a fit to the data. 2. Spectral breaks In order to illustrate this theoretical trend, we describe a specific example: the impact of the fact that primary cosmic ray fluxes in the GeV to TeV energy range, in particular protons and He nuclei, do not manifest a simple power-law spectrum. As already mentioned, the evidence in favour of spectral shapes closer to broken power-laws has accumulated over the past decade, from the indications in balloon-borne experiments, such as ATIC (Panov et al. 2009) and especially CREAM (Yoon et al. 2011), through the first measurements in a single space-based experiment, PAMELA (Adriani et al. 2011), till the recent high-precision determinations by AMS-02 on board the International Space Station (Aguilar et al. 2015a, b). In Fig. 1, the latest proton (top panel) and helium (bottom panel) fluxes from the AMS02 experiment are reported. They have been extracted with the on-line cosmic ray database tool http://lpsc. in2p3.fr/crdb/ (see, Maurin et al. 2014), which can also be easily used to compare with the older datasets (not reported here to avoid clutter). What is ‘wrong’ with these observations? To assess, take the simplest expectation which, nonetheless, matched data fairly well till recently. For stationary, homogeneous and isotropic diffusive propagation problems, and observations taken at a single location (i.e. the Earth) the diffusion operator ruling the flux  can be effectively replaced by a ‘diffusive confinement’ time

Figure 1. The proton (top) and He (bottom) fluxes measured by AMS-02 (Aguilar et al. 2015a, b) vs. rigidity R (ratio of momentum to charge, hence measured in GigaVolts, GV), rescaled by R 2.7 , extracted via the on-line cosmic ray database tool http://lpsc.in2p3.fr/crdb/. It is visible to the naked eye that the slope in tens of GV to ∼200 GV are different from the slopes above the latter rigidity value. Also note the remarkably small error bars.

τdiff (E):

∂ − K ∇ 2 = Q ∂t  = Q (at steady state). ⇒ τdiff (1)

If both the source term Q and the diffusion coefficient K (with τdiff ∝ K −1 ) are power-laws in rigidity R, as customarily believed and theorized, then a puzzle arises. This schematic exercise naturally suggests (classes of) solutions, where one drops one or several of the following assumptions (examples of actual physical motivations for that below, in italics): • Homogeneity (and possibly isotropy) of K. Example: multi-phase character of the Galactic interstellar medium (and nature of magnetohydro-dynamical (MHD) turbulence).

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• Power-law behaviour in K. Example: multiple sources/mechanisms for the MHD turbulence in the ISM. • Power-law behaviour in Q. Example: multiple classes of sources or spectral feature of a single source class. • Homogeneity in Q. Example: prominent local, discrete sources. Before coming back to the first options in the final part of this article, we will briefly concentrate on the latter option to illustrate some recent theoretical efforts within the above-mentioned strategy, while addressing the reader to Serpico (2016) for a broader overview of the alternatives, in particular, concerning multiple source or source spectral effects.

3. Local sources A number of publications have studied the possibility that the CR spectral breaks emerge from a ‘local’ source contribution becoming predominant over a diffuse contribution representative of a Galactic average. Usually, but not always, the local contribution is considered to dominate at high-energy. The emphasis has often been on finding a viable fit, sometimes supplemented by a qualitative assessment on the goodness of the model. For instance, one typically needs fast diffusion and low supernova explosion rates for these scenarios to work, which has often been argued to be in tension with other observations. One may however ask the more general question: How likely is such a hypothesis in itself, given ‘Galactic variance’, i.e., the spatial discreteness (and impulsive time-dependence) of the sources? Conventional models, in fact, replace the actual sources with a continuum ‘source jelly’, with a smoothly varying injection rate per unit volume and time. This corresponds to a ‘coarsegrained’ ensemble average of the actual physical model, and by construction the average theoretical expectation matches the prediction obtained in such a simplification. But, assuming that a discrepancy between observations and data is found, how safely can we attribute it to a failure of the model? Couldn’t it be due to a relatively large statistical fluctuation with respect to the average prediction, which is in fact compatible with the model in a more realistic calculation? In Genolini et al. (2017a), we have outlined the first elements of such a theory. The task is made non-trivial by the fact that the theoretical probability distribution for the flux is of ‘fat-tail’ type, with infinite variance:

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Stable law α = 4/3

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Figure 2. The blue histogram is the pdf of the Galactic CR flux at 1 TeV (vs. the flux normalized to its mean) obtained numerically via 106 Monte Carlo realizations of pure diffusive transport. The dot-dashed blue line represents the (highly unsatisfactory) Gaussian approximation fitted to the numerical results. The solid green line reports the theoretical prediction based on fat-type stable law distribution for the limiting case of an infinitely thin two-dimensional model of the Galactic magnetic halo, whereas the dashed red curve corresponds to the 3D isotropic limit, expected to be valid respectively at low and high flux (dominated respectively by far and near sources). The per cent residuals between theory and simulations are displayed in the panel below, with bands showing their 1-σ Poisson error. Adapted from Genolini et al. (2017a), which we address to for further details.

The Central Limit theorem does not apply and the familiar Gaussian statistics toolbox cannot be used. We have argued that a generalized Central Limit theorem holds, and that the flux probability distribution functions are remarkably well approximated by ‘stable laws’, characterized by analytically computable parameters. We tested these conclusions with extensive numerical simulations (see Fig. 2 for an example). As a result, we arrived at two interesting conclusions: • For currently viable homogeneous and isotropic diffusion models, the observed breaks only emerge rarely, with a realistic upper limit around 0.1%. Hence, such explanations appear to require a high-degree of fine-tuning. • Even if this effect is probably insufficient to account for the breaks, these ‘irreducible theoretical errors’ are not negligible anymore, given the precision of the data: by taking the experimental error σexp reported by AMS-02 on the proton flux measurement (Aguilar et al. 2015a), we estimate, for instance, that a 3 σexp deviation from the average flux expectation at E ∼ 50 GeV is obtained in about 5% of the theoretical realizations. Put otherwise, if the viability of a

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model is naively assessed only based on experimental error, a significant bias in the statistical level of the conclusion is likely. Till recently (including, for instance, PAMELA data), the precision was sufficiently low to make these ‘theory error’ effects negligible, justifying a posteriori that such fine effects were neglected in phenomenological analyses. This study represents more of a beginning than an end to the story. Extending the theory to account for energy bin-to-bin correlations or to include anisotropy observables is certainly something to wish for, to bypass the need for extensive Monte Carlo simulation in order to compare theoretical predictions with data. 4. Testing break models Of course, besides refining theory models and the uncertainty assessments, one is also interested in discriminating among competing models for the new features that have been uncovered by the data. As already stressed in Serpico (2016) regarding break models, the most promising channels to probe the different classes of explanations for the spectral breaks are the so-called ‘secondary’ nuclei. These are relatively fragile nuclei such as Li, Be, B, easily destroyed in stellar processes and thus present but in traces in stellar astrophysical environments. It turns out that they are comparatively abundant in CRs. This fact is interpreted as the result of spallation of ‘primary’ nuclei accelerated at sources (e.g. supernova remnants) onto interstellar material during the CR diffusive propagation to the Earth. While CR are sensitive to both acceleration and propagation effects, the ratio of secondary to primary species is used to constrain propagation parameters, being largely insensitive to injection spectra. Since the Lorentz factor of a nucleus is approximately conserved in a spallation event, with a bit of oversimplification for ratios plotted in terms of energy/nucleon (or, to some extent, rigidity) one expects the following: • For a ‘source’ origin for the break, the feature maps correspondingly in the secondaries (see the sketch in Fig. 3) and thus no feature is expected in the secondaries/primaries ratios. • For a ‘propagation’ origin for the break, the same break should be seen in secondaries/primaries, since secondary spectra should show a more pronounced break than primary ones, inheriting ‘twice’ the break present in the diffusion coefficient (see Fig. 4).

Figure 3. Sketch of the source term (top left), diffusion coefficient (bottom left), primary (top right), and secondary flux (bottom right) behaviour vs. R, for a source model of the primary break.

Figure 4. As in Fig. 3, for a propagation model of the primary break.

• For ‘local source’ models: qualitatively, since the interstellar target material on which secondaries are produced is more homogenous than the source distribution, the secondary source term should be closer to the naively computed ‘unbroken’ average Galactic source spectrum than the primary one (see Fig. 5). In most realizations, one thus expects that the ratio shows softening rather than hardening. However, this is just an average expectation, with the actual result depending upon the assumed properties of the local sources and of the local environment. In general, no deterministic prediction can be made. A pictorial summary of the secondary/primary behaviour vs. R for the three classes of models is reported in Fig. 6. In Genolini et al. (2017b), we have

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Figure 5. As in Fig. 3, for a local source model of the primary break.

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In all cases tested, a significant preference for the scenario with a break in K (R) is obtained (χ 2 > 10). This result is robust with respect to: (i) sub-leading transport phenomena (at high rigidity) such as convection or reacceleration, treated as nuisance parameters; (ii) different treatments of AMS-02 systematic errors; (iii) assumed spallation cross-sections (from existing libraries) as well as a physically motivated logarithmic growth with energy ‘inherited’ from nucleon–nucleon cross-sections; (iv) the expected amount of ‘grammage at the source’, the so-called secondaries at the source. A more recent analysis (Reinert & Winkler 2018), with different techniques for the solution of CR propagation equation, a different approach to the treatment of spallation cross-section, and a slightly different dataset has further corroborated our results.

5. Towards a new paradigm?

Figure 6. Summary of the secondary/primary behaviour vs. R expected for the source, propagation, and local source models (from top to bottom, respectively).

recently performed a first test a priori on the AMS-02 B/C data published only a few months before (Aguilar et al. 2016), comparing a baseline model with a powerlaw function K (R) vs. a case with a break in K (R), whose parameters are fixed by the proton and helium data, so that the fit to B/C data (above 15 GV) has the same number of free parameters in the two cases.2 2 Note that the two cases are not ‘epistemologically’ identical: the first leaves the p-He data unexplained (source effect?) and the second attributes the breaks to propagation.

Only a few months after our preliminary analysis (Genolini et al. 2017b), AMS-02 has published two important articles on ‘mostly primary’ and ‘mostly secondary’ CR species, respectively. In Aguilar et al. (2017), it reads as follows: “Above 60 GV, these three spectra [He, C, O] have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.” In the second article of Aguilar et al. (2018), it reads as follows: “All three fluxes [Li, Be, B] have an identical rigidity dependence above 30 GV […]. The three fluxes deviate from a single power law above 200 GV in an identical way. […] Above 200 GV, the secondary cosmic rays harden more than the primary cosmic rays.” These results confirm the basic predictions (Serpico 2016) as well as the first indications (Genolini et al. 2017b) in favour of a (diffusive) propagation origin of the observed spectral features, possibly marking another milestone in our description of CR propagation. Yet, even accepting that as dominant origin for the observed flux shapes, the theoretical interpretations may differ in the details. For instance, in Blasi et al. (2012), it was proposed that CR above the break essentially reflect the standard lore of diffusion onto external turbulence generated, e.g. by supernova explosions, while CR below the break are sufficiently numerous to alter the turbulence spectrum via waves generated by the CR streaming itself (a phenomenon already subject to general studies in the past (see Ptuskin et al. 2008). In this proposal, we would be thus observing an inherently non-linear aspect of the CR diffusion phenomenon, which is not captured by conven-

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tional propagation schemes (as those implemented in GALPROP (Moskalenko et al. 2006), USINE (Maurin et al. 2018), DRAGON (Evoli et al. 2015). This idea suffers perhaps from the technical difficulty of generalizing the solution to realistic geometries, but within the constrained situations to which it can be applied it leads to good fits (Aloisio et al. 2015). It has also the intellectually appealing property of offering a microscopic understanding of the observed features. On the other hand, it is also possible to fit the data by assuming that the CR transport properties are spatial-dependent in different regions of the Galaxy, in such a way that the diffusion coefficient is not separable into energy and space variables (Tomassetti 2012). In fact, this property would arise generically as a consequence of the idea in Blasi et al. (2012), but can have a different origin (without necessarily invoking non-linear effects), such as different sources for turbulence in different regions of the Galaxy. If adopted on a mere phenomenological level, the free parameters entering the generalized diffusion coefficient can, in fact, be fit to reproduce the data to great accuracy (Tomassetti 2012, Guo & Yuan 2018). Needless to say, the best way to confirm this generic expectation is to access ‘non-local’ information in CR, i.e. elsewhere in the Galaxy. This can be done to some extent via CR anisotropy studies (which depend among others on CR flux gradients) and the latitude profile of diffuse Galactic gamma-rays in the GeV range. These gamma-rays are dominantly emitted by π 0 decays, in turn produced via CR inelastic interactions onto the ISM, and probe the integral of the CR flux along the lineof-sight. Interestingly, both observables are difficult to explain within a homogeneous diffusion approach to CR. In Evoli et al. (2012), it was shown that both these long-standing problems could be solved if the diffusion coefficient also depends on the Galactocentric distance (qualitatively expected in scenarios such as the ones mentioned above). Recent analyses confirm the viability of these models in the light of AMS-02 data (Guo & Yuan 2018, Recchia et al. 2016, Liu et al. 2018). Another way to test the (lack of) viability of homogeneous diffusion is to perform a multi-channel CR analysis, separating ‘light’ (e.g. p, p, ¯ He) vs. ‘heavy’ species (e.g. Be, B, C, N, O), each group containing at least one dominantly primary and one dominantly secondary species. Due to their different inelastic crosssections, in a statistical sense the light (heavy) elements are collected from a larger (smaller) ISM region, so that e.g. the inferred diffusion coefficients are truly averages over different volumes. We are talking here about

J. Astrophys. Astr. (2018) 39:41

differences in radius of several kpc (see, for instance, Taillet and Maurin (2003)). The results in Johannesson et al. (2016) suggest that such differences are in fact present in the data. At a different spatial scale, another complementary (but concordant) piece of information concerning inhomogeneous diffusion comes from the detection of an extended TeV emission surrounding two nearby pulsars, Geminga and Monogem, by the HAWC collaboration (Abeysekara et al. 2017). The inferred diffusion coefficient has been argued to be in tension with a pulsar origin for the cosmic ray positrons, but this naive conclusion is strongly relying on the simplistic model now believed to be inconsistent with other data. It is more and more appreciated theoretically that self-confinement around the sources due to streaming instability (e.g., Yan & Lazarian 2004, Malkov et al. 2013, D’Angelo et al. 2016) is an important effect, with an effective diffusion coefficient on scales of tens of pc around the source much smaller than the truly ISM value. Not only this is believed to reconcile the apparent contradiction between HAWC data and the currently favored explanation for positron CR (Hooper & Linden 2017, Profumo et al. 2018), but it is probably associated to sizable production of the so-called secondary species from regions around the sources (see, for instance, D’Angelo et al. 2018). Very recently, Aharonian et al. (2018) have also discussed evidence for a one to two orders of magnitude reduced diffusion coefficient inferred from the radial profile of gamma-emission (from Fermi-LAT and HESS data) around a few prominent Galactic clusters. This also brings further support to the possibility that star clusters, rather than isolated massive stars, may be associated to acceleration of the highest energy Galactic CRs. Anyway, the realistic perspective of slow diffusion around sources, with a highly inhomogeneous diffusion coefficient at ‘small’ scales, raises particularly delicate questions when analyzing antiprotons, an exquisite channel for DM indirect searches. This novel astrophysical contribution, if unaccounted for, could easily fake a DM signal, a worry already expressed in the past (Blasi & Serpico 2009, Pettorino et al. 2014, Giesen et al. 2015) but still poorly appreciated, in my opinion.

6. Conclusion The observational improvements in cosmic ray (CR) astrophysics have shown the first cracks in the simplest models for CR production and propagation. Many ideas have been proposed for their origin, and still more are

J. Astrophys. Astr. (2018) 39:41

likely to appear. In general, however, we face a double theoretical challenge: To provide a more refined modeling to account for new facts and to keep theoretical errors under control, or at least assess them. Without the former, the models become less and less interesting, but without the latter, the newly attained experimental precision becomes worthless. Here we focused on the case of spectral breaks, which can be ‘naturally’ explained within broad classes of models. In fact, finding a model that fits the data is not the hardest task, notably if including a lot of additional free parameters. Much more challenging is to find models that provide statistically probable explanations, or that predict (as opposed to postdict) features that one can test. We have recently provided (Genolini et al. 2017a) a first estimate of the irreducible (‘Galactic variance’) theoretical error due to space–time discreteness of the CR sources, whose exact location and times are obviously unknown. Alone, this effect is unlikely to explain the spectral breaks firmly observed at least in p and He, but it introduces an uncertainty comparable or even larger than the AMS-02 statistical ones, and should be taken into account. We have summarized the results of a first test on the 2016 AMS-02 B/C data, to investigate if they prefer a propagation origin for the breaks, obtaining intriguing hints in that sense (Genolini et al. 2017b). Later, an independent analysis confirmed our findings (Reinert & Winkler 2018). Then AMS-02 published a new data that further reinforced these conclusions (Aguilar et al. 2017, 2018). We then argued that multi-channel and multi-messenger probes have reinforced the theoretical urge to go beyond the homogenous diffusion coefficient approximation for Galactic CR probes. Strong indications for variations with respect to the local ISM average value have been found both at the scale of few tens of pc around sources and at a more coarse-grained level, over several kpc distances from us. The likely culprits of this phenomenon are the inhomogeneous source distribution in the Galaxy, the varying ISM properties in the Galactic environment, and non-linear plasma phenomena coupling CRs to the MHD turbulence that determine transport properties, but other origins of course still deserve scrutiny. More experimental precision, resolving more CR species (including isotopic abundances), and accessing an even broader energy range will help refine such studies, but further theoretical and phenomenological progresses are crucial to bring us closer to a global understanding of the Galactic CR phenomenon.

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We have, for instance, still a rudimentary understanding of the possible causes of the non-universality of spectral indices (for some ideas, see Serpico 2016), which remains a trickier issue to settle, both experimentally and theoretically. In any case, major progresses in this area would also prove beneficial (if not essential) to sharpen the CR channel potential for astroparticle applications, such as indirect dark matter searches in CR antimatter fluxes. For the time being, we would caution that current analyses may be either underestimating or—more likely—overestimating the sensitivity of these probes to DM signals. Acknowledgements The author would like to thank all his collaborators on the topics covered in this manuscript, as well as the organizers of the AAPCOS2018 conference and, in particular, Pratik Majumdar for his kind invitation, and the warm atmosphere, which stimulated the considerations reported in this article. References Abeysekara A. U. et al. 2017, Science, 358(6365), 911 Adriani O. et al. 2009, Nature, 458, 607 Adriani O. et al. 2011, Science, 332, 69 Aguilar M. et al. 2015a, Phys. Rev. Lett., 114, 171103 Aguilar M. et al. 2015b, Phys. Rev. Lett., 115, 211101 Aguilar M. et al. 2016, Phys. Rev. Lett., 117, 231102 Aguilar M. et al. 2017, Phys. Rev. Lett., 119, 251101 Aguilar M. et al. 2018, Phys. Rev. Lett., 120, 021101 Aharonian F., Yang R., Wilhelmi E. D. O. 2018, preprint arXiv:1804.02331 Ahn H. S. et al. 2010, ApJ, 714, L89 Aloisio R., Blasi P., Serpico P. D. 2015, Astron. Astrophys., 583, A95. Blasi P., Serpico P. D. 2009, Phys. Rev. Lett., 103, 081103 Blasi P., Amato E., Serpico P. D. 2012, Phys. Rev. Lett., 109, 061101 Cummings A. C. et al. 2016, ApJ, 831, 18 D’Angelo M., Blasi P., Amato E. 2016, Phys. Rev. D, 94, 083003 D’Angelo M., Morlino G., Amato E., Blasi P. 2018, Mon. Not. R. Astron. Soc., 474(2), 1944 Evoli C., Gaggero D., Grasso D., Maccione L. 2012, Phys. Rev. Lett., 108, 211102 Evoli C. et al. 2015, http://www.dragonproject.org/ Genolini Y., Salati P., Serpico P. D., Taillet R. 2017a, Astron. Astrophys., 600, A68 Genolini Y. et al. 2017b, Phys. Rev. Lett., 119, 241101 Giesen G. et al. 2015, JCAP, 1509, 023 Guo Y. Q., Yuan Q. 2018, Phys. Rev. D, 97, 063008

41 Page 8 of 8 Hooper D., Linden T. 2017, preprint arXiv:1711.07482 Johannesson G. et al. 2016, ApJ, 824(1), 16 Liu W., Yao Y. H., Guo Y. Q. 2018, preprint arXiv:1802.03602 Malkov M. A. et al. 2013, ApJ, 768, 73 Maurin D., Melot F., Taillet R. 2014, Astron. Astrophys., 569, A32 Maurin D. et al. 2018, lpsc.in2p3.fr/usine Moskalenko I. et al. 2006, https://galprop.stanford.edu/ Panov A. D. et al. 2009, Bull. Russ. Acad. Sci. Phys., 73, 564 Pettorino V. et al. 2014, JCAP, 1410(10), 078. Profumo S., Reynoso-Cordova J., Kaaz N., Silverman M. 2018, preprint arXiv:1803.09731

J. Astrophys. Astr. (2018) 39:41 Ptuskin V. S., Zirakashvili V. N., Plesser A. A. 2008, Adv. Space Res., 42, 486 Recchia S., Blasi P., Morlino G. 2016, Mon. Not. R. Astron. Soc., 462(1), L88 Reinert A., Winkler M. W. 2018, JCAP, 1801, 055 Serpico P. D. 2012, Astropart. Phys., 39–40, 2 Serpico P. D. 2016, PoS ICRC 2015, 009 Stone E. C. et al. 2013, Science, 341, 150 Taillet R., Maurin D. 2003, Astron. Astrophys., 402, 971 Tomassetti N. 2012, ApJ, 752, L13 Yan H., Lazarian A. 2004, ApJ, 614, 757 Yoon Y. S. et al. 2011, ApJ, 728, 122

J. Astrophys. Astr. (2018) 39:42 https://doi.org/10.1007/s12036-018-9534-5

© Indian Academy of Sciences

Neutron stars and the equation of state S. SCHRAMM1,∗ , V. DEXHEIMER2 , A. MUKHERJEE1 and J. STEINHEIMER1 1 FIAS,

60438 Frankfurt am Main, Germany. of Physics, Kent State University, Kent, OH, USA. ∗ Corresponding author. E-mail: [email protected] 2 Department

MS received 24 May 2018; accepted 4 July 2018; published online 3 August 2018 Abstract. The interior of neutron stars consists of the densest, although relatively cold, matter known in the universe. Here, baryon number densities might reach values close to ten times the nuclear saturation density. These suggest that the constituents of neutron star cores not only consist of nucleons, but also of more exotic baryons like hyperons or a phase of deconfined quarks. We discuss the consequences of such exotic particles on the gross properties and phenomenology of neutron stars. In addition, we determine the general phase structure of dense and also hot matter in the chiral parity-doublet model and confront model results with the recent constraints derived from the neutron star merger observation. Keywords. Neutron stars—equation of state—hyper stars—hybrid stars.

1. Introduction Obtaining a better understanding of the equation of state (EoS) of strongly interacting matter has been a central goal of nuclear and heavy-ion physics for a number of decades. This comprises numerous experimental programs as well as a large range of theoretical studies. Because of the inherent difficulty of directly solving quantum chromodynamics as fundamental theory of strong interactions due to its non-perturbative nature, there are still many open questions concerning the EoS of dense matter from a theoretical perspective. Here, a central aspect is the largely unknown phase structure of the QCD and the change of the effective degrees of freedom from hadrons at low densities and temperatures to quarks and gluons in very dense and/or hot environments. Essentially, the only hard fact known so far is that there is a first-order transition to self-bound nuclear matter at low temperatures, the so-called liquid–gas transition. The other, meanwhile well-established property of the phase diagram is known from lattice QCD simulations, where a smooth crossover from hadrons to quarks is observed at vanishing baryon chemical potential (or net baryon number density) (Bazavov et al. 2012). It remains unclear whether there is another first-order transition connecting the

hadronic and quark world at large density, which would stop in a critical end-point of second order at some chemical potential and temperature, as has been seen in a specific lattice QCD calculation, but which still remains a matter of debate (Fodor & Katz 2004). From the experimental side, there are largely two approaches to shed light on the equation of state and the phase structure of strongly interacting matter. One possibility is to study highly relativistic heavy-ion collisions, which generate an intermittent hot and, depending on beam energy, dense fireball that decays into many hadrons. Here, many observables related to the decay products have been suggested as marker of the phase structure tested with the fireball. A very different and complementary approach is to study the observational signals from compact stars, in particular neutron stars, that contain matter with densities up to perhaps ten times nuclear matter saturation density. Here, information can be gathered from later-stage, rather cold, neutron stars, proto-neutron stars created in supernova explosions, or as has been observed recently, from neutron star merger signals. As mentioned above, the possibility of direct QCD calculations of strongly interacting matter is very limited, and therefore phenomenological model descriptions of such systems are unavoidable. Therefore,

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Figure 1. Binding energy Bi of uranium isotopes as a function of the neutron number for different Skyrme forces and a RMF parameter set. The minima of the curves mark the last neutron-stable isotope. Considerable variations of this point for different nuclear interactions can be observed.

J. Astrophys. Astr. (2018) 39:42

(not shown in the plot) up to N = 256. Thus, there is still a large theoretical uncertainty of more than 70 neutrons in the position of the drip line for these heavy elements (Schramm et al. 2012). Overall, this is an indication for the importance of having a unifying model approach that can be used for nuclear structure type calculations for matter in the crust up to including exotic hadrons and quarks in the description of the core region of the star. With this goal in mind we developed a relativistic hadronic description of strongly interacting matter, based on the lowest flavor-SU(3) multiplets of baryons and mesons, termed the chiral mean field (CMF) model (Papazoglou et al. 1998, 1999; Dexheimer & Schramm 2008; Schramm 2002). The main ingredients of this approach contain a linear coupling of the mesonic fields with the baryons as    Lint = − ψ¯i γ0 (giω ω + giφ φ +giρ ρ) + Mi∗ ψi . i

we investigate models of hadronic and quark matter for conditions of cold neutron stars as well as including temperature effects, relevant for merger events and heavy-ion collisions.

(1) Apart from a small explicit term M0i the effective baryon masses Mi∗ are generated by the coupling of the baryons to the scalar fields as given by Mi∗ = giσ σ + giδ δ + giζ ζ + M0i .

