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Causality is an essential factor in determining the maximum mass of a neutron star. Previous works study causality for smooth equations of state. The density at the core of neutron stars can be a few times nuclear saturation density, where the occurrence of first-order phase transition has not been ruled out. The causality condition for first-order phase transition is characteristically different from that of smooth EOS, which becomes evident in the mass-radius relation. In this letter, we find that equations of state having first-order phase transition, the causality line deviates considerably from the smooth equation of state. Depending on the onset density of phase transition, there is a narrow band in the mass-radius plot, which is available only to the stars having a smooth equation of state. This can have significant consequences in the sense that if some pulsars are to lie in this band, one can rule out the equation of state having first-order phase transition occurring at that particular onset density., Comment: 6 pages, 7 figures

The recent mass ($0.77 \pm ^{0.20}_{0.17}M_{\odot}$) and radius ($10.4\pm^{0.86}_{0.78} \text{km}$) measurement of HESS J1731-347 made it one of the most fascinating object if it is indeed a neutron star. In this work, we examine the current status of the dense matter equation of states in the context of this compact object being a neutron star. We use three sets of equation of states corresponding to the three classes - neutron stars, strange stars, and hybrid stars and perform Bayesian model selection on them. Our results show that for hadronic models, the EoS is preferred to be stiff at the intermediate densities. This makes the Brueckner-Hartree-Fock approximation and models based on Effective-interactions deviate from current astrophysical observations on the inclusion of HESS J1731-347. Furthermore, for the strange star family, the equation of states composed of three flavor quarks prefers relatively smaller bag parameters. Analyzing the hybrid family of equation of states consisting of a first-order phase transition revealed preferences for early first-order phase transition. Comparing all the preferred equations of state among each family, it was found that the current astrophysical constraints most prefer the hybrid equation of states., Comment: 15 figures, 19 pages

Proto-neutron stars have both high-density and relatively high-temperature in them. This study analyses how the equation of state changes with temperature, which is relevant for proto-neutron stars. We determine an equation of state for the proto-neutron stars in the relativistic mean field model in which the coupling parameters are density-dependent. The equation of state considerably affects the mass-radius curve, thereby affecting the f-mode oscillation frequency. Temperature makes the equation of state stiffer at relatively low and intermediate densities, thereby making the star less compact and the mass-radius curve flatter. The f-mode frequency for low and intermediate-mass neutron stars decreases with temperature and thus should be easier to detect. The universal relation (connecting f-mode frequency, mass and radius) changes non-linearly with temperature. The parameters defining the universal relation ($\omega M = a(T) \left(\frac{M}{R}\right) + b(T)$) becomes temperature dependent with the coefficients following a parabolic relation with temperature., Comment: 11 pages, 5 figures

Simultaneous measurement of mass and radius with high precision is essential to unravel the equation of state of matter at the centre of neutron stars. Measurement of massive pulsars indicates that the equation of state has to be stiff at low densities. The radius measurement of PSR J0030+0451 has rejected several relatively softer equations of state. In this work, an ensemble of agnostically constructed EoS was studied for the mass and radius measurement. The range of radius of neutron stars obtained from the ensemble was confined within a radius bound from 10.5 - 14.5 km. It is seen that higher masses prefer stiffer EoS. However, the slope of the speed of sound (the stiffness of the EoS) is very sensitive to the radius measurement. Assuming the radius measurement to be precise up to 2 km, then a higher radius indicates sharp stiffening of the equation of state at low density; however, it also indicates a sharp fall after the peak, indicating a relatively softer core for massive neutron stars. On the other hand, for the same precision, a lower radius measurement indicates a relatively softer equation of state., Comment: 11 pages, 7 figures

Quasi-normal modes of neutron stars are an exciting prospect for analyzing the internal composition of NSs and studying matter at high densities. In this work, we focus on studying the $f$- and $p$- quadrupolar oscillation modes, which couple with gravitational waves. We construct two different equation of state ensembles, one without and one with a first-order phase transition, and examine how $f$- and $p$-modes might help us differentiate them. We find ensemble specific exclusion regions in the $65\%$ and $95\%$ confidence contours of the frequency-damping time relations. The exclusion regions become more prominent for the higher-order oscillation modes. However, these modes have higher frequencies, which are beyond the detection capabilities of present gravitational wave detectors. The quasi-universal relations of dimensionless quantities prove to be ineffective in differentiating the equation of state ensembles, as they obscure the details of the equation of state., Comment: 14 pages, 7 figures