2. Hadronic matter in neutron stars A full description of neutron star matter is a very complex undertaking. In addition to the unknown constituents of the extremely dense region in the inner core of the star, the outer part of the neutron star with a typical width of about one kilometer, i.e., the neutron star crust consists of two parts: the outer crust with very neutron-rich nuclei surrounded by an electron plasma, and an additional neutron fluid for densities beyond the neutron drip line at about 4 × 1011 g/cm3 in the inner crust. In the subsequent transition region between the crust and the homogeneous core, unusual structures, the so-called ‘pasta’ structures can develop (Ravenhall et al. 1983). Here, due to the neutron richness of the material, the not very well-known nuclear interactions at high isospin values are tested. This will be addressed later in the discussion of the core region. Without entering into a detailed analysis of the role played by isospin in the physics of the neutron star crust, Fig. 1 shows the negative binding energies for uranium isotopes as a function of the neutron number N of the isotope. The figure compares the results of a two-dimensional nuclear structure calculation for different standard Skyrme-type and relativistic mean field interactions. The minimum energy, beyond which neutron drip sets in, varies in an astonishingly large range of N = 182

(2)

These expressions include couplings to the scalar mesonic fields, the isoscalar σ , isovector δ and hiddenstrangeness field ζ . Implementing a non-linear SU(3) symmetric potential for the scalar fields, they attain non-zero vacuum expectation values that generate the baryonic vacuum masses (see Papazoglou et al. 1998 for details). In addition, the different meson channels produce the effective baryon–baryon interactions, where, as in the usual relativistic mean field (RMF) descriptions, the scalar mesons mediate the attractive forces, whereas the vector mesons produce repulsion. Minimizing the grand-canonical potential for such a system provides the thermodynamic quantities like energy density and pressure as a function of baryochemical potential and temperature. Adding leptonic contributions and demanding beta equilibrium and local charge neutrality produces the equation of state of stellar matter. Considering the zero temperature case for now, one can plug the equation of state of cold matter into the Tolman–Oppenheimer–Volkoff equations for static stars (Tolman 1939; Oppenheimer & Volkoff 1939) and determine masses and radii of stars with different central pressure (Dexheimer & Schramm 2008). The corresponding mass-radius diagram is shown in Fig. 2, resulting in stellar masses of about 2 solar masses in agreement with observation (Demorest et al. 2010; Antoniadis et al. 2013). Note that the nuclear matter

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Page 3 of 8 42

Figure 3. Maximum neutron star mass as a function of the scaled hyperon- meson coupling strength. Switching off the coupling leads to a strong reduction of the maximum stellar mass. Figure 2. Masses and radii of static neutron stars calculated with the CMF model. The curves show nucleonic stars (solid line), stars including hyperons (dashed), as well as additionally Delta baryons (dotted).

compressibility of the model is relatively high (297 MeV, Tolman 1939) compared to values suggested by nuclear physics phenomenology. This has been remedied in a later work using the parity doublet model as discussed below, where a compressibility of 267 MeV has been obtained (Mukherjee et al. 2017a, b). The different curves illustrate the change in stellar masses if one allows only for nucleons, nucleons and hyperons, or nucleons, hyperons and Delta baryons inside the core of the star. The more degrees of freedom are included in the calculation, the softer the equation of state becomes, leading to a reduction of the maximum star mass. However, including hyperons does not yield a drastic change of the masses. This is in contrast to the often discussed ‘hyperon puzzle’, where the inclusion of hyperons leads to a substantial drop in masses in contradiction to the observed neutron star masses (Schulze & Rijken 2011). The reason for the minor change in masses in the CMF approach stems from the inclusion of the full meson octets in the model description, in particular the vector meson, which contains hidden strangeness and couples strongly to hyperons (Dexheimer & Schramm 2008). This field generates strong repulsion for the hyperons, reducing the total strangeness content of the system. Figure 3 illustrates this point. The figure shows the change in maximum masses when the hyperon- coupling constant is turned off. For that case a strong reduction of the stellar mass can be observed (Schramm et al. 2016). In the full CMF model calculation including the effect of the field, the various occupied particle states in the hyper star can be seen in Fig. 4. At higher densities,  and − hyperons appear, however due to their repulsive forces their

Figure 4. Normalized particle densities as a function of baryon density in stellar matter. At 3 times saturation density ρ0 , the  hyperon appears, and at about 4 times ρ0 , the − states start being populated.

densities remain rather low (Dexheimer & Schramm 2008). One common feature of stellar models that include hyperons and reproduce massive stars is the rather large radii of 14 km or higher of the reference star of 1.4 solar masses. These large values might lead to problems with radius observations of low-mass X-ray binaries, which point to smaller stellar radii (Steiner et al. 2013; Guillot et al. 2013; Ozel et al. 2016). In addition, the recent neutron star merger observation also suggests small stellar radii, which will be discussed below. As was pointed out in Fortin et al. (2015), the large radii correspond to high values of the pressure of stellar matter at saturation density, and are in contrast to results from chiral perturbation theory (Hebeler et al. 2013). However, this behaviour is not an intrinsic problem of flavor-SU(3) models. Taking into account nonlinear interactions between isoscalar and isovector vector mesons of the type gω2 ρ 2 , which were discussed in (Horowitz & Piekarewicz 2002; Schramm 2003), led to

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Figure 5. Mass–radius diagram for stars calculated with the CMF model (χ M ) and with a standard RMF parametrization NL3. The corresponding curves with smaller radii include an additional non-linear interaction between isoscalar and isovector vector mesons.

J. Astrophys. Astr. (2018) 39:42

consisting of a hadronic part (G300 parametrization, Glendenning 1989) and a MIT bag equation of state for the quark phase, the resulting mass–radius diagrams for different values of the MIT bag pressure is shown in the left panel of Fig. 6. One can observe a clear reduction of the obtainable maximum mass for the hadronic model, which in this case is 1.8 solar masses. For one case the onset of the quark core immediately leads to unstable stellar solutions (Negreiros et al. 2012), which has also been observed in the more advanced quark– hadron model calculations (Dexheimer & Schramm 2010). Such a general behaviour can be avoided by taking into account repulsive quark–quark interactions, which can effectively be introduced by changing the quark equation of state from Pq = a1 μ4 + a2 μ2 + BMIT

(3)

to a substantial reduction of the radii of intermediate mass stars without affecting maximum masses, as shown in Fig. 5. This will be discussed in comprehensive detail in an upcoming publication.

3. Quark matter in neutron stars In addition to hyperons, it is natural to assume that at some point also quarks populate the core of neutron stars. With typical densities of six or more times nuclear saturation density in the center of heavy neutron stars, nucleonic states overlap, which suggest a melting transition to a quark phase. Using a simple equation of state

Pq,int = a˜ 1 μ4 + a2 μ2 + BMIT ,

(4)

with the bag pressure BMIT · a˜ 1 = 4π3 2 (1 − 2 πα ) containing first-order gluon-exchange corrections with strength α (Fraga et al. 2001), and a2 = 4π3 2 m 2s takes into account corrections from the finite mass m s of the strange quark. The modification to the quark interactions leads to a stiffening of the quark equation of state and higher star masses, as demonstrated in the right panel of Fig. 6. However, such a strong repulsive quark–quark interaction generates severe problems with baryon number susceptibilities at low densities as determined in the lattice QCD (Bazavov et al. 2017). In Steinheimer and Schramm (2011, 2014), it was shown that already moderate repulsive quark interactions lead

Figure 6. Mass–radius diagram for hybrid stars with a G300 RMF hadronic model, coupled to a bag model EoS for the quarks. The kinks in the curves mark the onset of the quark core. The left-handed panel shows results for non-interacting 1 4 of 160, 165, 167.5, 170 and 180 MeV, where the quarks with increasing values for the bag pressure with values for BMIT highest bag pressure (yellow line) leads to unstable quark stars. The right-hand panel contains results including a repulsive interaction between the quarks. The curves show results for different coupling strengths α = 0.1, 0.4, 0.7 with increasing masses for higher values of α (Negreiros et al. 2012).

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Figure 7. Normalized scalar fields as function of baryochemical potential μB . The lower curves show the nonstrange scalar field for isospin-symmetric as well as betaequilibrated stellar matter. The upper curve display the result for the scalar field with hidden strangeness (ζ ) for star matter.

to large discrepancies between model and lattice results, rather independent of the specific quark model. In the following, we use instead a more advanced model approach. We include explicit quark degrees of freedom with couplings to the mean fields in the CMF approach and introduce an effective Polyakov loop field

with a corresponding potential V ( ) in analogy to PNJL models (Fukushima 2004; Ratti et al. 2006). The quarks are suppressed for small values of the field as can be seen in the quark contribution to the pressure    6  E i∗ − μi∗ 3 , d k ln 1 +

exp Pq = T (2π )3 T i∈Q

(5) with a corresponding term for the antiquarks, where  ∗ ∗ ∗2 2 E i is the effective quark mass E i = k + Mi and μi∗ denotes the effective chemical potential of particle i: μi ∗ = μi − giω ω + giφ φ + giρ ρ, shifted by the vector fields ω (isoscalar), ρ (isovector) and φ (state with hidden strangeness). Also assuming a strong coupling of the quarks to the vector fields, depending on the choice of parameters, one can observe a strong first-order phase transition in the scalar field with hidden strangeness, corresponding to the scalar strange quark condensate in the stellar matter. This is shown in Fig. 7. Note that there is no corresponding first-order transition in heavy-ion matter (isospin-symmetric with vanishing net strangeness). In this strong coupling case, one obtains a third branch of stable compact stars, in addition to white dwarfs and usual neutron stars, the so-called twin stars

Figure 8. Mass–radius diagram for the CMFq model with strong quark–quark interactions. At smaller radii, twin star solutions develop.

Figure 9. Normalized particle densities in the hybrid star. The shaded area marks the jump in density at the first-order phase transition.

(Negreiros et al. 2012) as shown in Fig. 8. Note that both solutions with similar masses around 1.6 solar masses and very different radii are actually hybrid stars with quarks in the stellar core. However, the twin star contains much more strange particles as can be seen from the various particle densities in the star given in Fig. 9. In recent studies, the description of quark–hadron matter was extended in the CMF model by adopting the parity-doublet approach to chiral symmetry breaking. Here, the baryonic octet was combined with the corresponding negative parity octet in a doublet structure. The observed potential candidate for the nucleonic parity partner is N(1535). Similar attributions can be made for the hyperonic states, however the experimental situation is rather unclear. Details of this approach can be found in (Steinheimer et al. 2011; Mukherjee et al. 2017a, b; Dexheimer et al. 2013). The main change of

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the calculation results from the changed expression of the effective masses of the baryons i, which can be written as Mi∗ (±) =

 

gσ i σ + gζ i ζ

∓gσ i σ ∓ gζ i ζ

2

+ (m 0 + n s m s )2

 (6)

with different masses for the two parity states ± . The term n s m s represents the explicit mass breaking due to the strange quark content of the respective baryonic state. The parity-doublet models allow for a chirallyinvariant mass term m 0 as the parity violating part of the mass term from one component of the doublet is exactly canceled by the contribution of the other parity state. This behaviour is quite similar to the chirally invariant combination σ 2 + π 2 of the scalar and pseudo scalar fields in the linear σ models. The doublet formulation also introduces a second set of coupling constants g  that generates the mass splitting of the doublets. The nucleonic coupling gσ N is determined by identifying N(1535) with the nucleonic parity partner, fixing the nucleonic mass splitting. For simplicity, not to be overwhelmed by too many couplings, the same value of this coupling has been used for all baryons and gζ i has been set to zero. This leads to equal vacuum mass splittings between the parity doublet states for the different baryons, which is in general agreement with lattice QCD findings (Aarts et al. 2018). Equation (6) shows that in the case of vanishing scalar fields the doublet states are degenerate. Calculating the phase diagram of this approach by varying the temperature T and baryochemical potential μ B , one can observe two first-order phase transitions, the usual liquid–gas transition as well as the chiral transition with a low-temperature critical end point at around 12 MeV. The transition regions of the scalar condensate and Polyakov loop field are also indicated in Fig. 10. The first lattice studies of the temperature dependence of masses of baryons and their parity partners have been performed in Aarts et al. (2017, 2018). As an example a comparison between model and lattice results at vanishing chemical potential for the hyperon and its opposite parity partner is shown in Fig. 11. There is a reasonable agreement between model and lattice results, both pointing to a rather steep drop of the mass of the parity partner towards the pseudocritical temperature Tc , while the mass of the positive parity state does not show a significant temperature dependence. Finally, given the first observation of a neutron star merger in 2017 with its gravitational wave signals (Abbott et al. 2017) and electromagnetic counterparts

Figure 10. Phase diagram of the parity-doublet version of the CMFq model in the temperature-chemical potential plane. The red band marks the region where the Polyakov loop field changes from 0.2 to 0.8, whereas the corresponding green area marks the drop of the scalar condensate from 80% to 20% of its vacuum value. The solid lines show first-order phase transitions.

Figure 11. Mass of the baryon and its parity partner as a function of the temperature T /Tc for vanishing chemical potential. The line denotes the model result, whereas the symbols show lattice data (from Aarts et al. 2018).

(Pian et al. 2017), an upper limit for the tidal deformability  has been deduced in Abbott et al. (2017). In a dimensionless representation using astrophysical units with the gravitational constant G = 1,  is given by  5 R 2 , (7)  = k2 3 M where k2 is the tidal Love number, which can be determined together with mass and radius of the star as described in Hinderer et al. (2010). Note that the tidal deformability is strongly dependent on the stellar radius. Following Abbott et al. (2017),  for a 1.4 solar mass star should be below 800. On the other hand, in

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possible solution. More upcoming observational data on stellar radii and, hopefully, further merger signals will tighten the existing constraints even more. Acknowledgements SS acknowledges support from the LOEWE Center HIC for FAIR. Numerical calculations were performed at the Center for Scientific Computing of Goethe University, Frankfurt am Main. AM was financially supported by the BMBF. Figure 12. Mass–radius diagram of hybrid stars for the parity doublet model. The points indicate a contribution of 25% and 40% respectively, of quarks to the total baryon mass of the star.

Radice (2018), a lower bound on  > 400 was derived based on the observation of a substantial amount of ejected matter. According to this argument, for smaller deformability or radius the merger of the very compact stars would have immediately created a black hole without time for ejecting much matter, in contradiction with observation. Determining the tidal deformability in the parity-doublet approach leads to a value of  = 422 for M = 1.4M in agreement with the observational constraints. Also, the corresponding mass–radius diagram, Fig. 12 with a maximum mass of about 2 solar masses in this model is in accordance with observations. Note that nearly the whole star consists of a hybrid phase of quarks and baryons and that no repulsive quark interaction is included in the model, in accordance with the lattice QCD results discussed earlier.

4. Conclusions In general, the high density of the core of neutron stars suggests that exotic matter should exist in such an environment. Given the increasing number of phenomenological constraints from mass and the increasing radius measurements of neutron stars, as well as the new limits deduced from the neutron star merger signals, point to stars with relatively small amount of strange baryons, i.e. hyperons. In our approach, the analysis of the effect of quarks in the star in combination with lattice QCD data results in stars with an extended phase consisting of baryons and quarks that can fulfil the limits on stellar masses as well as on the tidal deformability of the neutron star. Alternatively, a purely nucleonic star with the nonlinear isospin interactions might still be a

References Aarts G., Allton C., De Boni D., Hands S., Jger B., Praki C., Skullerud J. I. 2018, EPJ Web Conf., 175, 07016 Aarts G., Allton C., De Boni D., Hands S., Jger B., Praki C., Skullerud J. I. 2017, JHEP, 1706, 034 Antoniadis J. et al. 2013, Science (New York), 340, 448, 1233232 Abbott B. P. et al. 2017, [LIGO Scientific and Virgo Collaborations], Phys. Rev. Lett. 119(16), 161101 Bazavov A. et al. 2012, Phys. Rev. D, 85, 054503 Bazavov A et al. 2017, Phys. Rev. D, 95(5), 054504 Demorest P. B. et al. 2010, Nature, 467, 1081 Dexheimer V., Schramm S. 2008, , 683, 943 Dexheimer V. A., Schramm S. 2010, Phys. Rev. C, 81, 045201 Dexheimer V., Steinheimer J., Negreiros R., Schramm S. 2013, Phys. Rev. C, 87(1), 015804 Fodor Z., Katz S. D. 2004, JHEP, 0404, 050 Fortin M., Zdunik J. L., Haensel P., Bejger M. 2015, A&A, 576, A68 Fraga E. S., Pisarski R. D., Schaffner-Bielich J. 2001, Phys. Rev. D, 63, 121702 Fukushima K. 2004, Phys. Lett. B, 591, 277 Glendenning N. K. 1989, Nucl. Phys. A, 493, 521 Guillot S., Servillat M., Webb N. A., Rutledge R. E. 2013, Astrophys. J., 772, 7 Hebeler K., Lattimer J. M., Pethick C. J., Schwenk A. 2013, 773, 11 Hinderer T., Lackey B. D., Lang R. N., Read J. S. 2010, Phys. Rev. D, 81, 123016 Horowitz C., Piekarewicz J. 2002, Phys. Rev. C, 66, 055803 Mukherjee A., Steinheimer J., Schramm S. 2017, Phys. Rev. C, 96(2), 025205 Mukherjee A., Schramm S., Steinheimer J., Dexheimer V. 2017, Astron. Astrophys., 608, A110 Negreiros R., Dexheimer V. A., Schramm S. 2012, Phys. Rev. C, 85, 035805 Oppenheimer J. R., Volkoff G. M. 1939, Phys. Rev., 55, 374 Ozel F., Psaltis D., Guver T., Baym G., Heinke C., Guillot S. 2016, Astrophys. J., 820(1), 28 Papazoglou P. et al. 1998, Phys. Rev. C, 57, 2576 Papazoglou P. et al. 1999, Phys. Rev. C, 59, 411

42 Page 8 of 8 Pian E. et al. 2017, Nature, 551, 67 Radice D., Perego A., Zappa F., Bernuzzi S. 2018, Astrophys. J., 852(2), L29 Ratti C., Thaler M. A., Weise W. 2006, Phys. Rev. D, 73, 014019 Ravenhall D. G., Pethick C. J., Wilson J. R. 1983, Phys. Rev. Lett., 50, 2066 Schramm S. et al. 2012, Int. J. Mod. Phys. E, 21, 1250047 Schramm S. 2002, Phys. Rev. C, 66, 064310 Schramm S., Dexheimer V., Mallick R. 2016, in Schramm S., Schäfer M., eds, New Horizons in Fundamental Physics, Springer

J. Astrophys. Astr. (2018) 39:42 Schramm S. 2003, Phys. Lett. B, 560, 164 Schulze H.-J., Rijken T. 2011, Phys. Rev. C, 84, 035801 Steiner A. W., Lattimer J. M., Brown E. F. 2013, Astrophys. J., 765, L5 Steinheimer J., Schramm S. 2014, Phys. Lett. B, 736, 241 Steinheimer J., Schramm S. 2011, Phys. Lett. B, 696, 257 Steinheimer J., Schramm S., Stöcker H. 2011, Phys. Rev. C, 84, 045208 Tolman R. C. 1939, Phys. Rev. 55, 364

J. Astrophys. Astr. (2018) 39:43 https://doi.org/10.1007/s12036-018-9535-4

© Indian Academy of Sciences

Review

VHE gamma ray astronomy with HAGAR telescope array VARSHA CHITNIS, on behalf of HAGAR collaboration Department of High Energy Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India. E-mail: [email protected] MS received 11 June 2018; accepted 6 July 2018; published online 3 August 2018 Abstract. HAGAR, an array of seven atmospheric Cherenkov telescopes located at Hanle in Himalayas, has been observing VHE gamma ray sources since September 2008. Taking advantage of the high altitude location, HAGAR could achieve an energy threshold of about 200 GeV. Several astronomical sources, mostly pulsars and blazar class active galactic nuclei, have been observed in the last nine years. Pulsations from Crab pulsar and emission from blazars Mkn 421 and Mkn 501 has been detected successfully. Details of HAGAR telescope array will be given and some important results will be discussed. Also the future plans will be described briefly. Keywords. Instrumentation: miscellaneous—(galaxies:) BL Lacertae objects: individual (Mkn 421, Mkn 501, 1ES1011+496)—gamma rays: general—(stars:) pulsars: individual (Crab).

1. Introduction Ground-based very high energy (VHE) gamma ray astronomy has emerged as a mature branch of astronomy in the last fifteen years with detection of more than 200 sources of diverse classes by various telescopes. This is an interesting field with discovery potential in key areas of astrophysics and fundamental physics. VHE gamma rays are detected indirectly using groundbased atmospheric Cherenkov technique. We have been operating the HAGAR telescope array in the Ladakh region of the Himalayas for the last few years to study VHE gamma ray emission mainly from pulsars and blazar class AGNs. We are also carrying out multiwaveband studies for these objects. Details of the HAGAR telescope array are given followed by highlights of some important results. Finally future plans with HAGAR as well as proposed G-APD based imaging camera are discussed. 1.1 Physics motivation VHE gamma rays provide the best window to study nonthermal Universe. Cosmic rays form one important component of the nonthermal Universe, with energies extending up to 1020 eV following a powerlaw energy spectrum (for example, see, Swordy 2001). In spite of

their discovery more than 100 years ago, origin and acceleration of cosmic rays is still an unresolved mystery. Supernova remnants are thought to be the sites for acceleration of cosmic rays with energies below the knee (about 1015 eV) of the cosmic ray spectrum (Ginzburg & Syrovatskii 1964). Whereas higher energy cosmic rays could be accelerated in active galactic nuclei (Mannheim & Biermann 1989). When charged particles are accelerated to such high energies through various processes, gamma rays are also produced. So the study of VHE gamma ray emission from various celestial objects will give us a clue regarding cosmic ray origin. This study will also give some insight into the emission regions and the emission processes in these sources. Apart from this, there is also a possibility to study physics beyond the standard model through searches for dark matter. Annihilation of WIMPs, i.e. weakly interacting massive particles, is expected to produce a detectable signal in VHE gamma ray range. Also there are fundamental physics aspects like tests for Lorentz invariance violation which can be investigated through the detection of rapid time variation in VHE gamma ray emission from distant objects. In addition to this, there are cosmological aspects like an indirect estimation of extragalactic background light through the study of VHE gamma ray emission from AGNs.

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VHE gamma ray emission has been detected from 208 sources by various telescopes as of now.1 These include a variety of galactic objects like pulsar wind nebulae (34 sources detected so far), supernova remnants (25), binaries (8), pulsars (2) as well as extragalactic sources which are mainly AGNs (70). About 54 VHE gamma ray sources have not been identified with known sources from other wavebands. 1.2 Detection technique VHE gamma rays are detected using ground-based atmospheric Cherenkov technique. Gamma ray interacts at the top of the atmosphere producing electron– positron pair (see Fig. 1). These electron–positron pair lose part of their energy by emitting gamma ray photon through bremsstrahlung. Through successive pair production and bremsstrahlung processes, a shower of charged particles is generated in terrestrial atmosphere. These charged particles cause atmosphere to emit bluish Cherenkov light which comes as a flash lasting for a few ns. It is spread over a circular region with radius of about 100 m at an observation level. This light is detected by a telescope consisting of a mirror with PMTs at its focus. So the incident gamma ray is detected indirectly and the entire atmosphere acts as a detection medium. One advantage of this technique is the large detection areas which are roughly of the size of the Cherenkov pool. The main disadvantage is a low duty cycle. As Cherenkov light is very weak, these observations can be carried out only on nights with clear weather when moon is not there in the sky and this limits the duty cycle. There are two variants of this technique, wavefront sampling and angular imaging. Most of the telescopes of the present generation are based on the imaging technique. These telescopes consist of a large mirror and a cluster of PMTs at the focus. In this technique, images of air showers generated by gamma rays are recorded. HAGAR on the other hand is based on wavefront sampling technique. In this technique, a distributed array of small size telescopes is used. This array samples the Cherenkov light across the pool, records arrival time of the Cherenkov shower front and Cherenkov photon density at various locations in the Cherenkov pool. The arrival time information gives the direction of shower axis, whereas Cherenkov photon density gives the estimate of primary energy. The major atmospheric Cherenkov telescopes operational now include VERITAS2 in Arizona,

High Altitude GAmma Ray (HAGAR) telescope array is operational at Hanle in the Ladakh region of the Himalayas (32◦ 46 46 N, 78◦ 58 35 E), at an altitude of 4.3 km, for the last few years. The high altitude location was chosen for installation of HAGAR in order to reduce energy threshold of the experiment. To achieve science goals such as study of distant Active Galactic Nuclei (AGNs), Gamma Ray Bursts (GRBs) and pulsed component of pulsars, energy threshold in the neighbourhood of 100 GeV was desirable. The energy threshold can be lowered either using large mirrors or by installing telescopes at high altitude location as Cherenkov photon density is higher at higher altitude (see Fig. 1). Collaboration of four institutes (TIFR, IIA, BARC and SINP) called Himalayan Gamma Ray Observatory (HiGRO) was formed for setting up these experiments in the Himalayas. With HAGAR, which is the first phase of HiGRO, an energy threshold of about 208 GeV could be achieved (Saha et al. 2013). Whereas the Pachmarhi Array of Cherenkov Telescopes (PACT) operated by TIFR at Pachmarhi at an altitude of 1 km

1 http://tevcat.uchicago.edu/.

3 https://magic.mpp.mpg.de/.

2 https://veritas.sao.arizona.edu/.

4 https://www.mpi-hd.mpg.de/hfm/HESS/.

Figure 1. Atmospheric Cherenkov technique: Cherenkov light produced by extensive air showers initiated by gamma rays is detected using a telescope.

MAGIC3 in Canary Islands and HESS4 in Namibia. Indian telescopes include BARC-operated TACTIC at Mt. Abu (Koul et al. 2007) and HAGAR at Hanle in Ladakh. Another huge telescope called MACE in under installation at Hanle. 2. HAGAR telescope array

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Figure 2. Top left: Schematic representation of the HAGAR telescope array, top middle: one of the HAGAR telescopes, top right: closer view of the HAGAR mirror channel with PMT mounted at the focus, bottom: the seven telescope HAGAR array.

had an energy threshold of about 750 GeV (Bose et al. 2007). So almost a factor of four reduction in energy threshold was achieved by an increase in the altitude. HAGAR is an array of seven telescopes with six of them deployed in the form of a hexagon and one at the centre with spacing of 50 m between the telescopes (see Fig. 2). Each of these seven telescopes consists of seven para-axially mounted parabolic mirrors. The diameter of each mirror is about 0.9 m and there is a UV sensitive PMT mounted at the focus of each mirror. Pulses from individual PMTS are brought to the control room through low attenuation coaxial cables. Tracking system is based on alt-azimuth design (for further details, see Gothe et al. 2013). Data acquisition system is CAMAC based. Trigger is generated on coincidence of at least four telescope pulses in a window of 60 ns. The data recorded on trigger includes absolute arrival time of shower front accurate to micro second given by real time clock module synchronized with GPS, Cherenkov photon density or pulse height at each telescope given by QDC, relative arrival time of shower front at each mirror accurate to 0.25 ns given by TDC. We are also recording profiles for telescope pulses in 1 ns bins using waveform digitizer. See Chitnis et al. (2011) for details about the HAGAR instrument.

Installation of HAGAR was completed at Hanle during 2005–2008 and regular observational runs began in September 2008. We have collected more than 5500 h of observational data in the last nine years of operation. We have carried out long duration observations for several galactic sources like Crab nebula/pulsar, Geminga pulsar, some of the pulsars detected by Fermi satellite, gamma ray binary LS I + 61◦ 303 and extragalactic sources, which are mainly blazar class active galactic nuclei including Mkn 421, Mkn 501, 1ES 1959+650, 1ES 2344+514, 1ES 1011+496, etc.

3. Results from HAGAR Sources observed with HAGAR include mainly two categories, pulsars and blazars. The results from HAGAR observations of some of the sources are described below.

3.1 Pulsars Pulsars are highly magnetized neutron stars with the magnetic field axis misaligned with the rotation axis. Pulsations are detected from more than 200 pulsars at

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MeV–GeV energies by Large Area Telescope (LAT) onboard Fermi satellite. Whereas at VHE energies only two sources, Crab (Aliu et al. 2008, 2011) and Vela pulsars (Stegman 2014) have been detected so far. The main interest in pulsar studies is understanding emission mechanism and emission region for gamma rays. We have extensively observed Crab pulsar with HAGAR for the last several years. Using 300 h of data collected during 2009–2017, the pulsations are detected at a period of 33 ms. The pulse profile obtained by folding the light curve with this period is shown in Fig. 3. The phases where the excess counts are seen are marked and these are consistent with the results from other experiments including MAGIC. The significance of detection is 6.3σ and pulsed flux is less than 6% of the steady signal from Crab nebula (Singh et al. 2018). We have observed few more pulsars detected by Fermi-LAT, but we did not get a statistically significant detection (Singh et al. 2011). 3.2 AGN: Multiwaveband studies VHE gamma ray emission has been detected mainly from blazar subclass of AGNs which includes BL Lacs and FSRQs. So far VHE gamma rays have been detected from 70 blazars by various experiments. As blazars have jets directed towards us, emission that is seen is Doppler-boosted in jets. The blazars are characterized by variability in all wavebands on various time scales ranging from minutes to years. Their spectral energy distributions (SEDs) show two humps and depending on the location of the first peak, they are classified as LBL (low frequency-peaked blazars), IBL (intermediate frequency-peaked) or HBL (high frequency-peaked,

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Padovani & Giommi 1995). Most of the blazars detected at VHE energies are HBLs with the first peak in SED at X-ray energies and the second one at TeV energies. The first peak is generally attributed to synchrotron emission from energetic electrons in the jet, whereas the origin of the second peak is not clear. It could be either leptonic or hadronic in origin. Synchrotron self-Compton or SSC model is the most popular leptonic model. According to this model, electrons gyrating in magnetic field of the jet emit synchrotron photons giving rise to the first hump in SED and these photons are Compton upscattered to gamma ray energies by the same population of electrons producing the second hump. There is another version of leptonic models, external Compton model, which is similar to SSC, but seed photons for Comptonization come from the regions outside the jet. Amongst hadronic models there are proton synchrotron, proton induced cascades due to interaction of protons with ambient matter or photon fields, etc. A comprehensive review is given by Böttcher (2007). We have observed the blazar, Mkn 421 extensively with HAGAR. This is a nearby blazar (z = 0.031) and has shown frequently flaring activity in all wavebands including TeV. We detected flare from this source using HAGAR in February 2010. This flare was also detected by VERITAS, HESS and TACTIC (Singh et al. 2015). The light curve from HAGAR observations is shown in Fig. 4 along with the X-ray light curve from ASM onboard RXTE satellite for three observation

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Spectral Energy Distribution (SED) of Mrk421 on 17 Feb. 2010 -8

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seasons – February, March and April 2010. These two light curves show good correlation. Maximum flux was detected by HAGAR on the night of 17th February of about 6–7 crab units with a significance level of 12.7σ above 250 GeV (Shukla et al. 2012). We studied multiwaveband data during this flare from radio to VHE gamma rays. These data were obtained from various ground- as well as space-based telescopes. We studied multiwaveband light curves as well as multiwaveband SEDs during various stages of the flare. SED during the peak of the TeV flare on 17th February 2010 is shown in Fig. 5, along with the fit with a single zone SSC model. This model seems to fit data quite well and model parameters include the jet parameters like Doppler factor, magnetic field and the parameters related to particle distribution like electron density, electron spectrum in addition to the size of the emission region. This entire flaring episode is explained in terms of a passing shock (Shukla et al. 2012). This work was further extended using the data collected over 21 observation seasons of HAGAR spread over seven years. We studied multiwaveband light curves and SEDs for a seven-year period. Figure 6 shows light curves from radio to VHE gamma rays. The last panel shows the HAGAR light curve with each point corresponding to average gamma ray count rate per season. Several aspects were investigated using these light curves. The main findings from these studies include detection of increase in variability with the frequency from radio to X-rays and later from high energy to VHE gamma rays indicating similar origin for X-ray and VHE as well as for UV and GeV gamma rays. Spectral hardening is seen in X-rays but not in GeV gamma rays, again indicating

different origin for X-ray and GeV gamma rays. The time lag between various wavebands was studied using z-transformed discrete correlation function and radio flux was found to lag behind the gamma ray flux by 52 days. Distributions of flux measurements in various wavebands indicated lognormality. Also multiwaveband SEDs were generated for 21 observations seasons of HAGAR and fitted with one zone SSC model. It was found that the flux variations are mainly due to changes in underlying particle distribution rather than the changes in jet parameters like magnetic field or Doppler factor. See Sinha et al. (2016) for further details. Another blazar observed extensively by HAGAR is Mkn 501, which is again a nearby blazar at a redshift of 0.034. It was detected in moderately high state with a flux level of 1.5 crab units in April–May 2011 at 5σ significance level. For this source also, multiwaveband light curve and SEDs were studied. Here single zone SSC model was found to be inadequate and one more zone was added to the model. The fit with the two zone SSC model is shown in Fig. 7. This indicates the presence of multiple components like at least two emission zones in the jet. The outer zone is responsible for the quiescent state flux and inner zone for flaring behaviour (Shukla et al. 2015). One more blazar that we have studied is 1ES1011+496 at a redshift of 0.212. This source was observed with HAGAR in February 2014 after the flare was reported by Fermi-LAT and some VHE experiments. HAGAR observations corresponded to the epoch when flare had decayed as seen from Fermi-LAT and there was no statistically significant detection of signal from HAGAR observations. The multiwaveband SEDs were studied which were successfully reproduced with the single zone SSC model. In this case, curvature was found in the underlying particle or electron distribution. The energy-dependent escape of particles from emission region could reproduce the observed SED, see Fig. 8 (Sinha et al. 2017). There are few more sources we observed with HAGAR which did not give statistically significant detection. It should be noted that HAGAR is a small experiment and its sensitivity is quite inferior to telescopes like MAGIC, HESS and VERITAS. We have carried out broadband study for another blazar 1ES 1959+650 at a redshift of 0.047 during flare state. We did not have statistically significant detection from HAGAR observations. In this case, multiwaveband SED was fitted with a two zone SSC model (Patel et al. 2018). Another source that we have studied is a gamma ray binary LS I + 61◦ 303. Here SED is fitted with a

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combination of SSC and Comptonization of external photons from the companion star (Saha et al. 2016). 4. Future plans 4.1 Operations with TACTIC and MACE Apart from regular observations with HAGAR, we are planning to have coordinated observations with TACTIC and MACE. TACTIC is BARC-operated imaging telescope at Mt. Abu with low-energy threshold of

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about 850 GeV. The 21-m diameter imaging telescope MACE (Major Atmospheric Cherenkov Experiment), which is the second phase of HiGRO, is being installed at Hanle under the leadership of BARC (Koul et al. 2011). It is at an advanced stage of commissioning and the first light is expected towards the end of this year. MACE will have a threshold of about 40 GeV. So the energy threshold of HAGAR is between that of MACE and TACTIC, so coordinated observations will

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provide coverage over a wider energy range in the VHE gamma ray band. Secondly, considering the proximity of HAGAR and MACE, we expect some common triggers. MACE will be a single imaging telescope and will have substantial contribution from muon triggers producing gamma ray-like images. These muon showers are localized and hence can not be observed by more than one telescope at a time. So HAGAR may help in rejecting some of the muon showers seen by MACE and this will improve the sensitivity of MACE. The possible improvement in sensitivity can be estimated through simulations. 4.2 G-APD based imaging camera Another project in which TIFR group is involved is design and development of Geiger Avalanche Photodiode (G-APD) i.e. silicon photomultiplier based imaging camera for 4-m class telescope, which will be installed at Hanle. MACE telescope, which is at an advanced stage of installation at present, will be operated in discovery mode, most of the time looking at candidate sources or very faint objects. At the same time, it is necessary to keep track of known bright blazars. A 4-m class telescope will serve the purpose and whenever it detects flaring activity from any blazar, it will alert MACE to carry out deeper observations. The imaging camera that we are developing will be installed on one of the vertex elements of TACTIC at Mt. Abu and after successful completion of tests this telescope will be installed at Hanle. G-APDs are chosen rather than PMTs as photo sensors for this camera because of their superior qualities. The most important ones are higher photon detection efficiency and lower bias voltage requirement typically 8 km) where ρmax (r ) < 2 ρ0 the low temperature boundary of the colored surface increases and reaches values T ≈ 10 MeV. The highest temperature values (Tmax (r )) are reached at the waistline of the ‘peanut’, 90 ◦ shifted off its axis (see Fig. 6(b)). For small r (r < 3 km) the maximum temperature values Tmax (r ) increase steeply for increasing r until the maximum value of T ≈ 53 MeV is reached at r  3 km. This sharp increase of Tmax (r ) corresponds to the right boundary of the (T − ρ) diagram in Fig. 7. The flowlines of the tracers (see Fig. 6(a)) show that the fluid in the interior of the HMNS has two pronounced vortices. The two centers of these swirls, where the tracer particles are accelerated correspond to the two temperature hot spots. The occurrence of these hot spots and their spatial location is closely connected with the rotational properties of the HMNS (for details, see Hanauske et al. 2017a). The angular velocity within the 3 + 1 split can be expressed as  = α v φ − β φ ,

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Figure 6. Distribution of the rest-mass density (a) and temperature (b). Same as Fig. 4 but at t = 3.69 ms.

Figure 7. Same as Fig. 7 but at t = 3.69 ms.

where v φ and β φ describes the φ-component of the three-velocity and shift vector. The temperature hot spots overlap closely with the position of the maxima of the angular-velocity distribution, which is not surprising as in these regions, the fluid flow has the largest shear and compression (Hanauske et al. 2017a; Alford et al. 2018). During the late inspiral, merger and early, transient post-merger phase, the maximum value of the density does not exceed the threshold where a HQPT is expected to be present. However, for t ≥ 3.5 ms the maximum value of the density in the central region of the HMNS is clearly above the onset of a HQPT (ρmax ≥ 3.5 ρ0 ). As a result, within a realistic model of an EoS, a considerable amount of hadronic matter should

deconfine to quark matter within this time segment of the post-merger phase. Under the assumption of the ‘strange matter hypothesis’, where the strange-quark phase is the true ground state of elementary matter, the whole neutron star would suddenly transform into a pure-quark star after exceeding certain deconfinement barrier of the HQPT (Drago & Pagliara 2015; Bombaci et al. 2016). During such a process, a significant amount of energy would be released in the form of neutrinos and gamma-rays (Drago & Pagliara 2015). However, if the strange-matter hypothesis has not been adopted, a stable hybrid HMNS can be formed having only an inner core of deconfined strange quark matter. The properties of hybrid stars containing both the hadrons and quarks have been already studied for a long time in the context of static (Hanauske & Greiner 2001; Mishustin et al. 2003; Shovkovy et al. 2003) and uniformly rotating hybrid stars (Banik et al. 2004; Bhattacharyya et al. 2005) and the results show that tremendous changes in the star properties might occur including the existence of a third family of compact stars – the so-called ‘twin stars’ (Glendenning & Kettner 2000). A twin star behaviour is present, if the third stable sequence of compact stars is separated from the second one by an unstable region. Such twin stars opens the possibility of a catastrophic re-arrangement from one configuration to the other with a prompt burst of neutrinos followed by a gamma-ray burst (Mishustin et al. 2003; Hanauske et al. 2018a, b). Such an appearance of a HQPT in the interior region of the HMNS will change the spectral properties of the emitted GW if it is strong enough. If the unstable twin star region is reached during the

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Figure 8. Distribution of the rest-mass density (a) and temperature (b). Same as Fig. 4 but at t = 19.43 ms.

‘post-transient’ phase, the f 2 -frequency peak of the GW signal will change rapidly due to the sudden speed up of the differentially rotating HMNS. However, within the LS220-M135 run no HQPT has been implemented and as a result none of the discussed astrophysical consequences has been observed within this simulation study. At late post-merger times (t > 15 ms), the temperature hot spots have smeared out to become a ring-like structure, the ‘peanut’ shape has been dissolved and the area populated in the (T − ρ) plane has been constricted to a small quasi stable region. The central region of the HMNS consists of highly densed matter (ρ/ρ0 ≈ 5) at moderate temperature values T ≈ 10 MeV while the maximum of the temperature is reached at the top of the temperature ring like structure at r ≈ 6 km at moderate density values ρ/ρ0 ≈ 2 (see Figures 8 and 9). The tracer particles have diffused over the entire inner region of the HMNS and populate almost the whole area of the HMNS. Some of these tracers circulate in the highly densed, cold inner region, others circulate near the high temperature ring and some are moving in the outer surface of the HMNS within the low density regime (see Fig. 8(a)). The results presented so far show that within the first 20 ms, the matter inside the HMNS populate areas in the QCD phase diagram where an inclusion of the quark degrees of freedom in the EoS is necessary. Especially in the interior region of the HMNS for t > 3.5 ms, the density reaches values where a non neglectable amount of deconfined quark matter is expected to be present. So far, no simulation of a binary compact star merger containing a strong HQPT has been performed.

Figure 9. Same as Fig. 2 but at t = 19.43 ms.

Figure 10 summarizes the results presented so far by showing the time evolution of the maximum value of the temperature (triangles) and the rest mass density (diamonds) of the BNS merger simulation in the (T − ρ) QCD phase diagram. In this illustration, the spatial structure of the density and temperature profiles have been neglected and several points solely indicate the evolution of the maximum values of the temperature and density. The temperature maxima reached during the post-merger phase are in the range of 40 MeV ≤ T ≤ 80 MeV. As the position of these maxima is most of the time not placed in the central region of the HMNS, their corresponding density values do not exceed 3 ρ0 . Although these temperatures are quite high, it is not likely that in these (Tmax , ρ)-fluid elements a large amount of deconfined quark matter is present. The

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(a)

(b)

Figure 10. Time evolution of the maximum value of the temperature (a) and rest mass density (b) at the equatorial plane in the interior of a HMNS using the simulation results of the LS220-M135 run. The color coding of the points indicate the time of the simulation after merger.

situation is different if one focuses on the central region of the HMNS, where the maximum of the density is reached (see Fig. 10(b)). The time dependence of the maximum value of the density shows that values above 3 ρ0 are reached for most of the post-merger phase and that for late times values near the ρ ≈ 5 ρ0 can be achieved, which is clearly above the threshold where a HQPT is expected to take place.

4. Summary and outlook The recent detection of a gravitational wave from a BNS merger by the LIGO-VIRGO collaboration (GW170817) (Abbott et al. 2017a) marked the beginning of a new era in observational astrophysics. The independently detected gamma-ray burst (GRB 1708 17A) (Abbott et al. 2017b) and further electromagnetic radiation (Abbott et al. 2017c) resulted in a neutron star merger scenario which is in good agreement with numerical simulations of BNS mergers performed in full general relativistic hydrodynamics. The extracted constraints on the mass of the total system, in combination with the limitations on the EoS, which were estimated using the extracted tidal deformation of the two neutron stars right before merger results in a neutron star merger scenario which is remarkably similar to the APR4-M135 and LS220-M135 simulation discussed in detail in Hanauske et al. (2017a). After the detected GW, it is believed that a differentially rotating compact object, the HMNS had been produced. Matter in the interior of this object reached densities of up to several times the normal nuclear matter, and temperatures could

reach T ∼ 40–80 MeV. The numerical simulations showed that — after the violent transient post-merger phase — the HMNS stabilizes, after ≈10 ms, resulting in a quasi-stable configuration with a specific rotation profile (Hanauske et al. 2017a). This HMNS is stabilized by its differentially rotating nature which will become more uniform with time until the star gets unstable and collapses to a Kerr BH. The observation of the gamma-ray burst (GRB 170817A), which was detected with a time delay of 1.7 s with respect to the merger time, indicates the collapse of the HMNS at a postmerger time 1 s. In Hanauske et al. (2017a), the BNS merger scenarios within six different EoSs were analysed and it was found that with the exception of the APR4 and LS220 EoSs, all other binaries with masses (M = 1.35M ) collapse to a black hole within t < 40 ms. During the late post-merger time of the simulation (t ≈ 20 ms), the value of the central rest-mass density increases to ρc  5 ρnuc for the APR4-M135 and the LS220-M135 run. However, for such high densities the EoS is still poorly constrained. The main question which is still open is the lack of knowledge what happens exactly in the time span of 1.7 s between the merger of GW170817 and the detected gamma-ray burst GRB 170817A. The largely accepted opinion is that the created HMNS collapsed after approximately 1 s to a Kerr black hole and the infalling surrounding matter caused the delayed gamma-ray burst. However, within realistic QCD-motivated EoSs this scenario might be different. The astrophysical consequences of an appearance of a HQPT in the interior region of the HMNS have not been analysed until now using general relativistic

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BNS merger simulations. The ALF2-EoS (Alford et al. 2005), which was used within the BNS merger simulations, however, is a model which has implemented a phase transition to color-flavor-locked quark matter, but the properties of this EoS are hardly distinguishable from a neutron star matter EoS including hyperonic particles (Hanauske et al. 2017a). Hybrid stars within the ALF2-EoS masquerades as neutron stars. If the ‘strange matter hypothesis’ is true, the HMNS will promptly transform into a pure-quark star shortly after the first strange quark droplets were formed in the star’s central region. Depending on the properties of the quark matter EoS, this transformation could either be a collapse or an expansion of the HMNS. As a result of such a violent process, a second burst of dynamically ejected matter is expected and a significant amount of energy would be released in the form of neutrinos and gamma-rays (Drago & Pagliara 2015), which could alternatively explain the observed gammaray burst GRB 170817A. However, if the strange-matter hypothesis is not realised in nature, a HQPT is expected to be formed during the evolution of the HMNS, resulting in a hybrid HMNS having an inner core of deconfined pure quark matter, surrounded by a mixed phase and a purely hadronic region. The modelling of such a HQPT in the interior of the hybrid HMNS depends strongly on the properties of the used hadronic and quark model and on the surface tension of the quark matter droplets within the mixed phase region. A strong HQPT might give rise to a mass–radius relation with a twin star shape, where the third stable sequence of compact stars is separated from the second one by an unstable region. The astrophysical consequences of a rearrangement of a HMNS due to the quark core formation, namely a twin star collapse or twin star oscillation, will be analysed in a separate article (Hanauske et al. 2018b). If the unstable twin star region is reached during the ‘posttransient’ phase, the f 2 -frequency peak of the GW signal will change rapidly due to the sudden speed up of the differentially rotating HMNS and this second burst could give an additional contribution to the dynamically emitted outflow of mass and might additionally explain the observed gamma-ray burst GRB 170817A. The high energy heavy ion collision data are compatible with a HQPT, which then shall also be present in the interior of the HMNS. As predicted by Csernai et al. (2013), a strongly rotating quarkgluon plasma has been detected experimentally in the non-central ultra-relativistic heavy ion collisions (Adamczyk et al. 2017). The STAR Collaboration

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at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory created the hottest, least viscous and most vortical fluid ever produced in the laboratory. A remarkably different rotational behaviour is observed, compared to similarly dense and hot hadronic matter. Hence, the differentially rotating inner region of the HMNS which may consist of deconfined quark matter, can also act as a macroscopically vortical fluid with an intrinsic angular momentum. A similar effect as found in noncentral ultra-relativistic heavy ion collisions may be present during the post-merger evolution of a HMNS. For example, at t = 3.69 ms (see Fig. 6), the evolution of tracer particles show a swirling behaviour around two pronounced vortices which are centered in the two temperature hot spots of the HMNS. These tracers describe trajectories of fluid elements that could pass the deconfinement transition and confine again within less than 0.3 ms. After the hadronization process, an alignment between the angular momentum of the HMNS and the spin of hadronic particles is expected and such an effect would slow down the slowly rotating inner core of the HMNS even further. After hadronization, the polarized hadronic particles (e.g. ,  − , − ) will pass regions where the frame dragging and Lense– Thirring effect, quantified with β φ , is large and an additional gravitomagnetic force would act on these fluid cells. Last but not least, it should be mentioned that within the presented simulations the expected emission of neutrinos has only been implemented using a simplified neutrino-leakage scheme, and high energetic photons or viscosity effects have not been implemented so far. In order to simulate the discussed astrophysical impacts of an appearance of a HQPT in the interior region of the HMNS, including a re-arrangement of the HMNS due to quark core formation, an incooperation of shear/bulk viscosity and neutrino trapping might be important in future BNS merger simulations (Alford et al. 2018).

Acknowledgements The authors would like to thank Luciano Rezzolla. Without his profound knowledge and his comprehensive expertise in the field of numerical relativity and general relativistic hydrodynamics, the presented simulations and the whole article would not have been possible. They would like to thank Horst Stöcker who built the scientific bridge between general relativity and elementary particle physics and arranged financial support. MH would like to thank the Saha Institute of

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Nuclear Physics, Kolkata (India) and theorganisers of the workshop on ‘Advances in Astroparticle Physics and Cosmology’ (AAPCOS-2018), especially Pratik Majumdar and Debades Bandopadhyay. They would also like to thank Tetyana Galatyuk who initiated us to visualize the BNS merger simulation in a QCD phase diagram plot. MH gratefully acknowledges support from the Frankfurt Institute for Advanced Studies (FIAS) and the Goethe University, Frankfurt. The simulations were performed on SuperMUC at LRZ-Munich, on LOEWE at CSC-Frankfurt and on Hazelhen at HLRS in Stuttgart.

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J. Astrophys. Astr. (2018) 39:46 https://doi.org/10.1007/s12036-018-9543-4

© Indian Academy of Sciences

Review

σ8 Discrepancy and its solutions SUBHENDRA MOHANTY1,∗ , SAMPURN ANAND1 , PRAKRUT CHAUBAL1 , ARINDAM MAZUMDAR1 and PRIYANK PARASHARI1,2 1 Physical

Research Laboratory, Navrangpura, Ahmedabad 380 009, India. Institute of Technology Gandhinagar, Gandhinagar 382 355, India. ∗ Corresponding author. E-mail: [email protected] 2 Indian

MS received 8 June 2018; accepted 23 July 2018; published online 22 August 2018 Abstract. In the recent past, measurements of σ8 from large scale structure observations have shown some discordance with its value obtained from Planck CMB within the CDM frame. This discordance naturally leads to a mismatch in the value of H0 also. Under the presumption that these discordances are not due to systematics, several attempts have been made to ameliorate the tensions. In this article, we describe the methods of determination of σ8 from large scale as well as CMB observations. We discuss that these discrepancies vanish if we consider the energy momentum tensor for an imperfect fluid which could arise due to self-interaction of dark matter or in an effective description of large scale structure. We demonstrate how the presence of viscosities in cold dark fluid on large scales ameliorate the problem elegantly than other solutions. We also estimate the neutrino mass in the viscous cosmological setup. Keywords. CMB—large scale structure—viscosity—neutrino mass.

1. Introduction In the past few decades or so, it has been established that our Universe, at today’s epoch, is dominated by the dark components, i.e. dark matter and dark energy (Zwicky 1993; Rubin & Ford 1970; Perlmutter et al. 1997, 1999; Riess et al. 1998; Hinshaw et al. 2013; Ade et al. 2016a, b; Troxel et al. 2017). Most plausible theoretical construct, as of now, to understand the evolution of our Universe is provided by the so-called CDM model. Most of the predictions of CDM model are in agreement with Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) observations. However some conflicts between these two observations, within the CDM paradigm, have been consistently reported in the literature. To be specific, the value of σ8 , the rms fluctuation of perturbation 8 h−1 Mpc scale, and the value of Hubble constant today H0 inferred from the CMB and LSS experiments are not in agreement with each other (Troxel et al. 2017; Vikhlinin 2009; Macaulay et al. 2013; Battye et al. 2015; MacCrann et al. 2015; Aylor et al. 2017; Raveri 2016; Lin & Ishak 2017; Abbott et al. 2017). Several attempts have been made to address these discordances between CMB and LSS observations. A

list of attempts include the interaction between dark matter and dark energy (Pourtsidou & Tram 2016; Salvatelli et al. 2014; Yang & Xu 2014), interaction between dark matter and dark radiation (Ko & Tang 2016, 2017; Ko et al. 2017), dynamical dark energy model (Park & Ratra 2018; Lambiase et al. 2018) as well as modification in the neutrino sector (Wyman et al. 2014; Battye & Moss 2014; Riemer-Sørensen et al. 2014). However, these attempts fail to resolve both the conflicts simultaneously. In this work, we show that if we incorporate the dissipative effects in the energy momentum tensor describing the energy content of the Universe, the two discordances can be ameliorated simultaneously. It has been discussed that the dissipative effect, characterized by the coefficient of viscosity, in CDM has the ability to reduce the power on small length scales which leads to suppression in the matter power spectrum on those length scales (Blas et al. 2015; Velten et al. 2014; Thomas et al. 2016). Attempts to quantify the dissipative effects in dark matter have been done in Kunz et al. (2016) from Baryon Acoustic Oscillation (BAO) data. For a recent review on this topic, we refer to Brevik et al. (2017) and references therein. There are two different kinds of viscosities: bulk and shear

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viscosities. The bulk viscosity suppresses the growth of structures by imparting a negative pressure against the gravitational collapse while the shear viscosity reduces the amount of velocity perturbations which in turn stops the growth. Another distinction between bulk and shear viscosity is that the former acts homogeneously and isotropically while the latter breaks these symmetries. Therefore, on small length scales, where the homogeneity and isotropy are broken due to velocity gradients, effects of shear viscosity are expected to play a crucial role. Although the physics of these viscosities are different, we will show that their effect on large scale structure is more or less similar. Massive neutrinos also suppress the power on small length scales, but they fail to resolve the two discordances simultaneously. But viscous paradigm does explain them. Therefore, we consider the viscous cold dark matter along massive neutrinos to constrain neutrino mass and comment on the neutrino mass hierarchy. This article is structured as follows: We start by reviewing the concept of halo mass function and quantity of central importance for our discussion, σ8 , in section 2. We then describe the tensions between the Planck CMB and LSS observation as well as previous attempts made to ease the tensions in section 3. Thereafter, we move on to discuss the viscous paradigm in section 4 and discuss about the origin of cosmic viscosities. We write down the cosmological perturbation equation in viscous setup in section 5. Finally, we present the results in section 6 and conclude in section 7.

2. Halo mass function and σ8 Linear perturbation theory works perfectly well during the period of CMB. It is because the density perturbations are of the order of 10−3 in CDM and 10−5 for the baryonic matter. All the perturbations remain in the linear regime in this epoch. But around redshift z = 50, CDM perturbations start growing above one which makes the non-linear growth more important. Finally the large scale structures that we see today, completely get generated in a non-linear process. Although the collapse process is non-linear, at late time, the number density of virialized objects can be linked with the linear perturbation theory through the halo mass function. The halo mass function is defined as dN = n(M) . dM

(1)

The first type of halo mass function was proposed by Press and Schechter (1974) which assumes that the

initial distribution of over-densities is Gaussian in nature. Moreover, those over-densities which can reach a critical value δc , if linearly extrapolated, are expected to form a virialized object. These two assumptions lead to a halo mass function which can be written as    −δc2 2 dσ M ρ¯ δc n(M)dM = − exp dM, (2) 2 2 π dM M σ M 2σ M where σ M is the standard deviation of the distribution calculated from linear matter power spectrum P(k) at a length scale   3M 1/3 . (3) R= 4π ρ¯ The quantity ρ¯ is the background density at any epoch and the standard deviation σ M is given as  ∞ 1 dkk 2 P(k)|W (k, R)|2 (4) σM = 2π 2 2π/R with W (k, R) being the appropriate window function. The halo mass function can be matched with N -body simulation which allows cold dark matter to interact gravitationally and simulates non-linear structure formation. Although the Press–Schechter mass function provided the basic shape of the halo mass function, it fails to match with simulation in the low and high M region. Therefore, more precise mass functions have been proposed by different authors and parameters of those mass functions are fitted from N -body simulations. Amongst these, the most common are the Sheth-Tormen mass function (Sheth & Tormen 1999) and the Tinker et al. mass function (Tinker et al. 2008). The mass function proposed by Tinker et al. (2008) is given by 

 σ −a dn(σ ) 2 =A + 1 e−c/σ (5) dσ b The parameters A, a, b and c are dependant on z and their values are fitted from N -body simulation. Therefore, the mass function itself is a redshift-dependant quantity. The z dependence of σ8 (R = 8 h−1 Mpc) can be written as  ∞ 1 dkk 2 P(k, z)|W (k, R)|2 σ8 (z) = 2π 2 ki  ∞ 1 = g(z) 2 dkk 2 P(k, 0)|W (k, R)|2 , (6) 2π ki where ki = 2π h/8 Mpc and g(z) is the growth parameter which has to be normalized to 1 at z = 0. Moreover, the growth function can be parametrized in terms of m (z) as

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 σ8 (z) =

m (z) 0m

α

σ80 .

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(7)

Now any large scale observation gives its result in either of these two ways: number of halos at some particular z or the number of halos integrated over z (like SZ or lensing). Whatever be the type of result, once the other parameters of the mass function are determined from simulation, the unknown quantity to be determined is σ8 (z). Therefore, there always exists a degeneracy between the growth and the primordial amplitude of P(k), or equivalently, between 0m and σ80 . In order to estimate parameters from the observations, 0m in the denominator of equation (7) is generally taken as a reference value ref and m (z) = 0m (1 + z)3 . Therefore equation (7) turns out to be  0 α m σ8 (z) = σ80 ×(1 + z)3α . (8) ref

  S8

In case of z integrated observations, we get  0 α m σ80 = constant value. S8 = ref

Figure 1. KiDS lensing result is shown in the green patch which follows the form of equation (9). The red area is the Planck CMB result. This plot is taken from Joudaki et al. (2017).

In the previous section, we have described how a relation between σ8 and 0m is established by large scale observations. On the contrary, CMB observations determine the basic six cosmological parameters. Using these six cosmological parameters with linear perturbation theory, the value of σ80 can be calculated. Recently, it has been reported that there is a discordance between the values of σ8 , inferred from Planck-CMB data and that from LSS observations. In this section, we briefly discuss the tensions between CMB and LSS observations.

corresponding to the matter radiation equality, keq (Pan et al. 2014; Ade et al. 2016a, b). The amplitude of the matter power spectrum changes with change in As while the turning point shifts when keq changes. Thus, As and m determines the features of matter power spectrum. This effect get manifested in the lensing power spectrum as well. Moreover, σ8 is propositional to As and depends on m through the growth factor. In SZ surveys, what is measured is the number of clusters with the given mass in a given volume along the line-of-sight (Ade et al. 2014a). It is described as z integrated observation in the previous section. The best-fit value of 0m and As obtained from the CMB experiments gives a value of σ8 from the theoretically predicted matter power spectrum using CDM cosmology. This value does not match with the σ8 −0m degeneracy direction at 2-σ level. This degeneracy has been mentioned in many experiments. As an example from the recent observations we show the KiDS result in Fig. 1 taken from (Joudaki et al. 2017). The joint analyses by combining different LSS experiments (as described in the Introduction) is shown in Fig. 2 taken from Anand et al. (2017).

3.1 Tension in σ8 − 0m plane

3.2 Tension in H0 − 0m plane

The impact of lensing on the temperature power spectrum is quantified using the power spectrum of the lensing potential which is estimated from the lensing observations. The lensing potential depends on the amplitude of primordial perturbations As and the scale

The value of the Hubble parameter is determined in two ways: (a) directly, using supernova observations, and (b) indirectly using CMB and LSS observations. We highlight that we are addressing the discrepancy in the indirect observations only.

(9)

Therefore all the z integrated observations try to find some combination like equation (9) which are independent of 0m . The value of α varies from observation to observation and depends on the choice of mass function.

3. Discrepancies and earlier attempts to remove them

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Figure 2. Tension in allowed values of σ8 and H0 inferred from Planck CMB and LSS (Planck SZ survey, Ade et al. 2014a), Planck lensing survey (Ade et al. 2014b), Baryon Acoustic Oscillation data from BOSS (Anderson et al. 2013; Font-Ribera et al. 2014), South Pole Telescope (SPT) (Schaffer et al. 2011; Engelen 2012) and CFHTLens (Kilbinger et al. 2013; Heymans et al. 2013) observations are shown. In the viscous framework, this mismatch in the allowed values of σ8 and H0 are resolved simultaneously.

Indirect measurement of Hubble parameter is done through the scale of baryon acoustic oscillation (BAO) at the last scattering surface, θ MC , which is actually inferred from CMB. Similarly, acoustic oscillation in the matter power spectrum is also observed by LSS surveys like SDSS. The comoving acoustic oscillation scale is considered as the standard ruler in cosmology and hence, we can determine the comoving distance from BAO (Bassett and Hlozek 2009). The comoving distance at a particular z is  z dz  , (10) χ (z) =  0 H (z ) where H (z)2 = H02 (0m (1 + z)3 +  ) .

(11)

Thus, one can estimate the value of H0 from BAO observations provided the value of 0m is given. A joint analyses of LSS experiments give some best-fit value of 0m rather than a large range. This 0m is little less than the 0m obtained from Planck CMB observations, which makes the value of H0 derived from LSS joint analysis little higher than that derived from Planck CMB observation as seen in Fig. 2. 3.3 Attempts to ease the tensions Considerable efforts have been put to ease the discordance between CMB and LSS observations. It has been argued that the interaction between dark matter and dark energy (Pourtsidou & Tram 2016; Salvatelli et al. 2014; Yang & Xu 2014) as well as dark matter

and dark radiation (Ko & Tang 2016, 2017; Ko et al. 2017) have the potential to resolve this tension to some extent. In most of the cases, such models resolve one of the above mentioned tensions but fail to solve the other one. More importantly, interaction between the dark sectors can also modify the scale corresponding to matter radiation equality (Yang & Xu 2014) which might introduce greater problem than the σ8 mismatch. Another approach adopted to address these issues is to modify the neutrino sector (Wyman et al. 2014; Battye & Moss 2014; Riemer-Sørensen et al. 2014). For instance, addition of massive sterile neutrino in the system has been reported to reduce tension in H0 − 0m plane to some extent but not in σ8 − 0m plane (Wyman et al. 2014; Battye & Moss 2014). We discuss the reason behind not solving the tension in detail. Whatever be the model of interest, the main purpose was to suppress the linear matter power spectrum so that the value of σ8 goes down. But this should happen without affecting other parameters. Let us take the example of massive neutrinos. Massive neutrinos have an important property that they are relativistic in the early Universe and contribute to the radiation density while in the late time, when they turn non-relativistic, they contribute to the total matter density. The collision-less nature of the neutrinos, after they become non-relativistic, allow them to free-stream on scales k > kfs , where kfs is the wave number corresponding to the scale of neutrino free streaming. Hence, this will wash out the perturbations on length scales smaller than the characteristic scale kfs . Thus massive neutrinos be it sterile or active suppresses matter power

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viscosity has one more benefit. Unlike massive neutrinos it does not change 0m . 4. Cosmic viscosity Before we use the cosmic viscosity as a remedy for the above mentioned discrepancies, a small description about the origin of cosmic viscosity at this stage would be appropriate. 4.1 Origin of viscosity Depending on the origin of viscosities, they are classified into two classes:

Figure 3. The red part shows σ8 from CMB, the blue region is the LSS result without modifying the mass function, and the green region is the LSS result after modifying the mass function. This plot is taken from Costanzi et al. (2013).

spectrum, but with a cost of increasing 0m . Therefore massive neutrinos can resolve the H0 tension, but fails to resolve the σ8 problem. Since the inclusion of massive neutrinos resolve some tension in the parameter space, it leads to some improvement in χ 2 . However it has been argued that this improvement is most possibly an overestimation of the effect of massive neutrinos (Costanzi et al. 2013). It is because, as we have described in the previous section, determination of S8 requires the halo mass function. Halo mass function is expected to change for inclusion of massive neutrinos. Therefore the value of S8 will also change. This will even worsen the situation and increase the tension in the σ8 − 0m plane. This has been shown in detail in Costanzi et al. (2013). Figure 3 shows the effect of massive neutrinos on the σ8 − 0m plane. In the next section, we will show cosmic viscosities as the solution of the tension. We need to point out that similar problems like these are faced in the case of neutrinos and are expected to arise in the case of viscosity too. If the viscosities in CDM are of fundamental nature then we should perform N body simulation with viscous dark matter, derive the halo mass function and generate S8 from the observations. But viscosity is of effective nature and then we can get rid of that. The reason behind it will be evident in the next section when we describe different sort of viscosities. Moreover,

• Fundamental viscosity. The diffusive transport of momentum by the constituents of the fluid can lead to viscosity. Such a viscosity is ultimately related to the fundamental interactions between the constituents of the fluid under consideration. • Effective viscosity. The Universe is characterized by two well separated scales namely, the Hubble scale, over which perturbations are linear and the scale of non-linearity which is the scale over which gravitational collapse overtakes the expansion. These well separated scales make the study of large scale structure amenable to an effective field theory treatment. In this effective theory, the quasi linear modes of the perturbations evolve in the presence of an effective fluid whose properties are determined by non-linear short wavelength modes. To describe the coupling of UV-IR modes of cosmological fluctuations, we first decompose the Einstein tensor into (i) homogeneous background, (ii) terms that are linear and (iii) terms that are non-linear in metric perturbations, i.e., G¯ μν (g¯ μν ) + (G μν (δgμν ))L 2 +(G μν (δgμν ))NL = κ Tμν .

After re-organizing the Einstein equation by considering the background equation G¯ μν = κ T¯μν , the linearized equations (G μν )L = κ(Tμν )L are defined in the standard way. Thus, the non-linear Einstein equation can be written in the following form: (G μν )L = κ(π μν − T¯μν ),

(12)

where the effective stress energy pseudo-tensor is defined as (G μν )NL . (13) κ This pseudo-tensor captures the dissipative effects. π μν = Tμν −

46 Page 6 of 10

J. Astrophys. Astr. (2018) 39:46

5. Cosmological perturbation theory in viscous cosmology In this section, we will discuss the perturbation theory for the CDM with viscosity and massive neutrinos. Since neutrinos do not interact among themselves in the standard picture, their mean-free path is infinite and we can not treat them as a fluid. Therefore, we will solve the Boltzmann equation to get the evolution equation for neutrino and derive perturbation equation for CDM using the conservation equation. 5.1 Cold dark matter The energy momentum tensor for CDM with viscosity is given as (Weinberg 1972) μν

Tcdm = ρcdm u μ u ν + ( p + pb ) μν + π μν ,

(14)

where ρcdm and p is the energy density and pressure of the CDM respectively. u μ and pb = −ζ ∇μ u μ are respectively the fluid flow vector and the bulk pressure with the coefficient of bulk viscosity ζ . μν = u μ u ν + g μν is the projection operator which projects the quantity on the three dimensional space like hypersurface and π μν is the anisotropic stress tensor and is given by π μν = −2η σ μν   1  μα

∇α u ν + να ∇α u μ = −2η 2   1 μν  α − ∇α u , 3

where ρm = ρb + ρcdm + ρν is the total matter density and ρi stands for each species. Here dot denotes the derivative with respect to the conformal time τ and H is the Hubble parameter. We get the evolution equation for the density and velocity perturbations from the perturbed part of the continuity equation (Anand et al. 2017, 2018)     ζ˜ a ζ˜ a ˙ + (θ − 3φ) θ δ˙ = − 1 − cdm H˜ cdm H˜   3 H ζ˜ a − δ (20) cdm and

  k2 a θ 4η˜ ζ˜ + θ˙ = −H θ + k ψ − 3 3 H (cdm H˜ − ζ˜ a)    ζ˜ a cdm − 6Hθ 1 − , 4 cdm H˜ 2

(21) where η˜ = 8πHGη and ζ˜ = 0 parameters. (15)

where η is the coefficient of shear viscosity and ∇ denotes the covariant derivative compatible with the given metric which we will define later in this section.We treat baryonic matter as an ideal fluid. Assuming the homogeneity and isotropy of the background, the perturbations can be decomposed into the background and the perturbed part. Since Einstein equation relates the perturbations in matter field to that in metric and vice-versa, we introduce the perturbations in FRW metric as ds 2 = a 2 (τ )[−(1+2 ψ) dτ 2 +(1−2φ) dxi dx i ] , (16) where ψ ≡ ψ(τ, x) and φ ≡ φ(τ, x) are space–time dependent perturbations. We also introduce the perturbations in the fluid flow u μ as u μ = (1 − ψ, v i ) ,

background fields are given by the Friedmann equation and continuity equation, which are given as  2 a˙ 8π G 2 H = = (18) (ρm + ) a 2 , a 3 (19) ρ˙i + 3 H (ρi + pi ) = 0 ,

(17)

which satisfies u μ u μ = −1 in the first order limit of perturbations. The evolution equations for the

8π Gζ H0

are the dimensionless

5.2 Massive neutrino As discussed earlier, we will solve Boltzmann equation for massive neutrino to get the evolution equation for density and velocity perturbations. The energy momentum tensor for massive neutrinos is given in terms of distribution function. To write the perturbation equations for neutrino, we expand the distribution function f (x i , P j , τ ) around zeroth-order distribution function f 0 . The zeroth-order terms of Tμν gives the unperturbed energy density and pressure of massive neutrinos which reads as  −4 q 2 dq f 0 (q), ρ¯ = 4π a  4πa −4 q2 ¯ P= f 0 (q), q 2 dq (22) 3   where  = (q, τ ) = q 2 + m 2ν a 2 . Since  is dependant on both momentum and time, we can not directly integrate out the momentum dependence. Therefore we expand the perturbation in the distribution function in

J. Astrophys. Astr. (2018) 39:46

the Legendre series and use the series expansion to get the the perturbed energy density, pressure, energy flux and shear stress for the massive neutrinos (Ma & Bertschinger 1995). Boltzmann equations for different moments of distribution function take the following forms in conformal Newtonian gauge: qk d ln f 0 1 − φ˙ ,  d ln q qk k d ln f 0 ˙1 = (0 − 22 ) − ψ ,  3 3q d ln q qk ˙l = [ll−1 − (l + 1)l+1 ] ∀ l ≥ 2. (23)  (2l + 1)

˙0 = − 

5.3 Effects on matter power spectrum The perturbation equations obtained in the previous section is passed to the CLASS code (Blas et al. 2011; Lesgourgues & Tram 2011) to obtain the matter power spectrum P(k) which is shown in Fig. 4 which is taken from Anand et al. (2018). It is clear from Fig. 4 that both viscosity and massive neutrinos have a similar effect on the matter power spectrum. The effective viscosity reduces the growth of density perturbations δ which in turn effects the matter power spectrum. It is important to note that the perturbation equations contain terms in which viscosity coefficient always comes with k which, therefore implies that the viscous effects are more prominent on large k or small length scales. Hence, the effective viscosity suppresses the power on large k scales (see Fig. 4). Also the effect of both shear

Page 7 of 10 46

and bulk viscosities are similar in nature, therefore we use only shear viscosity for further analysis. It has already been pointed out that neutrinos also affect P(k) in a similar manner as viscosity does. The massive neutrinos have this important property that they stream freely on scales grater than the scale corresponding to the free streaming length of neutrinos, i.e, k > kfs . In general kfs depends on z and attain the minimum value knr . The knr is a mass dependant quantity and is defined as the scale which re-enter the horizon at the time when neutrino turns non-relativistic. It is given as m 1/2 i h Mpc−1 . (24) knr = 0.018 (0m )1/2 1 eV Hence, perturbations on the scales k > knr stream out of the high density regions and do not form a structure. On the other hand, perturbations on the scales k < knr behave as CDM and are washed out on these scales. Therefore, massive neutrino suppresses the power on the small length scales. This effect can be seen clearly in the matter power spectrum (see Fig. 4).

6. Results We have done MCMC analysis using MontePython (Audren et al. 2013) of Planck and LSS data. Here we refer Planck-CMB observations (Ade et al. 2016a, b) as Planck data, whereas LSS data includes data from Planck SZ survey (Ade et al. 2014a), Planck lensing survey (Ade et al. 2014b), Baryon Acoustic Oscillation data from BOSS (Anderson et al. 2013; Font-Ribera et al. 2014), South Pole Telescope (SPT) (Schaffer et al. 2011; Engelen 2012) and CFHTLens (Kilbinger et al. 2013; Heymans et al. 2013). First, we run MCMC analysis with Planck and LSS data separately with just six standard cosmological parameters and two derived parameters. We plot the two derived parameters σ8 and H0 against 0m (see Fig. 2). It is clear from Fig. 2 that there is discordance between values obtained from Planck and LSS observations. Thereafter we run the MCMC analysis with viscous effect taken into account and found that the tension between the values of σ8 and H0 inferred from Planck and LSS observations has resolved simultaneously in the viscous framework (see Fig. 2). 6.1 Viscous cosmological parameters

Figure 4. Both viscosity and neutrino suppress the matter power spectrum. Viscosity suppresses P(k) strongly on small length scales, whereas the effect of neutrinos is visible on scales greater than knr .

We have already discussed that viscosity resolves the tension between Planck and LSS observations. In this subsection, we discuss the cosmological parameters

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J. Astrophys. Astr. (2018) 39:46

obtained from the analysis with Planck and LSS observations. We perform MCMC analysis of Planck and LSS combined data sets to find the best fit value of viscosity parameters. We have performed three analyses. In the first run, we kept both the viscosity parameters η˜ and ζ˜ varying and obtained their best-fit values. In the next two runs, we kept either η˜ or ζ˜ to be zero and obtained the best-fit values for the other parameters. All the best-fit values are listed in Table 1. From these analyses, we also found the best-fit values of six cosmological parameters and two derived parameters. We found that the value of derived parameter σ8 is less than the Planck-fitted value. There is no significant difference between the best-fit value of σ8 obtained from the analysis done with either η˜ or ζ˜ to be zero and that of the analysis done with both the viscosity

Table 1. Best-fit values of viscosity parameters, obtained from the Plank–LSS joint analyses. The best-fit values of two derived parameters σ8 and H0 are also listed Parameters

1-σ value

2-σ value

+0.40 1.20−1.00 × 10−6

+1.00 1.20−1.00 × 10−6

η˜ ζ˜

+0.50 1.32−1.00 × 10−6

+2.00 1.32−1.00 × 10−6

ζ˜ = 0 η˜

−6 2.29+0.50 −0.60 × 10

−6 2.29+1.00 −1.00 × 10

η˜ = 0 ζ˜

−6 2.46+0.50 −0.60 × 10

−6 2.46+1.00 −1.00 × 10

H0 (km/s/Mpc)

68.39 ± 0.56

σ8

0.754 ± 0.011

+1.1 68.4−1.1

+0.022 0.754−0.021

parameters. We also list the values of two derived parameters obtained from the joint analysis of Planck and LSS data in Table 1. 6.2 Parameter space of neutrino mass: Viscous cosmology and other experiments Recently, it has been shown that effective viscosity can resolve both σ8 and H0 tension simultaneously. Also, the phenomenon of neutrino oscillation has been observed by many experiments, which suggest that neutrinos are massive. We have already discussed how viscosity and massive neutrino affect the matter power spectrum P(k). They have similar effects as both suppresses the P(k) at small length scales. Therefore, it is expected that constraints on the neutrino mass will be more stringent in the viscous framework of cosmology. First, we did MCMC analysis of Planck and LSS combined dataset with six standard cosmology parameter and lightest neutrino mass m 0 . We found that constraint on lightest neutrino mass is 0.012 eV ≤ m 0 ≤ 0.126 eV for NH, whereas it is 0 ≤ m 0 ≤ 0.119 eV in the case of IH. This non-zero mass in the case of NH has arisen because we have not taken the viscous effect into account. We have also done the MCMC analysis in the effective viscosity framework with massive neutrino and found that the upper bound on m 0 is 0.084 eV for NH and 0.03 eV for IH. Therefore, it is clear that bound on m 0 is more stringent in the effective viscous framework as well as it rules out the notion of finding the non-zero mass. We also calculated the constraints  on the sum of neutrino masses m ν using the lightest neutrino mass obtained from our analysis and other parameters taken from Capozzi et al. (2016). We found

 Figure 5. Constraint on the sum of neutrino masses m ν , obtained from the analysis of combined Planck and LSS data decreases significantly over the inclusion of viscosity in CDM.

J. Astrophys. Astr. (2018) 39:46

 that the upper bound on m ν changes from 0.396 eV and 0.378 eV to 0.267 eV and 0.146 eV for NH and IH respectively. This is shown in Fig. 5 which is taken from Anand et al. (2018).

7. Conclusion and discussion The discrepancies in the value of σ8 and H0 have been reported extensively in the literature. At the same time, many theoretical models have also been proposed to explain these tensions. However, these proposals are plagued with several issues. For instance, the interaction between dark sectors, which have been proposed as a solution, is completely ad-hoc. Moreover, most of these proposals do not explain both the problems simultaneously. On the other hand, we have considered the dissipative effects in the energy momentum tensor, which is characterized by the bulk and shear viscosities, in this analysis. These viscosities can be generated by the diffusive transport of momentum and by the constituent particles of the fluid. Alternatively, they can also be generated in an effective field theory treatment of large scale structure where small scale non-linearities are integrated to give rise to the large scale phenomenon. In this approach, UV and IR modes are coupled which can be described by an effective energy momentum tensor for imperfect fluid. We have found that either of the two viscosities or their combination affect the growth of linear overdensity which in turn changes the matter power spectrum at small length scales. To quantify the amount of viscosity supported by the current observations, we have considered the viscosity coefficients as model parameters and performed MCMC analysis with Planck and LSS data. We found that the value of bulk and shear viscosity parameters are of the same order and have similar effects. The best-fit values for these viscosity parameters (η and ζ ) are of the order of 3 × 102 Pa s. It is interesting to note that the best-fit value of viscosity coefficients obtained resolve the conflict between Planck CMB and LSS observations, both in the σ8 − m0 plane as well as the H0 − m0 plane, simultaneously. We would like to highlight that the value of H0 inferred from Planck does not change significantly due to the viscosities, while the same obtained from LSS changes appreciably. The reason for this is the following: H0 is obtained from the baryon acoustic oscillation scale and depends on the value of m0 . The LSS experiments constrain σ8 and m0 jointly which gives a scope to accommodate lower σ8 by increasing m0 . However, in the case of Planck

Page 9 of 10 46

data, σ8 is a derived parameter which comes down to a lower value, due to inclusion of viscosity, without affecting m0 . Therefore, in the case of σ8 , both Planck and LSS fitted values change on inclusion of viscosities, but for H0 , only the LSS value gets affected. We did not introduce any extra matter component to the CDM cosmology. As discussed earlier, inclusion of massive neutrinos does not solve both the problems simultaneously on its own but viscosity does. On the other hand, neutrino oscillation experiments have shown that the neutrinos are not massless. Thus, we consider the massive neutrinos in the viscous paradigm. Recall that the massive neutrinos have important property that they are relativistic in the early Universe and contribute to the radiation density while in the late time, when they turn non-relativistic, they contribute to the total matter density. The collisionless nature of the neutrinos, after they become non-relativistic, allow them to free-stream on scales k > kfs . Hence, this will wash out the perturbations on length scales smaller than the characteristic scale kfs leading to further suppression of power on small scales. Hence, in this viscous setup, stringent constraint on the mass of neutrinos can be put.

References Abbott T. M. C. et al. 2017, Dark energy survey year 1 results: Cosmological constraints from galaxy clustering and weak lensing Ade P. A. R. et al. 2016a Astron. Astrophys., 594, A13 Ade P. A. R. et al. 2016b, Astron. Astrophys., 594, A15 Ade P. A. R. et al. 2014a, Astron. Astrophys., 571, A20 Ade P. A. R. et al. 2014b, Astron. Astrophys., 571, A17 Anand S., Chaubal P., Mazumdar A., Mohanty S. 2017, JCAP, 1711, 005 Anand S., Chaubal P., Mazumdar A., Mohanty S., Parashari P. 2018, JCAP, 1805, 031 Anderson L. et al. MNRAS, 441, 24 Audren B., Lesgourgues J., Benabed K., Prunet S. 2013, JCAP, 1302, 001 Aylor K. et al. 2017, A comparison of cosmological parameters determined from CMB temperature power spectra from the South pole telescope and the Planck satellite Bassett B. A., Hlozek R. 2009, Baryon Acoustic Oscillations, 2009 Battye R. A., Charnock T., Moss A. 2015, Phys. Rev., D91, 103508 Battye R. A., Moss A. 2014, Phys. Rev. Lett., 112, 051303 Blas D., Lesgourgues J., Tram T. 2011, JCAP, 1107, 034 Blas D., Floerchinger S., Garny M., Tetradis N., Wiedemann U. A. 2015, JCAP, 1511, 049

46 Page 10 of 10 Brevik I., Grøn Ø., de Haro J., Odintsov S. D., Saridakis E. N. 2017, Viscous cosmology for early- and late-time Universe Capozzi F., Lisi E., Marrone A., Montanino D., Palazzo A. 2016, Nucl. Phys., B908, 218 Costanzi M., Villaescusa-Navarro F., Viel M., Xia J.-Q., Borgani S., Castorina E., Sefusatti E. 2013, JCAP, 1312, 012 Font-Ribera A. et al. 2014, JCAP, 1405, 027 Heymans C. et al. 2013, MNRAS, 432, 2433 Hinshaw G. et al. 2013 Astrophys. J. Suppl., 208, 19 Joudaki S. et al. 2017, MNRAS, 471, 1259 Kilbinger M. et al. 2013, MNRAS, 430, 2200 Ko P., Tang Y. 2016, Phys. Lett., B762, 462 Ko P., Tang Y. 2017, Phys. Lett., B768, 12 Ko P., Nagata N., Tang Y. 2017, Hidden charged dark matter and chiral dark radiation Kunz M., Nesseris S., Sawicki I. 2016, Phys. Rev., D94, 023510 Lambiase G., Mohanty S., Narang A., Parashari P. 2018, Testing dark energy models in the light of σ8 tension Lesgourgues J., Tram T. 2011, JCAP, 1109, 032 Lin W., Ishak M. 2017 Phys. Rev., D96, 023532 Ma C.-P., Bertschinger E. 1995, Astrophys. J., 455, 7 Macaulay E., Wehus I. K., Eriksen H. K. 2013, Phys. Rev. Lett., 111, 161301 MacCrann N., Zuntz J., Bridle S., Jain B., Becker M. R. 2015, MNRAS, 451, 2877 Pan Z., Knox L., White M. 2014, MNRAS, 445, 2941 Park C.-G., Ratra B. 2018, Observational constraints on the tilted flat-XCDM and the untilted non-flat XCDM dynamical dark energy inflation parameterizations Perlmutter S. et al. 1997, Astrophys. J., 483, 565

J. Astrophys. Astr. (2018) 39:46 Perlmutter S. et al. 1999, Astrophys. J., 517, 565 Pourtsidou A., Tram T. 2016, Phys. Rev., D94, 043518 Press W. H., Schechter P. 1974, Astrophys. J., 187, 425 Raveri M. 2016, Phys. Rev., D93, 043522 Riemer-Sørensen S., Parkinson D., Davis T. M. 2014, Phys. Rev., D89, 103505 Riess A. G. et al. 1998, Astron. J., 116, 1009 Rubin V. C., Ford W K. Jr. 1970, Astrophys. J., 159, 379 Salvatelli V., Said N., Bruni M., Melchiorri A., Wands D. 2014, Phys. Rev. Lett., 113, 181301 Schaffer K. K. et al. Astrophys. J., 743, 90 Sheth R. K., Tormen G. 1999, MNRAS, 308, 119 Thomas D. B., Kopp M., Skordis C. 2016, Astrophys. J., 830, 155 Tinker J. L., Kravtsov A. V., Klypin A., Abazajian K., Warren M. S., Yepes G., Gottlober S., Holz D. E. 2008, Astrophys. J., 688, 709 Troxel M. A. et al. 2017, Dark energy survey year 1 results: Cosmological constraints from cosmic shear van Engelen A. et al. 2012, Astrophys. J., 756, 142 Velten H., Caramłs T. R. P., Fabris J. C., Casarini L., Batista R. C. 2014, Phys. Rev., D90, 123526 Vikhlinin A. et al. 2009, Astrophys. J., 692, 1060 Weinberg S. 1972, Gravitation and Cosmology, John Wiley and Sons, New York, pp. 55–57 Wyman M., Rudd D. H., Vanderveld R. Ali, Hu W. 2014, Phys. Rev. Lett., 112, 051302 Yang W., Xu L. 2014, Phys. Rev., D89, 083517 Zwicky F. 1933, Helv. Phys. Acta, 6, 110 (Gen. Relativ. Gravit., 41, 207 (2009))

J. Astrophys. Astr. (2018) 39:47 https://doi.org/10.1007/s12036-018-9542-5

© Indian Academy of Sciences

Review

Prospects of detecting fast radio bursts using Indian radio telescopes SIDDHARTHA BHATTACHARYYA Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India. E-mail: [email protected] MS received 10 May 2018; accepted 24 July 2018; published online 23 August 2018 Abstract. Fast Radio Bursts (FRBs) are short duration highly energetic dispersed radio pulses. We developed a generic formalism (Bera et al. 2016, MNRAS, 457, 2530) to estimate the FRB detection rate for any radio telescope with given parameters. By using this model, we estimated the FRB detection rate for two Indian radio telescope; the Ooty Wide Field Array (OWFA) (Bhattacharyya et al. 2017, J. Astrophys. Astr., 38, 17) and the upgraded Giant Metrewave Radio Telescope (uGMRT) (Bhattacharyya et al. 2018, J. Astrophys. Astr.) with three beam-forming modes. Here, we summarize these two works. We considered the energy spectrum of FRBs as a power law and the energy distribution of FRBs as a Dirac delta function and a Schechter luminosity function. We also considered two scattering models proposed by Bhat et al. (2004, Astrophys. J. Suppl. Series, 206, 1) and Macquart & Koay (2013, ApJ, 776, 125) for these works and we consider FRB pulse without scattering as a special case. We found that the future prospects of detecting FRBs by using these two Indian radio telescopes is good. They are capable to detect a significant number of FRBs per day. According to our prediction, we can detect ∼ 105 −108 , ∼ 103 −106 and ∼ 105 −107 FRBs per day by using OWFA, commensal systems of GMRT and uGMRT respectively. Even a non detection of the predicted events will be very useful in constraining FRB properties. Keywords. Cosmology—observations.

1. Introduction Fast Radio Bursts (FRBs) are short duration (∼ ms), highly energetic (∼1032 −1034 J) dispersed radio pulses, first discovered (Lorimer et al. 2007) at the Parkes radio telescope. The high dispersion measure (DM) of the detected FRBs, which is in general ∼5–20 times excess DMs compared to what is expected from the Milky Way (Cordes & Lazio 2003), strongly suggests that FRBs are extragalactic events. The observed dispersion and the scattering indices imply the fact that the FRB signal propagates through the cold ionized plasma (Katz 2016) of the interstellar medium (ISM) of the Milky Way, host galaxy of the source and the intergalactic medium (IGM). A total of 35 FRBs have been reported1 to date. Of these 26 FRBs have been detected at the Parkes radio telescope (Petroff et al. 2016, 2017; Keane et al. 2016; Ravi et al. 2016; Bhandari et al. 2017; Shannon et al. 2017; Price et al. 2018; Oslowski et al. 2018a, b), six FRBs have been detected at the UTMOST radio 1 http://frbcat.org/.

telescope (Caleb et al. 2017; Farah et al. 2017, 2018) and one each has been detected at the Arecibo (Spitler et al. 2014), GBT (Masui et al. 2015) and ASKAP (Bannister et al. 2017) radio telescopes. One FRBs has been found to repeat (Scholz et al. 2016) and 17 detections from the same source have been reported to date. There are several models (Kulkarni et al. 2015) proposed for the emission mechanism of FRBs but the exact one is still unknown. The energy spectrum and the energy distribution of FRBs are not well constrained and moreover the estimates of the spectral index of FRBs are available only for few FRBs but they are not reliably estimated due to the poor localization of the source within the single dish beam. Bera et al. (2016) developed a generic formalism to estimate the detection rate and the redshift distribution of FRBs for a radio telescope with the given parameters. They assumed a power law E ν ∝ ν α with α as the spectral index for the energy spectrum of FRBs and two scattering models proposed by Bhat et al. (2004) and Macquart & Koay (2013) for the predicted pulse width of FRBs and they are denoted here as

47 Page 2 of 8

scattering model I (Sc-I) and II (Sc-II) respectively. Scattering model I (Sc-I) is an empirical fit to a large number of pulsar data in the Milky Way, whereas scattering model II (Sc-II) is purely theoretical without any observational consequences. The details of mathematical expression of scattering models I and II can be found in Bera et al. (2016). We also consider here FRB pulse without scattering as a special case, since for the most of the detected FRBs we did not find any scattering. The model is normalized by considering FRB 110220 as the reference event and the estimated energy (E 0 = 5.4 × 1033 J) of this FRB using our model as the reference energy. We also consider the prescribed FRB rate from Champion et al. (2016), i.e. 7 × 103 FRBs per sky per day as the reference event rate. Note that this prescribed FRB rate is differed from the FRB rate that was used in previous publications (Bera et al. 2016; Bhattacharyya et al. 2017, 2018) by a factor of ∼5 × 105 . Note that, the value of E 0 is estimated by using the model prescribed in Bera et al. (2016) with α = −1.4 (E ν ∝ ν α ), which is differed from the energy mentioned in Thornton et al. (2013) by a factor of 5. As described in Bera et al. (2016), all redshifts are inferred from the DM; the scattering time scale, when available gives an upper limit on the redshift. We also considered two energy distribution functions: a Dirac delta function and a Schechter luminosity function with the exponent in the range −2 ≤ γ ≤ 2, as the possible energy distribution functions of FRBs. Using the model mentioned above, we estimated the FRB detection rate for the two Indian radio telescopes, Ooty Wide Field Array (OWFA) (Bhattacharyya et al. 2017) and the upgraded Giant Metrewave Radio Telescope (uGMRT) (Bhattacharyya et al. 2018). We have found that the detection probability of FRBs largely depends on two factors: the field-of-view (FoV) of the telescope and the antenna sensitivity ( AS ), where the antenna sensitivity is the ratio of the antenna gain (G) and the system temperature (Tsys ) of the telescope. A telescope with large field-of-view (FoV) and high antenna sensitivity (AS ) is capable of detecting a large number of FRBs. Hence, the product FoV × AS is a measure of the FRB detection sensitivity for a telescope. The typical value of this product for OWFA with the observational frequency of 326.5 MHz and uGMRT with the observational frequency of 375 MHz are 1.054 and 1.63 × 10−2 deg2 Jy−1 respectively. However, this product is estimated by considering the higher galactic latitude (i.e., cold sky). For comparison, this value is 1.96 × 10−2 deg2 Jy−1 for the Parkes telescope and 3.93 × 10−4 deg2 Jy−1 for the Arecibo telescope. In this respect, both OWFA and

J. Astrophys. Astr. (2018) 39:47

uGMRT are capable of detecting a large number of FRBs in comparison to the Parkes and Arecibo radio telescopes. This paper is a review of our previous works. Our predictions of FRB detection rates for OWFA and uGMRT are summarized. A brief outline of the paper is as follows. Section 2 presents a brief description and the FRB detection rates for OWFA. Section 3 presents a brief description and the FRB detection rates for GMRT and uGMRT. Section 4 presents FRB detection rate and localization comparison among OWFA, commensal systems of GMRT and uGMRT. Finally, the results are discussed and summarized in section 5.

2. Ooty Wide Field Array (OWFA) The Ooty Wide Field Array (OWFA) is an upgraded version of the Ooty Radio Telescope (ORT) which was built in early 70s (Swarup et al. 1971) at Ooty, Tamil Nadu. ORT has a long cylindrical reflector of dimension 530 × 30 m,which contains 1056 half wavelength linear dipoles along the focal line of the reflector. The signal from the dipoles can be combined in different ways. Currently the signals from these dipoles are combined to form an analogue incoherent beam forming network which we refer to as the legacy system. The legacy system (LS) operates at an observational frequency ν0 = 326.5 MHz (λ = 0.91 m) with bandwidth B = 4 MHz. The system is being upgraded to two modes of operation: Phase I (PI) and Phase II (PII). In Phase I, 24 dipoles are combined together to form a single element and this system has a total 40 such elements. In Phase II, 4 dipoles are combined together to form a single element and this system has a total 264 such elements. The bandwidth of Phase I and Phase II are 19.2 MHz and 38.4 MHz respectively, centred at the same observational frequency of the ORT Legacy System. More technical information about OWFA can be found in Subrahmanya et al. (2017). The system specifications of LS, PI and PII are tabulated in Table 1. In this work, we considered three kinds of beam formations: incoherent (IA), coherent single (CA-SB) and coherent multiple (CA-MB) beam formations. In the case of incoherent beam formation (IA), the squares of the voltages from the individual elements are summed over to obtain the total power. This mode of beam formation does not contain any phase information. Here the FoV is proportional to λ/d, where d is the length of a single element. √ The sensitivity in this mode is increased by a factor of NA compared to the sensitivity achieved

CHIME

uGMRT

GMRT

OWFA

Telescope

−

Band 5

Band 4

Band 3

Band 2

Band S2

Band S1

PII

LS PI

System

600

1250

700

375

185

450

300

400

400

300

250

130

32

32

38.4

19.2

326.5

326.5

4

(MHz)

(MHz)

326.5

B

ν

IA CA-SB

IA CA-SB MIA IA CA-SB MIA IA CA-SB MIA IA CA-SB MIA

IA CA-SB MIA IA CA-SB MIA

IA IA CA-SB CA-MB IA CA-SB CA-MB

formation

Beam

5.80 0.16

5.21 0.95 2.71 0.90 0.16 0.47 0.69 0.13 0.36 0.63 0.12 0.33

2.25 0.41 1.17 2.25 0.41 1.17

6.88 22.80 3.61 1.08 38.10 2.34 0.70

(Jy ms)

Fth

(1.17 ± 0.64) × 106 (3.34 ± 0.91) × 107 (1.68 ± 0.53) × 106 (8.93 ± 0.31) × 107 (1.61 ± 1.03) × 108 (1.69 ± 0.45) × 106 (5.77 ± 0.22) × 108 (1.73 ± 0.48) × 106 (2.44 ± 0.16) × 104 (2.02 ± 0.37) × 106 (2.00 ± 0.27) × 105 (1.57 ± 0.10) × 104 (2.38 ± 0.12) × 105 (2.52 ± 0.77) × 106 (3.67 ± 0.52) × 104 (2.99 ± 0.66) × 106 (1.73 ± 0.22) × 107 (2.24 ± 0.11) × 104 (1.95 ± 0.08) × 107 (9.01 ± 0.31) × 105 (1.17 ± 0.26) × 104 (1.02 ± 0.35) × 106 (8.82 ± 0.60) × 104 (6.34 ± 0.36) × 103 (1.01 ± 0.49) × 105 (8.93 ± 0.32) × 108 (4.36 ± 0.24) × 106

(2.37 ± 1.09) × 105 (7.19 ± 1.29) × 106 (3.43 ± 0.98) × 105 (1.92 ± 0.82) × 107 (3.55 ± 1.42) × 107 (3.49 ± 0.92) × 105 (1.29 ± 0.77) × 108 (3.60 ± 0.95) × 105 (5.71 ± 0.74) × 103 (4.32 ± 0.87) × 105 (4.12 ± 0.73) × 104 (3.59 ± 0.55) × 103 (5.01 ± 0.66) × 104 (5.19 ± 1.46) × 105 (8.35 ± 1.12) × 103 (6.32 ± 1.31) × 105 (3.79 ± 0.78) × 106 (5.83 ± 0.59) × 103 (4.52 ± 0.70) × 106 (1.94 ± 0.37) × 105 (2.94 ± 0.24) × 103 (2.31 ± 0.32) × 105 (1.85 ± 0.03) × 104 (1.55 ± 0.13) × 103 (2.23 ± 0.07) × 104 (1.79 ± 0.82) × 108 (1.10 ± 0.37) × 106

132.00 0.29

4.26 1.38 × 10−5 4.26 1.04 3.36 × 10−6 1.04 0.30 9.64 × 10−7 0.30 0.09 3.02 × 10−7 0.09

1.62 5.25 × 10−6 1.62 0.72 2.33 × 10−6 0.72

Without scattering

(1.17 ± 0.11) × 109 (4.83 ± 0.18) × 106

(4.27 ± 0.41) × 106 (5.06 ± 0.09) × 104 (4.64 ± 0.29) × 106 (2.30 ± 0.12) × 107 (2.63 ± 0.10) × 104 (2.46 ± 0.14) × 107 (1.15 ± 0.28) × 106 (1.35 ± 0.18) × 104 (1.25 ± 0.23) × 106 (1.05 ± 0.45) × 105 (7.04 ± 0.29) × 103 (1.16 ± 0.37) × 105

(2.93 ± 0.10) × 106 (3.32 ± 0.10) × 104 (3.12 ± 0.12) × 106 (3.41 ± 0.20) × 105 (2.15 ± 0.13) × 104 (3.67 ± 0.18) × 105

(2.11 ± 0.23) × 106 (8.95 ± 0.32) × 107 (3.12 ± 0.10) × 106 (1.38 ± 0.13) × 108 (4.33 ± 0.48) × 108 (2.80 ± 0.10) × 106 (8.26 ± 0.13) × 108

Scattering Model II

Scattering Model I

(deg2 ) 0.52 24.11 0.60 24.11 143.34 0.55 143.34

FRB detection rate (day−1 )

FoV

Table 1. The number of FRBs expected to be detected per day by considering the Dirac delta function as the energy distribution function of FRBs and the mean value of α with error for the range −5 ≤ α ≤ 0, where E ν ∝ ν α . Two scattering models and FRB signal without scattering have been considered for the detection rate comparison. Here IA, CA-SB, CA-MB and MIA denote incoherent, coherent single beam, coherent multiple beam and multiple incoherent beam formations respectively. The symbols ν, B, Fth and FoV denote observational frequency of the telescope, bandwidth of the observation, threshold fluence of FRB required for the detection and the field-of-view of the telescope respectively.

J. Astrophys. Astr. (2018) 39:47 Page 3 of 8 47

10

8

10

7

Coherent Single Beam Formation (CA-SB)

106 105 10

4

10

7

OWFA : Phase I

OWFA : Phase II

UTMOST

CHIME

106 105 104

-5

-4

-3

-2

10

-1

-5 α

-4

-3

-2

-1

0

-2

-1

0

Incoherent Beam Formation (IA)

1010 9

-1

Detection Rates (day )

108 107 106 10

OWFA : Phase I

OWFA : Phase II

UTMOST

CHIME

5

109 10

8

10

7

106 105

-5

-4

-3

10

9

10

8

-2

-1

-5 α

-4

-3

Coherent Multiple Beam Formation (CA-MB)

1010

107 10

OWFA : Phase I

6

-5

-4

-3 Detection Rates (day-1)

-1 Detection Rates (day )

by a single element. Note that LS operates with incoherent beam forming mode. In the case of coherent single beam formation (CA-SB), the voltage signals from the individual elements with phase are added directly and then squared to obtain total power. In this mode, the field-of-view (FoV) is proportional to λ/D, where λ is the wavelength of the observation and D is the length of the largest baseline. Here the sensitivity is increased by a factor of NA compared to the sensitivity achieved by a single element. The coherent multiple beam formation is a mixture of IA and CA-SB mentioned above. In coherent multiple beam formation (CA-MB), one forms the IA to obtain a large instantaneous field-of-view but at a relatively shallow sensitivity. When an event is detected in the IA mode, the high time resolution signals are recorded to eventually form multiple coherent beams-offline in all possible directions. This will give us the sensitivity of the CA-SB, but with the field-of-view of the IA and hence the detection probability in this mode is larger than the same for IA and CA-SB modes. This specific kind of strategy was first demonstrated in a pilot transient survey with the Giant Metrewave Radio Telescope (GMRT) by Bhat et al. (2013). Note that the value of threshold signal-to-noise ratio ((S/N)th ) for this beam-forming mode is less when compared to the same for IA and CA-SB modes. In this work, (S/N)th = 3 for CA-MB mode and (S/N)th = 10 for IA and CA-SB beam forming modes. We considered the energy spectrum of FRBs as E ν ∝ ν α for this work and α is defined here as the spectral index. We estimated the FRBs detection rates for ORTlegacy system, OWFA Phase I and II and compared the results with other two cylindrical radio telescopes, UTMOST (Caleb et al. 2016) and CHIME (Newburgh et al. 2014). Note that UTMOST operates at an observational frequency of 843 MHz with a bandwidth of 31.25 MHz, whereas CHIME operates at an observational frequency of 600 MHz with a bandwidth of 400 MHz. Figure 1 shows the FRB detection rates as a function of α for OWFA Phase I and Phase II, UTMOST and CHIME with three beam forming modes IA, CASB and CA-MB and the ORT legacy system. It is found that the detection rate varies with different scattering models and the detection rate is maximum for the case of FRB pulse without scattering, which is roughly two order and one order of magnitude larger than the same for scattering models I and II respectively. Further the detection rate increases with decreasing α (α ≤ 0). In brief, we expect to detect ∼105 −108 FRBs per day by using OWFA Phase II with fluence F ≥ 0.7 Jy ms, which is also large when compared to that for UTMOST.

J. Astrophys. Astr. (2018) 39:47

Detection Rates (day-1)

47 Page 4 of 8

-2

-1

108 10

OWFA : Phase II -5 α

-4

-3

-2

-1

0

7

106 105 104

ORT LS -5

-4

-3

α

-2

-1

0

Figure 1. The variation of the FRB detection rate with the variation of α, where E ν ∝ ν α for ORT legacy system, OWFA Phase I and Phase II, UTMOST and CHIME with three kinds of beam formations: IA, CA-SB and CA-MB. Two scattering models Sc-I (green region) and Sc-II (yellow region) and FRB pulse without scattering (orange region) have been considered here. The solid black lines denote the Dirac delta function, while the boundaries of the regions enclosing the curves correspond to the Schechter luminosity function with an exponent in the range −2 ≤ γ ≤ 2.

J. Astrophys. Astr. (2018) 39:47

However, the detection rate is maximum for the CHIME due to its large field-of-view but these three telescopes operate in different frequency ranges and hence complementary.

3. Upgraded Giant Metrewave Radio Telescope (uGMRT) The GMRT antennas are distributed in a Y-shaped pattern with a shortest baseline of 200 m and a longest baseline of 25 km. Each dish has five prime focus feeds, only one of which is available at a given time, having five discrete operational frequencies centered at 150, 235, 325, 610 and 1280 MHz with a maximum backend instantaneous frequency bandwidth of 32 MHz. Currently the GMRT is going through an upgradation (Gupta et al. 2017), to provide significantly large instantaneous bandwidths with four operational frequencies, viz., Band 2 at 185 MHz with a bandwidth of 130 MHz, Band 3 at 375 MHz with a bandwidth of 250 MHz, Band 4 at 700 MHz with a bandwidth of 300 MHz and Band 5 at 1250 MHz with a bandwidth of 400 MHz. In this work, we also considered the proposed commensal system for the GMRT (Bhattacharyya et al. 2018). This system as currently envisaged, would reuse the legacy signal transport chain of the GMRT, which has a bandwidth of 32 MHz. The feed system is proposed to be mounted off-focus on the quadripod feed legs of the GMRT, and hence will be available at all times, unlike the main feeds, which are mounted on a rotating turret, and of which only one feed is available at a given time. We examined the expected detection rate for two possible central frequencies, viz. 300 and 450 MHz with a bandwidth of 32 MHz, which roughly span the possible frequencies of the proposed system and they are denoted here as Bands S1 and S2 respectively. In both the GMRT commensal systems and uGMRT, we considered three kinds of beam formations: incoherent (IA), coherent single (CA-SB) and multiple incoherent (MIA) beam formations. The description of IA and CA-SB have been mentioned earlier and MIA mode is a special beam-forming mode for the both the commensal systems of GMRT and the four frequency bands of uGMRT. In the MIA beam-forming mode, the entire array is divided into multiple (NArray ) sub-arrays each of which operates in the IA mode. This will give us the large fieldof-view of the IA with shallow sensitivity compared to IA. A signal is considered as an event if and only if it is detected in all the sub arrays. In practice, because the co-incidence filtering greatly reduces false alarms (Bhat

Page 5 of 8 47

et al. 2013), one can use a lower signal-to-noise ratio threshold (S/N)th (≥3) for each sub-array. Although the MIA mode has a lower sensitivity compared to the IA mode, the reduced detection threshold more than compensates for this and we found a higher FRB detection rate for the MIA mode as compared to the IA mode. Note that in this work, we considered (S/N)th = 3 and NArray = 3 for the MIA beam forming mode. The system specifications of two commensal systems of GMRT and four frequency bands of uGMRT are tabulated in Table 1. Figure 2 shows the variation of FRB detection rates with the variation of α for the commensal systems of GMRT and the four frequency bands of uGMRT with three beam-forming modes (IA, CA-SB and MIA). As mentioned earlier, it is also found here that the detection rate varies with different scattering models and the detection rate is maximum for the case of FRB pulse without scattering, which is roughly ∼10 and ∼2 times larger than the same for scattering models I and II respectively. Further it also increases with decreasing α. In a brief, we expect to detect ∼103 −106 FRBs per day with fluence F ≥ 0.41 Jy ms for the commensal system of GMRT and ∼105 −107 FRBs per day with fluence F ≥ 0.12 Jy ms for the four frequency bands of uGMRT respectively.

4. FRB detection rate and localization comparison In this section, we compare FRB detection rate and localization of the event for the three phases of OWFA (LS, PI and PII), the two commensal systems of GMRT (Bands S1 and S2), the four observational frequency bands of uGMRT (Bands 2, 3, 4 and 5) and CHIME. Table 1 shows the number of FRBs expected to be detected per day by considering the Dirac delta function as the energy distribution function of FRBs and the mean value of α with error for the range −5 ≤ α ≤ 0, where E ν ∝ ν α , for different systems of OWFA, GMRT, uGMRT and CHIME with their observational frequency, bandwidth, beam formations, field of view and threshold fluence of the event required for the detection. It is found that the detection rate is larger for FRB pulse without scattering than the same for scattering models I and II respectively. In Table 1, the detection rate is large (∼8.26 × 108 FRBs per day) for OWFA Phase II with CA-MB beam forming mode in comparison to the commensal systems of GMRT and uGMRT, but the detection rate is maximum (∼1.17 × 109 FRBs per day) for CHIME with IA beam forming mode. However, OWFA and the commensal systems of GMRT,

47 Page 6 of 8

J. Astrophys. Astr. (2018) 39:47 10

8

10

7

10

6

Band S1

Band S2

IA

FRB Rates (day-1)

105

108 10

7

10

6

104 105 104

CA-SB

103 102 10

7

10

6

10

5

10

4

MIA

-5

-4

Band 2

-3

-2

-1

Band 3

-5 α

-4

-3

Band 4

-2

-1

0

Band 5

IA

FRB Rates (day-1)

105 104 105 104 10

3

10

2

10

7

10

6

10

5

10

4

CA-SB

MIA

-5 -4 -3 -2 -1 -5 -4 -3 -2 -1 -5 -4 -3 -2 -1 -5 -4 -3 -2 -1 0 α

Figure 2. The variation of the FRB detection rate with the variation of α for the proposed commesal system of GMRT and the four frequency bands of uGMRT with three kinds of beam formations: IA, CA-SB and MIA. Two scattering models Sc-I (green region) and Sc-II (yellow region) and the FRB pulse without scattering (orange region) have been considered here. The solid black lines denote the Dirac delta function, while the boundaries of the regions enclosing the curves correspond to the Schechter luminosity function with an exponent in the range −2 ≤ γ ≤ 2.

uGMRT and CHIME operate in different frequency ranges and hence complementary. The quantity Fth is an important parameter of FRB detection. We can detect a FRB if and only if the fluence of this event is larger than the value of Fth for a given radio telescope. For OWFA, it is found that we can detect bright FRBs by using the IA beam-forming mode, whereas CA-MB mode can be used to detect a variety of FRBs. Similarly for the two commensal systems of GMRT and the four frequency bands of uGMRT, we can detect a variety of FRBs by using MIA beam forming mode, whereas IA mode can be used to detect only bright FRBs. In contrast, CHIME can only detect bright FRBs. The localization of the event depends on the fieldof-view (FoV) of the telescope. A telescope with large field-of-view can localize an event poorly in comparison

to the same for a telescope with small field-of-view. From Table 1, it is found that the localization of FRBs is much better for the two commensal systems of GMRT and the four frequency bands of uGMRT with CA-SB beam forming mode in comparison to others. The localization of the event is much poorer for OWFA, where the dipoles are aligned along the focal line of the cylindrical reflector and hence it can only localize the event along a straight line in the North–South direction. However as mentioned earlier, the detection probability of FRBs largely depend on the product of field-of-view and sensitivity of the telescope and hence OWFA is capable to detect a large number of FRBs in comparison to the same for others mentioned in Table 1. In brief, we can detect a large number of FRBs with poor localization by using OWFA, whereas the two commensal systems of GMRT and the four frequency bands of uGMRT can

J. Astrophys. Astr. (2018) 39:47

be used to detect a comparatively less number of FRBs with better localization. For CHIME, the localization of detected FRBs (field-of-view = 132 deg2 ) is quite poor in comparison to OWFA, the commensal systems of GMRT and uGMRT.

5. Summary and conclusion Fast Radio Bursts (FRBs) are short duration highly energetic dispersed radio pulses. Here we have summarized our predictions of detecting FRBs using OWFA (Bhattacharyya et al. 2017) and uGMRT (Bhattacharyya et al. 2018) with different beam forming modes. We used the model prescribed by Bera et al. (2016) for those predictions. We considered the energy spectrum of FRBs as a power law and the energy distribution of FRBs as a Dirac delta function and Schechter luminosity function with both positive and negative exponents. We also considered two scattering models prescribed by Bhat et al. (2004) and Macquart & Koay (2013) and FRB pulse without scattering as a special case for the prediction of FRB pulse width. We have first discussed our predictions of FRB detection rate for the Ooty Wide Field Array (OWFA). OWFA is an upgraded version of the Ooty Radio Telescope (ORT). ORT has a long cylindrical reflector of dimension 530 × 30 m,which contains 1056 half wavelength linear dipoles along the focal line of the reflector. The signals from these dipoles are combined in a different way and we have discussed our predictions for the old analogue beam-forming network, legacy system, and the upcoming Phase I and Phase II and compared the results with UTMOST and CHIME. In this work, we considered three kinds of beam formations: incoherent (IA), coherent single (CA-SB) and coherent multiple (CA-MB) beam formations. We found that we can expect to detect ∼105 −108 FRBs per day by using OWFA with a fluence of F ≥ 0.7 Jy ms. We next discussed our predictions of FRB detection rate for the upgraded Giant Metrewave Radio Telescope (uGMRT) with three kinds of beam formations: incoherent (IA), coherent single (CA-SB) and multiple incoherent (MIA) beam formations. The uGMRT is an upgraded version of the GMRT, which has 30 parabolic dishes having 45 m diameter each and they are distributed in a Y-shaped pattern with a shortest baseline of 200 m and a longest baseline of 25 km. Each dish has five prime focus feeds having five discrete operational frequencies centered at 150, 235, 325, 610 and 1280 MHz with a maximum backend instantaneous frequency bandwidth of 32 MHz. uGMRT will

Page 7 of 8 47

provide significantly large instantaneous bandwidths with four operational frequencies centered at 185, 375, 700 and 1250 MHz with a wide variation of bandwidths from 130 to 400 MHz. In this work, we also considered the proposed commensal system for the GMRT for transient search. We found that we expect to detect ∼103 −106 FRBs per day with fluence F ≥ 0.41 Jy ms for the commensal system of GMRT and ∼105 −107 FRBs per day with fluence F ≥ 0.12 Jy ms for the four frequency bands of uGMRT respectively. Further it is found that OWFA and the lower frequency bands of GMRT and uGMRT can detect bright FRBs only, whereas the higher frequency bands of GMRT and uGMRT can be used to detect a variety of FRBs. It is also found that we can detect a large number of FRBs with poor localization by using OWFA, whereas the two commensal systems of GMRT and the four frequency bands of uGMRT can be used to detect a comparatively less number of FRBs with better localization. However, there are some uncertainties and limitations in our predictions. The scattering mechanism in the intervening medium is still unknown. Further, there is no unique and direct way to estimate the spectral index of FRBs. Moreover, the energy distribution function of FRBs is another important unknown quantity, and we have considered two possible energy distribution models in this analysis. The detection of a large number of FRBs in future will help us to constrain these uncertainties and refine the FRBs models. References Bannister K. W. et al. 2017, ApJL, 841, L12 Bera A. et al. 2016, MNRAS, 457, 2530 Bhandari S. et al. 2017, ArXiv e-prints: arXiv:1711.08110 Bhat N. D. R., Cordes J. M. et al. 2004, ApJ, 605, 759 Bhat N. D. R. et al. 2013, Astrophys. J. Suppl. Series, 206, 1 Bhattacharyya S. et al. 2017, J. Astrophys. Astr., 38, 17 Bhattacharyya S. et al. 2018, J. Astrophys. Astr., submitted Caleb M. et al. 2016, MNRAS, 458, 718 Caleb M. et al. 2017, MNRAS, 468, 3746 Champion D. J. et al. 2016, MNRAS, 460, L30 Cordes J. M., Lazio T. J. W. 2003, ArXiv eprint: arXiv:astro-ph/0207156 Farah W. et al. 2017, The Astronomer’s Telegram, 10697 Farah W. et al. 2018, The Astronomer’s Telegram, 11675 Gupta Y. et al. 2017, Curr. Sci., 113, 4 Katz J. I. 2016, Mod. Phys. Lett. A, 31, 14 Keane E. F. et al. 2016, Nature, 530, 453 Kulkarni S. R. et al. 2015, ArXiv e-prints: arXiv:1511.09137 Lorimer D. R. et al. 2007, Science, 318, 777 Macquart J. P., Koay J. Y. 2013, ApJ, 776, 125 Masui K. et al. 2015, Nature, 528, 523

47 Page 8 of 8 Newburgh L. B. et al. 2014, SPIE Proc., 9145 Oslowski S. et al. 2018a, The Astronomer’s Telegram, 11396 Oslowski S. et al. 2018b, The Astronomer’s Telegram, 11851 Petroff E. et al. 2016, PASA, 33 Petroff E. et al. 2017, MNRAS, 469, 4465 Price D. C. et al. 2018, The Astronomer’s Telegram, 11376 Ravi V. et al. 2016, Science, https://doi.org/10.1126/science. aaf6807

J. Astrophys. Astr. (2018) 39:47 Scholz P. et al. 2016, ApJ, 833, 177 Shannon R. M. et al. 2017, The Astronomer’s Telegram, 11046 Spitler L. G. et al. 2014, ApJ, 790, 101 Subrahmanya C. R. et al. 2017, J. Astrophys. Astr., 38, 10 Swarup G., Sarma N. V. G. et al. 1971, Nat. Phys. Sci., 230, 185 Thornton D. et al. 2013, Science, 341, 53

J. Astrophys. Astr. (2018) 39:48 https://doi.org/10.1007/s12036-018-9544-3

© Indian Academy of Sciences

Review

The many faces of pulsars – the case of PSR B0833-45 B. RUDAK Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Rabia´nska 8, 87-100 Toru´n, Poland. E-mail: [email protected] MS received 16 June 2018; accepted 31 July 2018; published online 23 August 2018 Abstract. A review of observational properties of the Vela pulsar across a wide energy spectrum is given. Then current approaches to the modelling of pulsars and their wind zones are briefly presented. The challenges posed to the models by the diversity of Vela’s light curves in different energy ranges are discussed. Keywords. Pulsars—PSR B0833-45—observations—models.

1. Introduction Almost 51 years after their discovery, pulsars are still an enigmatic phenomenon. Their key role as tools used in physics and astronomy is widely appreciated.1 However, these tools themselves require thorough investigations in order to understand the mechanism(s) responsible for their activity. Pulsars are rapidly spinning and highly magnetized neutron stars and their electromagnetic radiation patterns are highly anisotropic. Therefore, the complete radiation characteristics of a single pulsar is impossible to determine. Moreover, ultrarelativistic charged particles (ions, electrons and positrons) escaping from pulsars in the form of magnetospheric wind can be studied only indirectly. There are more than 2600 pulsars detected in radio pulsars (Manchester et al. 2005). However, pulsars are non-thermal sources, with non-coherent radiation spectra reaching X-ray and gamma-ray energy domains. Very few pulsars, however, have been detected so far at intermediate energy ranges: 1 or 2 pulsars in midIR, 5 in near-IR,2 10 in optical, 10 in near-UV and 4 in far-UV (Mignani 2017). More than 100 pulsars have been detected in soft and hard X-rays, mostly by Chandra and XMM Newton. The largest progress has been made in the gamma-ray domain (mostly by Fermi

1 David Finley (NRAO) aptly called them ’Pulsars: The Universe’s Gift to Physics’. 2 The IR observations could not be carried out in phased modes, hence the measured fluxes are unpulsed.

LAT, but also AGILE and earlier by SAS-2, COS B and CGRO). There are 211 gamma-ray pulsars known to date, with 115 classical pulsars and 96 millisecond pulsars. An important scientific result also came from the Imaging Atmospheric Cherenkov Telescope arrays: MAGIC, VERITAS and HESS. The Crab pulsar has its pulsed spectrum reaching now up to 1.5 TeV (Ansoldi et al. 2016) while the Vela pulsar has been detected between 10 GeV and 100 GeV with HESS in its mono mode (Djannati-Ataï et al. 2017a), and very recently around 3 TeV and 7 TeV with HESS in stereo mode (Djannati-Ataï et al. 2017b). The aim of this contribution is to present the diversity of light curves across spectral frequency range observed from single pulsars as a challenge to the theories of radiation mechanism of pulsars. One of the two beststudied pulsars across wide frequency range – covering almost eighteen decades – is the Vela pulsar (the other one being the Crab pulsar). Limitations of present-day models in confrontation with Vela, as well as apparently necessary ingredients of prospect models are presented and discussed. Moreover, major models and their status are briefly presented.

2. Pulsar multiwavelength spectra and light curves Non-thermal radiation spectra can generally be approximated by a broken power-law function and subexponential cutoff at high energies. In the case of Crab pulsar, the high-energy cutoff has the form of the steep power-law tail, reaching 1.5 TeV.

48 Page 2 of 7

J. Astrophys. Astr. (2018) 39:48

Non-thermal light curves consist of rather narrow pulses, with high pulsed fraction, and are energy dependent in most cases. Thermal spectral components (in soft X-rays) are fitted either by blackbody or by strongly magnetized atmospheric models (H, He or Fe). The soft X-ray light curves show smooth pulsations, with low-pulsed fraction. A good example of a pulsar containing all such radiation properties is for instance, Geminga (see Mori et al. 2014). 2.1 The Vela pulsar (PSR B0833-45) The non-coherent radiation from Vela extends from (at least) near-IR (Zyuzin et al. 2013) in the low-frequency end of the spectrum, to optical (Gouiffes 1998), nearUV and far-UV (Romani et al. 2005), to soft (Pavlov et al. 2001) and hard X-rays (Harding et al. 2002), to gamma-rays (Abdo et al. 2010; Djannati-Ataï et al. 2017a), reaching the VHE range at 3 TeV and 7 TeV (Djannati-Ataï et al. 2017b). The subset of Vela’s light curves is shown in Fig. 1 and Fig. 2, and its energy flux density is shown in Fig. 3. The shapes and phases of the pulses observed from Vela impose questions which are difficult to answer: – What is the origin of radiation at different frequency ranges? The overall shape of the flux density spectrum does not look too complex. Therefore, it is tempting to look for a single radiative process as responsible for the entire spectrum. – Why two main peaks in optical are not aligned with two main peaks in gamma-rays (indicated with two vertical blue lines)? – Why their shapes are so different from the gamma-ray pulse shapes? – What is the origin of a narrow peak at phase 0.0 present in optical, UV and hard X-rays (note another narrow peak in hard X-rays at phase 0.85), aligned with the radio pulse (vertical red line)? – Why an analogous peak is not present in gammarays (the bottom panel)? We are not aware of any attempts to address these questions within the existing (but otherwise elaborated and detailed in many aspects) models of pulsar mechanism.3 3 We note, however, that the peak-to-peak separation of 0.25 in optical had been reproduced with simple estimates within the outergap scenario (Cheng et al. 1986).

Figure 1. The many faces of the Vela pulsar: its light curves in radio, optical, hard X-rays and gamma rays (based on Fig. 4 of Kuiper & Hermsen (2015)).

3. A brief account of present-day pulsar models 3.1 The co-rotating magnetosphere models The co-rotating magnetospheres in low-density, chargeseparation limit, are so far the most popular models using different types of accelerating gaps. Three major types of magnetospheric accelerators (coming in many flavours) have been proposed: – inner gap, – outer gap, – TPC-slot gap. Their popularity evolves with time, as more and more high-quality observations in different energy domains become available (the inner gap models are not

J. Astrophys. Astr. (2018) 39:48

Page 3 of 7 48

Figure 2. The Vela phasogram above 10 GeV according to HESS II monodata (top) and Fermi-LAT data (bottom) (DjannatiAtaï et al. 2017a).

Figure 3. The flux density of Vela pulsar. Encircled in blue are the (phase-averaged) data points in four energy bands corresponding to four panels of Fig. 1 with the light curves. This figure is based on Fig. 2 of Mignani et al. (2017).

preferred any more for young or middle-aged classical pulsars, and even for millisecond pulsars). The models require simultaneous solution in the magnetosphere of non-vacuum Poisson equation, Boltzmann equation for pairs, and radiative transfer (e.g. Hirotani 2015). The boundary conditions are assumed and hence many flavours of each type of model are possible. Global current closure problem is not addressed in those models. Despite many elaborations in the numerical 3D simulations, the results are not fully satisfactory, either with respect to the spectra or with respect to the light curves, or both.

The three-dimensional slot gap model of the spectral energy distribution by Harding and Kalapotharakos (2015) is one of latest and detailed attempts to model the radiation spectrum of Vela pulsar. However, their slot gap follows the magnetic field lines of different shapes (see the next subsection) than the Deutsch solution used in the low-density magnetosphere; moreover, it extends beyond the light-cylinder radius. 3.2 Global electrodynamics with the plasma The aim of this approach is to formulate self-consistent electrodynamics, with global current closure.

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This became possible with the seminal paper of Contopoulos et al. (1999) presenting a method to solve the force-free axisymmetric magnetosphere numerically. Further, an important step came with the numerical solution of the force-free magnetosphere in an oblique rotator case (Spitkovsky 2006). The existence of the current sheet was also confirmed there. The starting point in this ambitious approach were force-free electrodynamics (FFE) models of magnetospheres and winds. The entire dissipation of the rotational energy is, therefore, occuring outside the magnetosphere, beyond the light cylinder (i.e. in the winds). The next step is the modelling of dissipative magnetospheres and winds (outflow of dense plasma and Poynting flux). The simplest approach is to use the MHD approximation with some macroscopic conductivity – a purely phenomenological, free parameter. Modelling microscopic conductivity has been carried out with particle-in-cell (PiC) simulations, including e± -pair creation and acceleration (due to magnetic reconnections). Strong synchrotron emission is then possible in the current sheet and in the separatrix sheets inside the light cylinder (Lyubarsky 1990; Spitkovsky 2006; Cerutti et al. 2016; Philippov & Spitkovsky 2018).

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For an inclined rotator the current sheet becomes corrugated, and the striped wind forms, leading in turn to pulsed emission. An example of such an emission is presented in Fig. 4, where the Crab pulsar data from CGRO COMPTEL, Fermi-LAT and MAGIC are fitted with the current-sheet model of Mochol and Pétri (2015) and Mochol (2017). The main part of the presented model SED (between 10 MeV and ∼100 GeV) is due to Doppler-boosted synchrotron emission within the current sheet. Below 10 MeV, another component (not discused in the framework of the current sheet model) apparently takes over and dominates the entire SED of the Crab pulsar. In the case of the Vela pulsar, however, single synchrotron component originating in the current sheet is sufficient to reproduce the phase-averaged SED, according to Mochol and Pétri (2015). No light curves are included in the model, though. Within the presented framework, the current sheet model is not expected to reproduce the diversity of the light curves in Fig. 1 and Fig. 2 as well as their mutual phase shifts. In particular, the current sheet model cannot reproduce the phase lag of ∼0.1 of the leading gamma-ray peak behind the radio peak (see panels (a) and (p) connected by the dashed vertical line in Fig. 1, and Abdo et al. (2013) for the

Figure 4. The high energy (below 100 GeV) and VHE (above 100 GeV) spectral energy distribution for the Crab pulsar in the current sheet model of Mochol and Pétri (2015) and Mochol (2017). The model reproduces the shape and magnitude of the VHE spectral component reaching 1.5 TeV (Ansoldi et al. 2016).

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Figure 5. Top: The P1 and P2 pulses from Vela in optical (Gouiffes 1998) and gamma rays (Abdo et al. 2010). Bottom: Their reconstruction in the uniform-emissivity version of the OG model, obtained for inclination angle α = 70◦ and viewing angle ζ = 79◦ (Rudak & Dyks 2017).

gamma-radio phase lags in other pulsars); its capabilities in this respect are limited to just a few pulsars with gamma-ray and radio light curves showing a mirror symmetry with respect to the phase 0.5 (see Fig. 8 of Pétri 2011). Therefore, the case of the Vela pulsar light curves seems to be particularly difficult to understand within the scenario of the current sheet. Some contribution to the pulsed radiation coming from the inner magnetospere and/or the separatrix seems to be unavoidable. The presence of magnetospheric gaps (as addressed in section 3.1) is also necessary to supply the electron– positron plasma. The gaps also impose the boundary conditions on the force-free zone of the magnetosphere. 4. The arguments for the presence and co-existence of outer gaps and inner gaps in the Vela pulsar The semi-phenomenological model capable of reproducing (at least qualitatively) the observed properties of Vela radiation has been proposed recently (Rudak & Dyks 2017). It is based on the 3D outer gap model. It reproduces two main pulses in gamma-rays (as due to curvature emission) and optical (as due to synchrotron emission), in terms of their phases and shapes (see Fig. 5). The model contains an additional inner gap; this is essentially possible, since both types of gaps occupy different open magnetic field lines. The idea of coexisting gaps is not new and was used in many papers (by the tacit assumption), like Watters et al. (2009) or Venter et al. (2009) in the context of confronting the outer-gap models and slot-gap models with the Fermi LAT gamma-ray pulsars. Polar gaps exist in these models and are assumed to be responsible

for a narrow radio pulse (whenever observed) in the gamma-ray pulsars. On the theoretical side, this concept has attracted some interest in the context of studying the properties of force-free magnetospheres (e.g. numerical simulations of the coexisting gaps by Yuki & Shibata (2012) and the analytical model by Petrova (2013). Three different inverse Compton scattering processes involving the proposed gaps are considered (see Fig. 6): (1) outer-gap primary electrons colliding with soft (i.e. optical-infrared) photons originating from the adjacent synchrotron (SR) layer, (2) inner-gap pairs interacting with optical-infrared photons originating from the SR layer, (3) inner-gap pairs interacting with thermal X-ray photons from the neutron star surface. These processes lead to the formation of (1) spectral component in the VHE range (the prediction), (2) core-like pulse detected in optical as well as in UV at the phase of the radio core pulse, (3) core-like pulse detected in hard X-rays at the phase of the radio core pulse. The numerical calculations show the formation of core-like pulses in optical, UV and in hard X-rays, aligned in phase with the core-like radio pulse, as observed. In very high energy domain, a new spectral component emerges, with the light curve shown in Fig. 7. Its predicted flux is within reach by the future CTA observatory (see Rudak & Dyks (2017) for the results).

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Figure 6. Cartoon of coexisting gaps (inner and outer) and the hot NS surface in the model of Vela (Rudak & Dyks 2017). Screened region: secondary pairs with γ± ∼ 100–1000 emit synchrotron photons from hard X-rays to optical to mid-IR. The SR photon trajectories (dashed green) are shown in the co-rotating reference frame (CF) Accelerating gap region: primary electrons with γe > 107 (blue arrow trajectories in CF) emit curvature photons. They also upscatter some SR photons due to colliding trajectories, preferentially on the trailing side of the open magnetic field-line volume. The inner gap region is a postulated site of pair creation with γ± ∼ 100–1000; these pairs are thought to be responsible for coherent radio emission forming the ‘core’ pulse at phase 0 in Fig. 1. The photon field of thermal X-rays due to initial cooling from the NS surface is a target for the pairs in Compton upscattering, leading to the formation of P4 in optical, UV and X-rays (see Fig. 1).

Figure 7. The light curve at 3 TeV of the inverse Compton scattering spectral component resulting from the model depicted in Fig. 6. It consists of two pulses of different shapes and amplitude. The leading and trailing pulses are located at the phase interval of 0.2–0.3 and 0.5–0.6, respectively.

5. Summary and conclusions The outer gap model with an adjacent layer of the e± -pair formation reproduces simultaneously two main pulses in gamma-rays and in optical, in terms of their phases and shapes, as observed in the Vela pulsar.

Introducing an inner gap with e± pairs as coexisting with the outer gap leads to the formation of core-like pulses in optical, UV and hard X-rays, in phase with the core-like radio pulse, as observed in the Vela pulsar. A distinct spectral component is formed in the VHE range. Its light curve consists of two pulses at phases

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0.2 and 0.6, and its expected flux at 3 TeV for the Vela pulsar should be of interest to CTA South (for >50 h). Multiwavelength properties of the Vela pulsar should be taken into account when developing the models relying on the wind and current-sheet activity only.

Acknowledgement The author acknowledges financial support by the National Science Centre, Grant DEC- 2011/02/A/ST9/ 00256.

References Abdo A. A., Ackermann M., Ajello M., Allafort A. et al. 2010, ApJ, 713, 154 Ansoldi S. et al. 2016, Astron. Astrophys. 585, A133 Cheng K. S., Ho C., Ruderman M. 1986, ApJ, 300, 522 Cerutti B., Philippov A. A., Spitkovsky A. 2016, MNRAS, 463, 89 Contopoulos I., Kazanas D., Fendt C. 1999, ApJ, 511, 351 Deutsch A. J. 1955, AnAp, 18, 1 Djannati-Ataï A. et al. 2017a, 6th International Symposium on High Energy Gamma-Ray Astronomy, vol. 1792 of American Institute of Physics Conference Series, 040028 Djannati-Ataï A. et al. 2017b, 29th Texas Symposium on Relativistic Astrophysics Gouiffes C. 1998, Proceedings of the International Conference on Neutron Stars and Pulsars, Tokyo (Japan) 1997, edited by Shibazaki N. et al., Universal Academy Press, Tokyo, Japan (Frontiers Science Series) 24, 363

Page 7 of 7 48 Harding A. K. et al. 2002, ApJ, 576, 376 Harding A. K., Kalapotharakos C. 2015, ApJ, 811, 63 Hirotani K. 2015, ApJ, 798, 40 Kalapotharakos C., Kazanas D., Harding A. K., Contopoulos I. 2012, ApJ, 749, 2 Kuiper L., Hermsen W. 2015, MNRAS, 449, 3827 Lyubarsky Y. E. 1990, Sov. Astron. Lett., 16, 16 Manchester R. N., Hobbs G. B., Teoh A., Hobbs M. 2005, Astron. J., 129, 1993, astro-ph/0412641 Mignani R. P. 2017, Contribution to IV Workshop sull’astronomia millimetrica in Italia Mignani R. P., Paladino R., Rudak B., Zajczyk A. et al. 2017, ApJ, 851L, 10 Mochol I., Pétri J. 2015, MNRAS, 449, L51 Mochol I. 2017, ASSL, 446, 135 Mori K., Gotthelf E. V., Dufour F., Kaspi V. M. et al. 2014, ApJ, 793, 88 Pavlov G. G., Zavlin V. E., Sanwal D., Burwitz V. et al. 2001, ApJ, 552, L129 Pétri J. 2011, MNRAS, 412, 1870 Petrova S. A. 2013, ApJ, 764, 129 Philippov A. A., Spitkovsky A. 2018, ApJ, 855, 94 Romani R. W., Kargaltsev O., Pavlov G. G. 2005, ApJ, 627, 383 Rudak B., Dyks J. 2017, Proceedings of 35th ICRC, Busan (Korea) 2017, journal-ref: PoS(ICRC2017)680 Spitkovsky A. 2006, ApJ, 648, L51 Spitkovsky A. 2016, ApJ, 648, 51 Venter C., Harding A. K., Guillemot L. 2009, ApJ, 707, 800 Watters K. P., Romani R. W., Weltevrede P., Johnston S. 2009, ApJ, 695, 1289 Yuki S., Shibata S. 2012, PASJ, 64, 4 Zyuzin D., Shibanov Y., Danilenko A., Mennickent R. E., Zharikov S. 2013, ApJ, 775, 101

J. Astrophys. Astr. (2018) 39:49 https://doi.org/10.1007/s12036-018-9546-1

© Indian Academy of Sciences

Review

Supernova neutrinos: Flavor conversion independent of their mass S. CHAKRABORTY Indian Institute of Technology Guwahati, Guwahati 781 039, India. E-mail: [email protected] MS received 14 June 2018; accepted 2 August 2018; published online 27 August 2018 Abstract. In extremely dense neutrino environments like in supernova core, the neutrino-neutrino refraction may give rise to self-induced flavor conversion. These neutrino flavor oscillations are well understood from the idea of the exponentially growing modes of the interacting oscillators in the flavor space. Until recently, the growth rates of these modes were found to be of the order of the vacuum oscillation frequency m 2 /2E [O(1 km−1 )] and were considered slow growing. However, in the last couple of years it was found that if the system was allowed to have different zenith-angle distributions for the √emitted νe and ν¯ e beams then the fastest growing modes of the interacting oscillators grew at the order of μ = 2G F n ν , a typical ν–ν interaction energy [O(105 km−1 )]. Thus the growth rates are very large in comparison to the so-called ‘slow oscillations’ and can result in neutrino flavor conversion on a much faster scale. In fact, the point that the growth rates are no longer dependent on the vacuum oscillation frequency m 2 /2E, makes these ‘fast flavor conversions’ independent of m 2 (thus mass) and energy. This is a surprising result as neutrino flavor conversions are considered to be the ultimate proof of massive neutrinos. However, the importance of this effect in the realistic astrophysical scenarios still remains to be understood. Keywords. Supernovae—dense neutrinos—flavor conversion.

1. Introduction Almost 99% of the energy liberated in core collapse supernova (SN) explosion or in neutron-star mergers are released in the form of neutrinos and antineutrinos of all flavors. However, the fluxes and spectra differ strongly between νe , ν¯ e and the other heavy lepton (μ, τ ) flavor neutrinos (referred as νx ). Flavor evolution of these neutrinos can influence the energy deposition away from the decoupling sphere (neutrino sphere), nucleosynthesis, and detection of the neutrino signal from the next galactic supernova or the diffuse neutrino flux from all past core-collapse events (Mirizzi et al. 2015). However, all these would require a proper understanding of flavor evolution in neutrino dense environments like SN. This has still remained elusive because of complications arising from the nonlinear nature of collective flavor oscillations. Recently another new idea (Sawyer 2015) got added to this list of complications, i.e., the surprising fact that under certain conditions the collective flavor conversion may not depend on neutrino mixing parameters.

Collective neutrino oscillations are understood in the form of two generic phenomena. The synchronization, i.e., the different modes (different vacuum oscillation frequencies ω = m 2 /2E) of the neutrino mean field oscillate together with a single mean frequency. The other phenomenon is that of the self-induced flavor conversion, connected to the collective modes growing exponential. The growth rates in the linear regime and the overall evolution were thought to be dependent on m 2 /2E. However, it has been found that under certain circumstances, i.e., given an appropriate seed the effect can occur even for unmixed neutrinos. Thus flavor conversion can happen even in the absence of neutrino mass (Chakraborty et al. 2016). Collective flavor oscillations effectively represents a flavor reshuffling among different modes but any change of flavor in the overall ensemble. For example, in a dense neutrino gas, the νe and ν¯ e can convert to νμ and ν¯ μ without change of total lepton number, such pair processes can happen in the form of non-forward scattering (proportional to G 2F ), and can also take place at the refractive level (proportional to G F ). In general, the conversion rate was actually found to be of the order of

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m 2 /2E, i.e., ω driven. The other possible frequency for such √ a system is the neutrino–neutrino interaction μ = 2G F n ν and for a ‘dense’ neutrino gas μ  ω. However, this frequency μ remains dominant only when the neutrino and anti-neutrino angle distributions are different and that would translate into ‘fast’ oscillations. On the other hand, with similar angle distributions the conversion rates are still driven by ω, corresponding to slow conversion. Thus, fast conversions can occur even without any vacuum frequency ω, i.e, even in the absence of neutrino masses (Dasgupta et al. 2016; Izaguirre et al. 2016; Capozzi et al. 2017; Dasgupta 2017). Therefore, self-induced flavor conversion (in the sense of flavor reshuffling among modes) can occur even without flavor mixing, the pre-condition is that there should exist fluctuations in flavor space which acts as seeds to the unstable modes. Even quantum fluctuations of the mean-field quantities could act as seeds. In fact, the ordinary neutrino oscillations are driven by their masses and mixing parameters, thus the fluctuations in flavor space should always exist and can seed the self-induced flavor conversion. In the next subsections, we describe the basic mathematical formulation of the problem. 1.1 Defining the model: two-bulb supernova Our mathematical formulation is based on the model of Sawyer (2015), mimicking the typical supernova emission features. Here, neutrinos are emerging from a spherical surface, defined as the ‘neutrino bulb’, and angular characteristic is considered to be blackbodylike. Thus to a distant observer the zenith-angle distribution will be uniform in the variable sin2 θ up to a maximum. This maximum is described by the angular size of the neutrino bulb at the observation point. The flavors νe and ν¯ e decouple at different radius, i.e., they are emitted from different neutrino surfaces giving rise to this twobulb emission model. The νe and ν¯ e zenith-angle distributions depend on this two-bulb emission model and in the supernova environment, the νe flux exceeds ν¯ e . This supernova-motivated model can be formulated in terms of the transverse velocities (Chakraborty et al. 2015) and is very similar to the colliding-beam examples but with different velocity distributions for different flavors. In our description, we consider a stationary twoflavor neutrino flux where the flavor evolution is only in the radial direction and no small-scale effects in the transverse direction. The neutrino field beyond the emitting surface is described by the azimuth (ϕ) and the zenith-angle (u ∝ sin2 θ ). The occupied zenith angle range is normalized to some chosen radius. Thus the

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u-range is independent of the test radius where we perform the stability analysis. The emission spectrum g(ω, u) has continuous labels ω and u and we assume axial symmetry of emission. Thus g(ω, u) is independent of ϕ. 1.2 Stability equations The eigenvalue equations used for the case of axially symmetric neutrino emission were developed by Raffelt et al. 2013. The eigenvalue equations are expressed in terms of the integrals  u n g(ω, u) (1) In = μ dω du ω + u λ¯ − for n = 0, 1 and 2. There is no ϕ dependence as the emission is assumed to be axially symmetric. Here, the effective multi-angle√matter effect is described by λ¯ = λ + μ, where λ = 2G F n e with 

= dω du g(ω, u) . (2)  The spectrum g(ω, u) is normalized with du dω sign(ω) g(ω, u) = 2, which also defines μ. Here μ has the meaning of a typical neutrino–neutrino interaction. The following eigenvalue equations give the solutions for the eigenvalue , (I1 − 1)2 − I0 I2 = 0 and I1 + 1 = 0 .

(3)

The solutions of the first equation correspond to axial symmetry conservation, whereas the solutions of the second one break the axial symmetry spontaneously. The instabilities are found in the limit ω = 0. We also assume that νx and ν¯ x have the same emission characteristics and would drop out from g(ω, u). The ω-integrated zenith-angle distribution for ∞ neutrinos (positive ω) is h νe (u) = 0 dω g(ω, u) and for anti-neutrinos it is (negative ω) h ν¯ e (u) = 0 − −∞ dω g(ω, u). Thus we have  du [h νe (u) + h ν¯ e (u)] = 2, (4)  du [h νe (u) − h ν¯ e (u)] = . (5) After the ω integration, the above integrals become  un In = du [h νe (u) − h ν¯ e (u)]. (6) u ( + m) − w Here w = /μ is the normalized eigenvalue and m = λ/μ describes the matter effect. The two-bulb model of neutrino emission would mean top-hat u distributions. The occupied u-range

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0.20 0.0

0.15 0.10

–0.5

–1.0 –1.0

0.05

–0.5

0.0

0.5

1.0

Zenith– angle parameter b

Figure 1. Contour plot of the growth rates (units of μ) for the axial-symmetry breaking case without matter. The normalized density for νe is 1 + a and 1 − a for ν¯ e . In this case, there is no instability in the SN-motivated parameters (a > 0 and b > 0), i.e., the first quadrant.

1.0

0.9

0.5

0.7 0.0

0.5 0.3

–0.5

Growth Rate

a

–1.0 –1.0

0.1

–0.5

0.0

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Zenith–angle parameter b

2. Results

b Asymmetry parameter a

2.1 Without matter In the first approximation, we neglect the matter term (m = 0). This enables a better understanding of the simple system. The first equation (3) is the the axially symmetric solution. In this case, we do not find any instability over the parameter space −1 < a < 1 and −1 < b < 1. The solution of the other equation in (3), breaks axial symmetry and allows fast flavor conversion. The contour plot in Fig. 1 shows the imaginary part of w (in units of μ), i.e., the growth rates. These results suggest that there are no instabilities when a and b have the same sign, i.e., the first and third quadrants. The fast flavor conversion needs that the flavor (νe or ν¯ e ) having broader zenith-angle distribution should have a smaller flux.

0.25 Growth Rate

Asymmetry parameter a

0.5

1.0

0.5

0.25 0.20

0.0

0.15 0.10

–0.5

–1.0 –1.0

Growth Rate

where the upper sign refers to νe and the lower sign to ν¯ e . Therefore the final integrals are  1 + a 1+b un In = du 1+b 0 u (2a + m) − w  1−b 1−a un , (8) − du 1−b 0 u (2a + m) − w here = 2a. We can find the integrals analytically, but the eigenvalues can be only found numerically. For b = 0 (i.e., same zenith-angle distributions for νe and ν¯ e ) but with different number density (a  = 0), the integrals are  1 un . (9) In = 2a du u (2a + m) − w 0 We found that in this case the eigenvalues are always real, i.e., no fast instability with similar angular distribution for νe and ν¯ e . In the following, we study the stability analysis of our described model. The analysis is shown for both with or without matter effect.

1.0

Asymmetry parameter a

is described by the width parameter −1 < b < +1 in the form u νe = 1 + b and u ν¯ e = 1 − b. For supernova, the νe decouple at a larger distance, and correspond to b > 0. The normalized neutrino densities are described by n νe = 1 + a and n ν¯ e = 1 − a where a is the ‘asymmetry parameter’ −1 < a < +1. Thus the supernova-motivated situation would correspond to the first quadrant a, b > 0 and thus the the zenith-angle distribution is  1±a 1 for 0 ≤ u ≤ 1 ± b, × (7) h(u) = 1±b 0 otherwise,

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0.05

–0.5

0.0

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Figure 2. Growth rate (units of μ) similar to Fig. 1, but with matter m = λ/μ = 1. (a) Axially symmetric. (b) Axial symmetry broken.

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In this regard, for the neutron-star mergers, a < 0, as the flux is dominated by ν¯ e . Similarly, LESA is another interesting scenario with parameters other than the traditional supernova-motivated case.

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The results are very different in the presence of matter. A realistic matter effect would imply λ of the order of μ (say, m = λ/μ = 1). The growth rates are shown in Fig. 2. Here one can find fast growth rates for both the axially symmetric and symmetry breaking cases. Thus there are unstable solutions for the parameter space (first quadrant) motivated by SNe, i.e., νe distribution is the broader one (b > 0) and more νe than ν¯ e (a > 0). However, for very large matter effect (λ  μ, corresponding to m  1), the axially symmetric solution disappears, so it exists only for some range of matter density. Like during the supernova accretion phase, the fast instability would be matter suppressed similar to the ‘slow’ instabilities (Chakraborty et al. 2011a, b). Of course, our discussion was for the homogeneous case only (k = 0) by assuming stationarity of the solution. Thus what would happen in the practical case remains to be understood.

role, such fast flavor conversions are rather associated to nontrivial angle distributions. The initial angle distribution must not be too symmetric, a general mathematical condition on the angle distribution would need further studies. In the supernovae or neutron–star mergers context, the most important query remains if the flavor dependent spectral characteristics of neutrinos after decoupling can be sustained and the self-induced flavor conversion together with the matter effects can lead to this fast flavor decoherence. The spatial and the temporal symmetry breaking with the fast flavor conversions can generate quick decoherence. However, the breaking of spatial homogeneity may be suppressed by the multi-angle matter effect and the breaking of stationarity depends on a narrow resonance condition. This stability study is too simple to describe the realistic neutrino evolution near the decoupling region of a compact object. The present description of the neutrino mean field with a freely outward streaming neutrino flux is not complete. The neutrino flow is in all directions with different intensities. These toy examples keep the important questions open and are yet to provide the final conclusions for realistic flavor evolution in SN or neutron–star merger events.

3. Conclusion

Acknowledgements

We discussed a few examples of the interacting neutrino systems, showing the ‘fast flavor conversion’. Here the unstable modes in flavor space grow with rates of the √ order of the neutrino–neutrino interaction energy μ = 2G F n ν instead of the smaller vacuum oscillation frequency ω = 2 m/2E. The main conceptual point being that the self-induced flavor conversions are independent of flavor mixing. In the SN context, neutrino flavor conversion would have happened even if flavor mixing among neutrinos did not exist. Notice that the self-induced flavor conversion corresponds to flavor reshuffling among different modes which however may result in flavor decoherence if neighboring modes become effectively uncorrelated. The idea of fast flavor conversion was proposed twelve years ago by Ray Sawyer (Sawyer 2005) in a three-flavor setup with only a few modes. The system predicted to flavor-equilibrate over very short distances (meters to even centimeters). Our discussion further these studies and now we understand that the fast flavor conversions are independent of the vacuum oscillation frequencies and thus of the neutrino energy. Hence, the energy spectrum has no

The author would like to thank the organizers of the workshop ‘Advances in Astroparticle Physics and Cosmology, AAPCOS-2018’ at the Saha Institute of Nuclear Physics. This project has also received funding/support from the European Unions Horizon 2020 research, innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 690575 and innovation programme under the Marie SkłodowskaCurie Grant Agreement No. 674896.

2.2 With matter

References Capozzi F. et al. 2017, Phys. Rev. D, 96, 043016 Chakraborty S. et al. 2011a, Phys. Rev. Lett., 107, 151101 Chakraborty S. et al. 2011b, Phys. Rev. D, 84, 025002 Chakraborty S. et al. 2015, JCAP, 1601 Chakraborty S. et al. 2016, JCAP, 1603 Dasgupta B. et al. 2016, JCAP, 1702 Dasgupta B., Sen M. 2017, Phys. Rev. D, 97, 023017 Izaguirre I. et al. 2016, Phys. Rev. Lett., 118, 021101 Mirizzi A. M. et al. 2015, Riv. Nuovo Cim., 39, 1 Raffelt G., de Sousa Seixas D. 2013, Phys. Rev. D, 88, 045031 Sawyer R. F. 2005, Phys. Rev. D, 72, 045003 Sawyer R. F. 2015, Phys. Rev. Lett., 116, 081101

J. Astrophys. Astr. (2018) 39:50 https://doi.org/10.1007/s12036-018-9545-2

© Indian Academy of Sciences

Lightning black holes as unidentified TeV sources KOUICHI HIROTANI1,∗ , HUNG-YI PU2 and SATOKI MATSUSHITA1 1 Academia

Sinica Institute of Astronomy and Astrophysics, 11F of AS/NTU Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China. 2 Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada. ∗ Corresponding author. E-mail: [email protected] MS received 12 June 2018; accepted 31 July 2018; published online 29 August 2018 Abstract. Imaging Atmospheric Cherenkov Telescopes have revealed more than 100 TeV sources along the galactic plane, around 45% of them remain unidentified. However, radio observations revealed that dense molecular clumps are associated with 67% of 18 unidentified TeV sources. In this paper, we propose that an electron–positron magnetospheric accelerator emits detectable TeV gamma-rays when a rapidly rotating black hole enters a gaseous cloud. Since the general-relativistic effect plays an essential role in this magnetospheric lepton accelerator scenario, the emissions take place in the direct vicinity of the event horizon, resulting in a point-like gamma-ray image. We demonstrate that their gamma-ray spectra have two peaks around 0.1 GeV and 0.1 TeV and that the accelerators become most luminous when the mass accretion rate becomes about 0.01% of the Eddington accretion rate. We compare the results with alternative scenarios such as the cosmic-ray hadron scenario, which predicts an extended morphology of the gamma-ray image with a single power-law photon spectrum from GeV to 100 TeV. Keywords. Black hole physics—gamma-rays—magnetic fields.

1. Introduction The Imaging Atmospheric Cherenkov Telescopes (IACTs) provide a wealth of new data on various energetic astrophysical objects, increasing the number of detected very high energy (VHE) gamma-ray sources, typically between 0.01 and 100 TeV, from 7 to more than 200 in this century.1 Among the presently operating three IACTs, High Energy Stereoscopic System (HESS) (De Ona Wilhelmi 2009) has so far discovered 42 new VHE sources along the galactic plane, 22 of which are still unidentified. The nature of these unidentified VHE sources may be of hadronic origin (Black & Fazio 1973; Issa & Wolfendale 1981), because protons can be efficiently accelerated into VHE in a supernova remnant to penetrate into adjacent dense molecular clouds, which leads to an extended gamma-ray image. By a systematic comparison between the published HESS data and the molecular radio line data, 38 sources are found to be associated with dense molecular clumps out of the 49

1 TeV Catalog (http://www.tevcat.uchicado.edu).

galactic VHE sources covered by 12 mm observations (de Wilt et al. 2017). There is, however, an alternative scenario for the VHE emissions from gaseous clouds. In the Milky Way, molecular gas is mostly located in giant molecular clouds, in which massive stars are occasionally formed. If a massive star evolves into a black hole and encounters an adjacent molecular clouds, it accretes gases. It is, therefore, noteworthy that a rapidly rotating, stellar-mass black hole emits copious gamma-rays in 0.001–1 TeV (Hirotani et al. 2016), provided that ˙ M˙ Edd satisfies its dimensionless accretion rate m˙ ≡ M/ −5 −4 6 × 10 < m˙ < 2 × 10 , where M˙ designates the mass accretion rate, M˙ Edd ≡ 1.39×1019 M1 g s−1 is the Eddington accretion rate, M1 = M/(10M ) and M denotes the solar mass. The electric currents flowing in such an accreting plasma create the magnetic field threading the event horizon. In this leptonic scenario, migratory electrons and positrons (e± s) are accelerated to TeV by a strong electric field exerted along these magnetic field lines, and cascade into many pairs as a result of the collisions between the VHE photons emitted by the gap-accelerated e±s and the IR photons emitted by

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the hot e−s in the equatorial accretion flow. The resulting gamma radiation takes place only near the black hole; thus, their VHE image should have pointlike morphology with a spectral turnover around TeV.

J. Astrophys. Astr. (2018) 39:50

Bondi–Hoyle accretion rate m˙ B , for simplicity, in the present paper.

3. Development of charge-starved magnetosphere 2. Black hole accretion in a gaseous cloud When a black hole moves in a gaseous cloud, the particles are captured by the hole’s gravity to form an accretion flow. Since the temperature is very low in a molecular cloud, the black hole will move with a supersonic velocity V , forming a bow shock behind. Under this situation, the gas pressure can be neglected and the particles within the impact parameter rB ∼ G M V −2 from the black hole will be captured. For a homogeneous gas, the mass accretion rate (Bondi & Hoyle 1944) becomes M˙ B = 4π λ(G M)2 (CS 2 + V 2 )−3/2 ρ ≈ 4π λ(G M)2 V −3 ρ, where ρ denotes the mass density of the gas, λ a constant of order unity, G the gravitational constant and CS the speed of sound in the homogeneous gas; the last near equality comes from the supersonic nature (i.e., V  CS ) of accretion. For a molecular hydrogen gas, we obtain the dimensionless Bondi accretion rate m˙ B ≡ M˙ B / M˙ Edd = 5.4 × 10−9 λn H2 M1 (V /102 km s−1 )−3 , where n H2 denotes the number density of hydrogen molecules per cm3 . Representative values of m˙ B are plotted as the five straight lines in Fig. 1(a). Since the accreting gases have little angular momentum as a whole with respect to the black hole, they form an accretion disk only within a radius that is much less than rB . Thus, we neglect the mass loss as a disk wind between rB and the inner-most region, and evaluate the accretion rate near the black hole, m, ˙ with m˙ B . In what follows, we consider a ten solar mass black hole, which is typical as a stellar-mass black hole (Tetarenko et al. 2016; Corral-Santana et al. 2016). It is reasonable to suppose that such black holes have kick velocities of V < 102 km s−1 with respect to the star-forming region. Under this circumstance, a typical velocity dispersion in a molecular cloud, V < 10 km s−1 , is an order of magnitude less than V . Accordingly, the net specific angular momentum of the gas at rB , which is typically rB√V , is much less than the Keplerian value, rB V = G MrB . At a much smaller radius r = (V /V )2rB < 0.01rB , rB V equals the Keplerian value; therefore, a disk is formed within this radius. Since the accreting gas does not have to lose angular momentum when falling from r = rB to (V /V )2rB , we neglect the mass loss in this region and evaluate the accretion rate m˙ near the BH with the

When m˙ becomes typically less than 10−2 , Coulomb collisions become so inefficient that the accreting protons thermal energy cannot be efficiently transferred to the electrons. If the accretion rate decreases to m˙ < 10−2.5 , such a radiatively inefficient accretion flow (RIAF) (Ichimaru 1979; Narayan & Yi 1994; Mahadevan 1997) cannot supply enough soft gammarays that are needed to sustain the magnetosphere force-free (Levinson & Rieger 2011). Accordingly, a charge-starved, nearly vacuum magnetosphere develops in the polar funnel (Fig. 1(b)), because the equatorial accreting plasmas cannot penetrate there due to the centrifugal-force barrier. If the accretion rate further decreases to m˙ < 6 × 10−5 , stationary pair production cascade cannot be sustained. However, the luminosity of such a non-stationary accelerator becomes less than the stationary cases, because only a weaker magnetic field can be confined near the black hole for a lower accretion rate. Thus, we consider only the range 6 × 10−5 < m˙ < 2 × 10−4 (green-black region in Fig. 1(a)) and concentrate on stationary accelerators. It is noteworthy that if a stellar-mass black hole moves slowly (i.e. V 102 km s−1 ), its accelerator can be activated with a low gas density (e.g., n H2 103 cm−3 ; Fig. 1(a)). Thus, a significant gamma-ray emission is possible when a black hole encounters not only a dense molecular cloud but also a diffuse molecular gas or even an atomic gas.

4. Lepton accelerator in black hole magnetospheres In a vacuum magnetosphere, an electric field, E , arises along the magnetic field lines. Accordingly, electrons and positrons (red arrows in Fig. 1(b)) are accelerated into ultra-relativistic energies to emit high-energy gamma-rays (wavy line with middle wavelength) via the curvature process (a kind of synchrotron process whose electron’s gyro radius is replaced with the macroscopic curvature radius of the three-dimensional electron’s motion) and VHE gamma-rays (wavy line with shortest wavelength) via the inverse-Compton (IC) scatterings of the soft photons (wavy line with the longest wavelength) emitted from the RIAF. A fraction of such VHE photons collide with the soft RIAF photons to materialize as e± pairs, which partially screen the original E

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Figure 1. (a) Luminosity of black-hole lepton accelerators when a ten solar mass, extremely rotating (a = 0.99rg ) black hole is moving with velocity V in a cloud with molecule hydrogen density n H2 . For an atomic hydrogen gas with density n HI , put n H2 = n HI /2, because the mass is halved. The five straight lines correspond to the Bondi–Hoyle accretion rates 10−2 , 10−3 , 10−4 , 10−5 and 10−6 , as labeled. In the lower-right white region, the enhanced photon illumination from the equatorial accretion flow results in an efficient pair production, and hence a complete screening of the magnetic field aligned electric field; thus, the accelerator vanishes in this region. In the upper-left white region, stationary accelerators cannot be formed (see text). Thus, stationary accelerators arise only in the green-black region. (b) Schematic diagram (side view) of a black-hole magnetosphere. The polar funnel is assumed to be bounded from the radiatively inefficient accretion flow (cyan region) at co-latitude θ = 60◦ (dashed line) from the rotation axis (ordinate).

when they separate. It is noteworthy that pair annihilation is negligible compared to pair production in BH gaps. To compute the actual strength of E , we solve the e± pair production cascade in a stationary and axisymmetric magnetosphere on the meridional plane (r ,θ ), where r denotes the Boyer–Lindquist radial coordinate, and θ does the co-latitude measured from the rotation axis. The black hole’s rotational energy is electromagnetically extracted via the Blandford– Znajek process (Blandford & Znajek 1977) and partially dissipated as particle acceleration and the resultant radiation within the accelerator. It is noteworthy that the electrodynamics of this lepton accelerator is essentially described by the general-relativistic Goldreich–Julian charge density, which is governed by the magneticfield strength and the frame-dragging effects. Thus, the accelerator solution little depends on the magnetic field configuration near the event horizon. We therefore assume that the magnetic field is radial in the meridional plane and that magnetic axis is aligned with the rotation axis. The magnetic field lines are twisted in the azimuthal direction due to the frame-dragging effect, and its curvature radius is assumed to be rg in the local reference frame. This assumption modestly affects the curvature spectrum, but does not affect the entire electrodynamics, because the pair-production process, and hence the screening of E is governed by the highestenergy, IC-scattered photons.

5. Basic equations Let us quantify the accelerator electrodynamics. In a rotating black-hole magnetosphere, electron–positron accelerator is formed in the direct vicinity of the event horizon. Thus, we start with describing the background space-time in a fully general relativistic way. We adopt the geometrized unit, putting c = G = 1, where c and G denote the speed of light and the gravitational constant, respectively. Around a rotating BH, the spacetime geometry is described by the Kerr metric (Kerr 1963). In the Boyer–Lindquist co-ordinates, it becomes (Boyer & Lindquist 1967) ds 2 = gtt dt 2 +2gtϕ dtdϕ + gϕϕ dϕ 2 + grr dr 2 + gθ θ dθ 2 , (1) where  − a 2 sin2 θ ,  A sin2 θ , gϕϕ ≡ 

gtt ≡ −

gtϕ ≡ − grr ≡

 , 

2Mar sin2 θ , (2)  gθ θ ≡ ; (3)

 ≡ r 2 − 2Mr + a 2 ,  ≡ r 2 + a 2 cos2 θ , A ≡ (r 2 + a 2 )2 − a 2 sin2 θ . At the horizon, we obtain √  = 0, which gives the horizon radius, rH ≡ M + M 2 − a 2 , where M corresponds to the gravitational radius, rg ≡ G Mc−2 = M. The spin parameter a becomes a = M

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for a maximally rotating BH, and becomes a = 0 for a non-rotating BH. The space-time dragging frequency is given by ω(r, θ ) = −gtϕ /gϕϕ , which decreases outwards as ω ∝ r −3 at r  rg = M. We assume that the non-corotational potential Φ depends on t and ϕ only through the form ϕ − F t, and put Fμt + F Fμϕ = −∂μ (r, θ, ϕ − F t),

(4)

where F denotes the magnetic field line rotational angular frequency. We refer to such a solution as a ‘stationary’ solution in the present paper. The Gauss’s law gives the Poisson equation that describes in a three dimensional magnetosphere (Hirotani 2006), √  −g μν 1 g gϕϕ ∂ν = 4π(ρ − ρGJ ), (5) − √ ∂μ −g ρw2 2 2 −g g where ρw2 ≡ gtϕ tt ϕϕ =  sin θ , and the general relativistic Goldreich–Julian (GJ) charge density is defined as (Hirotani 2006) √  −g μν 1 g gϕϕ (F − ω)Fϕν . (6) ρGJ ≡ √ ∂μ 4π −g ρw2

Far away from the horizon, r  M, equation (6) reduces to the ordinary, special relativistic expression of the GJ charge density (Goldreich & Julian 1969; Mestel 1971)  · B ( × r) · (∇ × B) + . (7) ρGJ ≡ − 2π c 4π c Therefore, the corrections due to magnetospheric currents, which are expressed by the second term of equation (7), are included in equation (6). If the real charge density ρ deviates from the rotationally-induced Goldreich–Julian charge density, ρGJ , in some region, equation (5) shows that changes as a function of position. Thus, an acceleration electric field, E = −∂ /∂s, arises along the magnetic field line, where s denotes the distance along the magnetic field line. A gap is defined as the spatial region in which E is non-vanishing. At the null charge surface, ρGJ changes sign by definition. Thus, a vacuum gap, in which |ρ| |ρGJ |, appears around the null-charge surface, because ∂ E /∂s should have opposite signs at the inner and outer boundaries (Cheng et al. 1986; Chiang & Romani 1992; Romani 1996; Cheng et al. 2000). As an extension of the vacuum gap, a non-vacuum gap, in which |ρ| becomes a good fraction of |ρGJ |, also appears around the null-charge surface (§ 2.3.2 of Hirotani & Pu 2016), unless the injected current across either the inner or the outer boundary becomes a substantial fraction of the GJ value.

In previous series of our papers (e.g., Hirotani & Pu 2016), we have assumed  M 2 in equation (5), expanding the left-hand side in the series of /M 2 and picking up only the leading orders. However, in the present paper, we discard this approximation, and consider all the terms that arise at  ∼ M 2 or   M 2 . It should be noted that ρGJ vanishes, and hence the null surface appears near the place where F coincides with the space-time dragging angular frequency, ω (Beskin et al. 1992). The deviation of the null surface from this ω(r, θ ) = F surface is indeed small, as indicated in Fig. 1 of Hirotani and Okamoto (1998). Since ω can match F only near the horizon, the null surface, and hence the gap generally appears within one or two gravitational radii above the horizon, irrespective of the BH mass.

6. Results We apply the method to a stellar-mass black hole with mass M = 10M . To consider an efficient emission, we consider an extremely rotating black hole, a = 0.99rg , because the accelerator luminosity rapidly increases as a → rg (10). Owing to the frame-dragging effects, the Goldreich–Julian charge density decreases outwards around a rotating black hole. As a result, a negative E

arises near the null-charge surface, which is located very close to the event horizon (Fig. 2). In Fig. 3, we also plot E (r, θ ) at four discrete co-latitudes, θ = 0◦ , 15◦ , 30◦ and 45◦ . It follows that E peaks slightly inside the null surface (vertical dashed line), and that it maximizes at θ = 0◦ (i.e., along the rotation axis). The reason why E maximizes along the rotation axis is that magnetic fluxes concentrate towards the rotation axis as the black hole spin approaches its maximum value (i.e., as a → rg ) (Komissarov & McKinney 2007; Tchekhovskoy et al. 2010). Therefore, to consider the greatest gamma-ray flux, we focus on the emission along the rotation axis, θ = 0◦ . The acceleration electric field, E , decreases slowly outside the null surface in the same way as pulsar outer gaps (Hirotani & Shibata 1999). This is because the two-dimensional screening effect of E works when the gap longitudinal (i.e., radial) width becomes nonnegligible compared to its trans-field (i.e., meridional) thickness. The created e± s are accelerated by the E in opposite directions, emitting copious gamma-rays via the curvature process in 0.01−3 GeV and via the IC process in 0.01−1 TeV (Fig. 4). The characteristic photon energy in the curvature process is given by hνc =

J. Astrophys. Astr. (2018) 39:50

Figure 2. Magnetic field aligned electric field, E , on the meridional plane. The filled black circle on the bottom left corner shows a black hole rotating along the ordinate. The mass and the spin parameter of the black hole are M = 10M and a = 0.99rg . Both axes are normalized by the gravitational radius, rg = G Mc−2 . The lepton accelerator appears only in the polar funnel, θ < 60◦ . The dimensionless accretion rate is m˙ = 10−4 . The magnetic field is assumed to be radial on the meridional plane, and will be rotating with angular frequency ΩF = 0.5ωH , where ωH denotes the black holes spin angular frequency. The null-charge surface is located at radial co-ordinate, r = 1.73rg , whose θ dependence is weak.

(3/2)h¯ cγ 3 /ρc , where h denotes the Planck constant and h¯ ≡ h/2π . At each place in the gap, electrons have Lorentz factors typically in the range 106 < γ < 3 × 106 . To evaluate the curvature radius ρc , we assume that the horizon-threading magnetic field lines bend in the toroidal direction due to frame dragging and adopt ρc = rg . Since the pair production is sustained by the TeV photons (emitted via the IC process), the gap electrodynamics is little affected by the actual value of ρc , which appears only in the curvature process. Thus, we adopt this representative value, ρc = rg . The IC photon energy is limited by the electron kinetic energy whose upper bound is about 1.5 TeV. Thus, the IC photons have typical energies between 0.01 TeV and 1 TeV. It also follows from Fig. 4 that the gamma-ray luminosity increases with decreasing accretion rates. This is because the decreased RIAF soft photon field increases the pair-production mean-free path, the accelerator width along the magnetic field lines, and hence the electric potential drop. What is more, the emission

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becomes detectable with Fermi/LAT2 and IACTs such as CTA3 , if the distance is within 1 kpc, and if the dimensionless accretion rate resides in the narrow range 6 × 10−5 < m˙ < 2 × 10−4 . The gamma-ray spectrum exhibits a turnover around TeV, because electron Lorentz factors are limited below 1.6 TeV due to the curvature-radiation drag force. A caution should be made, however, on the assumption of a stationary electron–positron pair cascade. If the cascade takes place in a time-dependent manner as suggested with Particle-in-Cell simulations (Levinson & Segev 2017), the spectra might appear different from the present stationary analysis. The present gap luminosity gives an estimate of the maximally possible luminosity of a gap, whose electrodynamic structure may be variable in time. The dependence of the solutions on the BH spin will be discussed in our subsequent paper (Hirotani et al. 2018). Let us analytically examine why the gap luminosity maximizes when m˙ ≈ 10−4 . At radius r , the soft photon number density, n s , can be estimated as ns =

L s /c 4πr 2 hνs

2  10rg d = 1.3 × 1020 M1 −2 r 10 kpc   νs Fνs eV cm−3 , × hνs eV cm−2 s−1

(8)

where νs Fνs denotes the ADAF energy flux whose value lies around 10−12 TeV cm−2 s−1 = eV cm−2 s−1 at distance d = 10 kpc; the ADAF spectrum peaks at hνs ≈ a few eV (thin four curves on the left in Fig. 4). We evaluate the ADAF luminosity (in near-IR energies) with L s ≈ 4π d 2 νs Fνs , where d = 10 kpc. To compute n s , we assume that the photon density is uniform within r = 10rg , a typical radius in which the equatorial ADAF is confined vertically by the magnetic pressure (McKinney et al. 2012). The electrons Lorentz factors are limited above 106 (Hirotani et al. 2018). Thus, the Klein–Nishina cross section becomes σIC ≈ 0.2σT , where σT denotes the Thomson cross section. Thus, the mean-free path for the IC scatterings, λIC = 1/(n s σIC ) becomes

2 LAT Performance (https://www.slac.stanford.edu/exp/glast/group

s/canda/lat_Performance.htm). 3 CTA Performance (https://portal.cta-observatory.org/CTA_Obser vatory/performance/SitePages/Hom.aspx).

J. Astrophys. Astr. (2018) 39:50

Acceleration electric field, E|| (statvolt cm-1)

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0

-104

-2 104

-3 10

M=10M a=0.99M m=1.00 10

4

-0.4

-0.2

0

0.2

0.4

45o 30o 15o 0o

4

0.6

0 .8

1.0

Distance along magnetic field line from the null-charge surface / rg Figure 3. Distribution of the magnetic field aligned electric field, E , that is presented in Fig. 1, at four discrete co-latitudes as labeled in the box, where θ = 0◦ corresponds to the rotation axis. The abscissa denotes the distance along the magnetic field from the null-charge surface, where the general relativistic Goldreich–Julian charge density vanishes due to the spacetime dragging around a rotating black hole. Black hole’s mass (M = 10M ), spin (a = 0.99rg ), and the accretion rate (m˙ = 1.00 × 10−4 ) are common with Fig. 1. The vertical dashed line shows the position of the null-charge surface along θ = 0◦ ; however, its position little depends on θ because we assume ΩF = 0.5ωH (see the main text).

−2  10rg d λIC −2 ≈ 4.0 × 10 M1 rg r 10 kpc −1    νs Fνs σIC −1 eV × . hνs eV cm−2 s−1 σT

We find that the gap becomes most luminous when

(9)

The pair-production cross section becomes slightly below 0.2σT for the collisions of TeV and eV photons with moderate angles. Thus, the sum of the IC and pairproduction mean-free paths becomes  −1 λIC + λpp νs Fνs eV λIC ≈2 ≈ 0.08M1 . rg rg hνs eV cm−2 s−1 (10) Note that the Klein–Nishina and the pair-production cross sections are exactly computed in the numerical analysis, taking account of the photon specific intensity and the particle distribution functions at each point. Electrons are accelerated by E and attain the terminal Lorentz factor, γ ∼ 106 , after running the distance λacc =

γ m e c2 eE

= 1.7 × 10

 5

|E | 4 10 statvolt cm−1

which is less than rg .

−1

γ , 106

(11)

λIC + λpp + λacc ≈ λIC + λpp ≈ rg = 1.5 × 106 M1 cm. (12) It follows from equation (10) that λIC +λpp ≈ 0.26rg (or ≈ 0.40rg ) is realized when m˙ ≈ 10−4 (or ≈ 6 × 10−5 ), which gives hνs ≈ eV and νs Fνs ≈ 0.3 (or ≈ 0.2) eV cm−2 s−1 . It might appear that λIC + λpp ≈ rg holds if m˙ 10−4 . However, in this case, the gap width rapidly increases to diverge; that is, there exist no stationary solutions (Fig. 8 of Hirotani et al. 2016). Because of the simplification adopted around equations (8)–(12), we could not obtain λIC + λpp ≈ rg in this simplistic argument in a consistent manner with the numerical results of E , γ , and the gamma-ray spectrum. Nevertheless, we can analytically conclude that the gap longitudinal width becomes comparable to the horizon radius and its luminosity maximizes when m˙ ≈ 10−4 for stellar-mass BHs. To further analytically estimate E , Lorentz factors, γ -ray energies, and so on without invoking on the numerical results, we have to perform similar computations as described in § 2 of Hirotani (2013) for rotation-powered pulsars. In this case, we would have to replace the curvature process with the IC process, the neutron-star surface X-ray field with the ADAF IR field, the neutron-star magnetic field with that

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12

2

2

1

1

11

13

14

15

16

Figure 4. Spectrum of a black-hole lepton accelerator. The black hole mass and spin are common with Fig. 1. The red dotted, blue dashed, black solid and green dash-dotted curves correspond to the dimensionless accretion rates 10−3.50 , 10−3.75 , 10−4 and 10−4.25 , respectively. The distance is assumed to be 1 kpc. The thin curves on the left denote the input spectra of the advection-dominated accretion flow, a kind of RIAF. Such soft photons illuminate the accelerator in the polar funnel. The thick lines denote the spectra of the gamma-rays emitted from the accelerator. The 0.1–10 GeV photons are emitted via the curvature process, while those in 0.01–1 TeV are via the inverse-Compton (IC) process. The detection limits of the Large Area Telescope (LAT) aboard the Fermi Space Observatory after ten-year observation are indicated by thin solid curves. Also, the detection limits of the Cherenkov Telescope Array (CTA) after a 50-hour observation are shown by thin dashed and dotted curves; (N) denotes the detection limit of the CTA in the northern-hemisphere, while (S) denotes those in the southern hemisphere.

created/supported by the ADAF, and the light-cylinder radius with rg (to compute the spatial gradient of ρGJ ). For pulsars, the pair-production optical depth, τpp , is much less than unity for the out-going curvature GeV photons, which tail-on collide with the neutron-star surface X-rays. However, for BHs, τpp ∼ 1 holds for the IC TeV photons whose collision angles are typically 0.5–1.0 rad with the ADAF-emitted near-IR photons. It is noteworthy that the gap longitudinal width becomes approximately λIC + λpp + λacc , because τpp ∼ 1 holds for BH gaps. It is, however, out of the scope of the present paper to inquire further details of this analytical method.

7. Discussion Let us compare the related gamma-ray emission scenarios. In the protostellar jet scenario (Bosch-Ramon et al. 2010), electrons and protons are accelerated at the

termination shocks when the jets from massive protostars interact with the surrounding dense molecular clouds. Thus, the size of the emission region becomes comparable to the jet transverse thickness at the shock. In the hadronic cosmic ray scenario (Ginzburg & Syrovatskii 1964; Blandford & Eichler 1987), protons and helium nuclei are accelerated in the supernova shock fronts and propagate into dense molecular clouds, resulting in a single power-law photon spectrum in 0.001–100 TeV through neutral pion decays. The size becomes comparable to the core of a dense molecular cloud. In the leptonic cosmic ray scenario (Aharonian et al. 1997; van der Swaluw et al. 2001; Hillas et al. 1998), electrons are accelerated at pulsar wind nebulae or shell-type supernova remnants, and radiate gammarays via IC process and radio/X-rays via synchrotron process. Since the cosmic microwave background radiation provides the main soft photon field in the interstellar medium, the size may be comparable to the plerions, whose size increases with the pulsar age. In the

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black-hole lepton accelerator scenario (Beskin et al. 1992; Hirotani & Okamoto 1998; Neronov & Aharonian 2007; Levinson & Rieger 2011; Globus & Levinson 2014; Broderick & Tchekhovskoy 2015; Hirotani et al. 2017; Levinson & Segev 2017; Song et al. 2017), emission size does not exceed 10rg . Noting that the angular resolution of the CTA is about five times better than the current IACTs, we propose to discriminate the present black-hole lepton accelerator scenario from other scenarios by comparing the gamma-ray image and spectral properties. Namely, if a VHE source has a point-like morphology like HESS J1800-2400C in a gaseous cloud, and has two spectral peaks in 0.01–3 GeV and 0.01–1 TeV, but shows (synchrotron) powerlaw component in neither radio nor X-ray wavelengths, we consider that the present scenario accounts for its emission mechanism. References Aharonian F. A., Atoyan A. M., Kifune T. 1997, MNRAS, 291, 162 Beskin V. S., Istomin Ya. N., Parev V. 1992, Sov. Astron., 36(6), 642 Black J. H., Fazio G. G. 1973, ApJ, 185, L7 Blandford R. D., Znajek R. L., 1977, MNRAS, 179, 433 Blandford R. D., Eichler D. 1987, Phys. Rep., 154, 1 Bondi H., Hoyle F. 1944, MNRAS, 104, 273 Broderick A. E., Tchekhovskoy A. 2015, 809, 97 Bosch-Ramon, Romero G. E., Araudo A. T., Paredes J. M. 2010, Astron. Astroph., 511, 8 Boyer R. H., Lindquist R. W. 1967, J. Math. Phys., 265, 281 Cheng K. S., Ho C., Ruderman M. 1986, Astroph. J., 300, 500 Cheng K. S., Ruderman M., Zhang L. 2000, Astroph. J., 537, 964 Chiang J., Romani R. W. 1992, Astroph. J., 400, 629 Corral-Santana J. M., Casares J., Munoz-Daias T., Bauer F. E., Martinez-Pairs I. G., Russel D. M. 2016, Astron. Astroph., 587 De Ona Wilhelmi E. 2009, AIP Conf. Ser., 1112, pp. 16–22

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J. Astrophys. Astr. (2018) 39:51 https://doi.org/10.1007/s12036-018-9549-y

© Indian Academy of Sciences

Review

Precision pulsar timing with the ORT and the GMRT and its applications in pulsar astrophysics BHAL CHANDRA JOSHI1,∗ , PRAKASH ARUMUGASAMY1 , MANJARI BAGCHI3,12 , DEBADES BANDYOPADHYAY4 , AVISHEK BASU1 , NEELAM DHANDA BATRA5,6 , SURYARAO BETHAPUDI7 , ARPITA CHOUDHARY3 , KISHALAY DE8 , L. DEY2 , A. GOPAKUMAR2 , Y. GUPTA1 , M. A. KRISHNAKUMAR1,9 , YOGESH MAAN10 , P. K. MANOHARAN1,9 , ARUN NAIDU11 , RANA NANDI14 , DHRUV PATHAK3,12 , MAYURESH SURNIS13,15 and ABHIMANYU SUSOBHANAN2 1 National

Centre for Radio Astrophysics (Tata Institute of Fundamental Research), Post Bag No 3, Ganeshkhind, Pune 411 007, India. 2 Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai 400 005, India. 3 The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600 113, India. 4 Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700 064, India. 5 Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India. 6 Department of Physics, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Shameerpet Mandal, Hyderabad 500 078, India. 7 Department of Physics, Indian Institute of Technology Hyderabad, Kandi, Hyderabad 502 285, India. 8 Cahill Centre for Astrophysics, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA. 9 Radio Astronomy Centre (NCRA-TIFR), Ooty, India. 10 ASTRON, The Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands. 11 Mcgill Space Institute, McGill University, Montreal, Canada. 12 Homi Bhabha National Institute Training School Complex, Anushakti Nagar, Mumbai 400 094, India. 13 Department of Physics and Astronomy, West Virginia University, P. O. Box 6315, Morgantown, WV, USA. 14 Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India. 15 Center for Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge Research Building, Morgantown, WV, USA. ∗ Corresponding author. E-mail: [email protected] MS received 12 July 2018; accepted 16 August 2018; published online 29 August 2018 Abstract. Radio pulsars show remarkable clock-like stability, which make them useful astronomy tools in experiments to test equation of state of neutron stars and detecting gravitational waves using pulsar timing techniques. A brief review of relevant astrophysical experiments is provided in this paper highlighting the current state-of-the-art of these experiments. A program to monitor frequently glitching pulsars with Indian radio telescopes using high cadence observations is presented, with illustrations of glitches detected in this program, including the largest ever glitch in PSR B0531+21. An Indian initiative to discover sub-μHz gravitational waves, called Indian Pulsar Timing Array (InPTA), is also described briefly, where time-of-arrival uncertainties and post-fit residuals of the order of μs are already achievable, comparable to other international pulsar timing array experiments. While timing the glitches and their recoveries are likely to provide constraints on the structure of neutron stars, InPTA will provide upper limits on sub-μHz gravitational waves apart from auxiliary pulsar science. Future directions for these experiments are outlined. Keywords. Equation of state—gravitational waves—pulsars: general—stars: neutron.

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1. Introduction Highly magnetized rotating neutron stars, discovered first as radio pulsars emitting a train of narrow periodic pulses (Hewish et al. 1968), provide excellent celestial clocks, primarily due to their massive and compact nature (mass ∼ 1.4M ; radius ∼10 km). A stability of their periods up to one part in 1020 , allows measurements in astrophysical experiments with precision, unprecedented in astronomy, for constraining Equation of State (EoS) of these stars and detecting sub-μHz gravitational waves (GW). About 2600 pulsars have been discovered so far1 (Manchester et al. 2005), which are broadly classified as normal pulsars, young pulsars and millisecond pulsars, based on their rotation period and magnetic field strength. The latter two of these classes are relevant for this paper. Young pulsars with high magnetic dipolar surface field (1012 < B < 1014 G) and/or short periods (P ∼ 100 ms) show rotational irregularities, such as abrupt spin-ups, also called glitches (Radhakrishnan & Manchester 1969; Lyne et al. 2000; Krawczyk et al. 2003; Espinoza et al. 2011; Yu et al. 2013), as well as slow wander in rotation rate, known as timing noise (Boynton et al. 1972; Cordes 1980; Cordes & Helfand 1980). Measurements of these rotational irregularities are useful for characterizing the internal structure of neutron star and constraining its EoS (Link et al. 1999, 1992; Haskell & Melatos 2015; Ho et al. 2015). On the other hand, older pulsars with relatively lower magnetic fields (108 < B < 1011 G) and millisecond periods (P ∼ 1.5–30 ms) exhibit a much smaller rotational slow-down and highly stable rotation rates. An ensemble of these millisecond pulsars (MSPs) is useful as a celestial detector to measure small metric perturbation caused by GW passing near the Earth (Foster & Backer 1990; Joshi 2013). High precision observations of such ensembles are carried out by the Pulsar Timing Arrays (PTA), which are experiments for detection of sub-μHz GW (Manchester et al. 2013; Demorest et al. 2013). High-sensitivity observations using large collecting area radio telescopes, such as the Ooty Radio Telescope (ORT: Swarup et al. 1971) and the upgraded Giant Meterwave Radio Telescope (GMRT, uGMRT: Swarup et al. 1991; Gupta et al. 2017) are analysed with pulsar timing technique to obtain high precision measurements for such experiments. In this paper, a brief review of state-of-the-art in this field is presented followed by a description of our efforts in this direction using the ORT and the GMRT. The plan 1 http://www.atnf.csiro.au/people/pulsar/psrcat/.

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of the paper is as follows. The pulsar timing technique is briefly described in section 2. Current constraints on neutron star structure and EoS are discussed in section 3 followed by a description of the glitch monitoring program using the ORT and the uGMRT and its preliminary results. A brief review of PTA experiments is presented in section 4 followed by details and current status of Indian PTA experiment called Indian Pulsar Timing Array (InPTA).

2. Pulsar timing Pulsar timing involves comparison of the prediction of pulse time-of-arrival (ToA) from an assumed rotational model of star with the observed ToA to refine the model parameters. The key point of this technique is keeping track of rotation cycles of pulsar, which improves precision as a function of time. As discussed below, the assumed model is usually complex involving several parameters, all of which are estimated in this process. As pulsars are weak sources, ToAs are measured from an average pulse, obtained after averaging the pulsed time series over several thousand pulses. A fiducial point on the pulse is chosen, which usually comes with a random shift from a noise-free template in a given observation. Template matching is used to find this shift and adjust time of observations (Taylor 1992) to get the ToA of the pulse up to a precision of few nano-seconds using an atomic clock, usually a hydrogen maser synchronized to an international time scale, called Temps Atomic Internationale. These observed ToAs are first referred to Solar System Barycentre (SSB – an inertial frame) and then onwards to an inertial frame for the pulsar as shown below: tp = ttopo + tclock − D/ f 2 + R + S + E ,

(1)

where ttopo are observed topocentric ToAs, tclock are clock corrections, D is the dispersion constant accounting for dispersive delay in the inter-stellar medium and R , S and E are the Roemer, Shapiro and Einstein delays respectively (see Stairs (2003) for details on these delays). Additionally, the timing model may also include dynamics of the star itself and that of its companion if the pulsar happens to be in a binary system. Finally, the timing model also assumes a rotational model of the neutron star given by 1 ν(t) = ν0 + ν˙ (t − t0 ) + ν¨ (t − t0 )2 , 2

(2)

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Figure 1. Timing noise seen in the rotation rate of Crab pulsar (PSR B0531+21) from radio- to high-energies. The data are from the ORT, the legacy GMRT and the ASTROSAT. We also used archival data obtained by Fermi telescope. The timing noise, which is a slow wander of rotation rate, is seen as systematic deviation from zero residuals. The timing residuals for the four telescopes are offset from each other by the amount of relative offset in the data acquisition pipeline

where ν, ν0 , ν˙ and ν¨ are the rotational frequency and its higher order derivatives assumed at an epoch t0 . The timing model is used to predict the pulse number N , N = ν(t − t0 ).

(3)

If the prediction is correct, N should be an integer. If not, the fractional part, called timing residual, is minimized in a least-square sense to obtain the bestfit parameters of the model (see Edwards et al. (2006) for more details). The timing model is usually complex. The commonly included parameters are pulsar spin period and its higher-order derivatives, position and proper motion of the star, parallax, dispersion measure2 (DM) and binary Keplerian and post-Keplerian parameters, such as orbital period, orbital separation, component masses, advance of periastron, orbital period decay, gravitational red-shift and range and shape of Shapiro delay in the binary. In addition, model of the solar wind, ephemeris for solar system bodies and position of the Sun in the absolute International Celestial Reference Frame also play a role. A ‘good model’ yields ‘white noise’ timing residuals, whereas systematics in timing residuals imply unmodeled effects. One such unmodeled effect is timing noise. An example is shown in Fig. 1 for PSR B0531+21 from 2 Dispersion Measure is the integrated column density of electrons in the line-of-sight.

Figure 2. A small glitch detected in PSR B0740−28 at the ORT on MJD 56727. The top panel shows the pre- and postglitch timing residuals as a function of MJD. The middle panel shows pre- and post-glitch spin frequency (ν) and the bottom panel shows the frequency derivative (˙ν ). The pulsar was observed at 334.5 MHz.

our high cadence monitoring of this pulsar with the ORT and the GMRT. Another rotational irregularity is pulsar glitch, seen as an abrupt increase in rotation rate of the star, illustrated in Fig. 2 for PSR B0740−28. Also relevant to this paper is systematics in the timing residuals of an ensemble of pulsars due to correlated unmodeled perturbation caused by a passing GW. A precision of tens of nanoseconds is already achieved in experiments to detect GW. 3. Monitoring pulsar glitches 3.1 Pulsar glitches and the internal structure of neutron stars Glitches provide a peek into the internal structure of the neutron star. Initially, glitches were interpreted as star-quakes (Pines & Shaham 1972). Now, glitches are believed to be the result of transfer of angular momentum from a differentially rotating interior super-fluid to the star-crust (Anderson & Itoh 1975). Direct evidence of such super-fluid is inferred from the cooling rate of neutron star in CasA (Baym et al. 1971; Heinke & Ho 2010; Shternin et al. 2011). It is energetically more favourable for vortex cores of super-fluid to ‘pin’ at lattice sites in the crust, magnetically or otherwise (Alpar 1977; Link 2009, 2012a, b). This leads to conservation of areal density of super-fluid vortex constraining the super-fluid rotation to be a constant. While crust slows down due to electromagnetic torques, associated ‘pinned’ neutron super-fluid component cannot

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3 http://www.jb.man.ac.uk/pulsar/glitches/gTable.html.

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slow down and develops a differential rotation storing angular momentum. When the differential rotation between the crust and ‘pinned’ super-fluid exceeds a critical lag, the magnus force is large enough to ‘unpin’ crustal super-fluid and the stored angular momentum is transferred from the super-fluid to the crust during a glitch event (Link et al. 1999). Till date, 529 glitches have been reported in 188 pulsars (Espinoza et al. 2011) with about 36 pulsars having 4 or more glitches.3 Most glitching pulsars are young with characteristic ages of about 100 kyr. There are two broad types of glitches: Crab-like (Crab pulsar – PSR B0531+21 with 27 reported glitches), which are small amplitude glitches and are accompanied by a permanent change in spin-down, and vela-like (Vela pulsar – B0833−45 with 20 reported glitches), which are very regular large amplitude glitches with linear recovery (Espinoza et al. 2011). There are pulsars, which show both large and small glitches, such as PSRs B1046−58, B1338−62 and B1737−30. This bimodality is apparent from a distribution of fractional glitch sizes shown in Fig. 3. While the reasons for this dichotomy are unknown, one possibility is that small and large glitches originate in different parts of the star, with neutron star crust contributing to smaller glitches, whereas the core participates in larger glitches. Thus, glitches can provide a probe of structure as well as EoS of the star. An important sub-class of glitching pulsars is pulsars with frequent glitches. PSRs J0537−6910 (23 glitches), B1338−62 (23 glitches) and B1737−30 (35 glitches) are the best known representatives of this class. The frequent glitches in these pulsars show almost a linear cumulative spin-up, when averaged over all the glitches in a pulsar. The average rate of angular momentum transferred can be estimated from observed cumulative spin-up of the crust. Equating this to average rate of angular momentum transferred from the reservoir (Ires ν˙ ), a lower limit on crustal super-fluid (Ires /Ic ) can be obtained from observations and implies that about 0.9 to 1.8% of Moment of Inertia (MoI) of the star participates in these glitches (Link et al. 1999). It is possible to theoretically estimate crustal MoI assuming a given EoS. A comparison with the observed glitch sizes would be interesting to examine if all glitches originate in the crust. Such a comparison can become even more constraining if one considers non-dissipative coupling of inter-penetrating neutron super-fluid and e − p normal fluid, called ‘entrainment’ (Chamel & Carter 2006; Chamel 2013). It has been shown in laboratory experiments that the net effect of

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entrainment is an increase in the effective neutron mass by a factor of about 4.3−5.1 (Andersson et al. 2012; Delsate et al. 2016). This increases the lower limit for MoI of reservoir to about 7% for Vela pulsar and brings EoS in tension with data as the crustal super-fluid is just not enough (Andersson et al. 2012) to explain the glitch events. Possible solutions being explored range from large glitching pulsars being low mass neutron star (