Recycled millisecond pulsars are susceptible to starquakes as they are continuously accreting matter from their binary companion. A starquake happens when the rotational frequency of the star crosses its breaking frequency. In this study, we perform a model analysis of an accreting neutron star suffering a starquake. We analyze two models: a spherical star with accreting mountains and a deformed star with accreting mountains. We find that as the star crosses the breaking frequency and suffers a starquake there is a sudden change in the continuous gravitational wave signal arriving from them. It is interesting to note that the amplitude of the gravitational wave signals increases suddenly for the spherical star. In contrast, for the deformed star, the amplitude of the continuous gravitational wave signal decreases suddenly. This sudden change in the continuous gravitational wave signal in recycled millisecond pulsars can be a unique signature for such pulsars undergoing a starquake., Comment: 10 pages, 9 figures (accepted for publication in MNRAS)

The concept of quarkyonic matter presents a promising alternative to the conventional models used to describe high-density matter and provides a more nuanced and detailed understanding of the properties of matter under extreme conditions that exist in astrophysical bodies. The aim of this study is to showcase the effectiveness of utilizing the quarkyonic model, in combination with the relativistic mean-field formalism, to parameterize the equation of state at high densities. Through this approach, we intend to investigate and gain insights into various fundamental properties of a static neutron star, such as its compositional ingredients, speed of sound, mass-radius profile, and tidal deformability. The obtained results revealed that the quarkyonic matter equation of state (EOS) is capable of producing a heavy neutron star with the mass range of $\sim$ $2.8 M_\odot$. The results of our inquiry have demonstrated that the EOS for quarkyonic matter not only yields a neutron star with a significantly high mass but also showcases a remarkable degree of coherence with the conformal limit of the speed of sound originating from deconfined QCD matter. Furthermore, we have observed that the tidal deformability of the neutron star, corresponding to the EOSs of quarkyonic matter, is in excellent agreement with the observational constraints derived from the GW170817 and GW190425 events. This finding implies that the quarkyonic model is capable of forecasting the behavior of neutron stars associated with binary merger systems. This aspect has been meticulously scrutinized in terms of merger time, gravitational wave signatures, and collapse times using numerical relativity simulations.

In this work we have analyzed the variation of speed of sound and trace anomaly inside a neutron star using neural network. We construct family of agnostic equation of state by maintaining thermodynamic stability, speed of sound bound with constraints from recent observation of neutron stars. The data of mass and radius serves an input for the neural network and we obtain speed of sound as an output. The speed of sound shows non-monotonic behaviour and the trained data predicts softer equation of state. The neural network predicts stiff equation of state at the centre of intermediate mass stars and massive stars have relatively softer equation of state at their centre. The trace anomaly shows a non-monotonic behaviour for the untrained data however, when we train our data; with neural network the trace anomaly shows monotonic behaviour and the condition of $\Delta \ge 0$ is maintained., Comment: 9 pages, 8 figures

Universal relations are important in testing many theories of physics. In the case of general relativity, we have the celebrated no-hair theorem for black holes. Unfortunately, the other compact stars, like neutron stars and white dwarfs, do not have such universal relation. However, neutron stars (and quark stars) have recently been found to follow certain universality, the I-Love-Q relations. These relations can provide a greater understanding of the structural and macro properties of compact astrophysical objects with knowledge of any one of the observables. The reason behind this is the lack of sensitivity to the relations with the equation of state of matter. In our present work, we have investigated the consistency of universal relations for a generic family of equations of state, which follows all the recent astrophysical constraints. Although the spread in the EoS is significant the universal nature of the trio holds relatively well up to a certain tolerance limit. The deviation from universality is seen to cross the tolerance limit with EoS, which is characteristically different from the original set., Comment: 8 pages, 14 figures

The fundamental constituent of matter at high temperature and density has intrigued physicists for quite some time. Recent results from heavy-ion colliders have enriched the Quantum Chromodynamics phase diagram at high temperatures and low baryon density. However, the phase at low temperatures and finite (mostly intermediate) baryon density remain unexplored. Theoretical Quantum Chromodynamics calculation predicts phase transition from hadronic matter to quark matter at such densities. Presently, the best laboratories available to probe such densities lie at the core of neutron stars. Recent results of how such phase transition signatures can be probed using gravitational waves both in isolated neutron stars and neutron star in binaries. The isolated neutron star would probe the very low-temperature regime, whereas neutron stars in binaries would probe finite baryon density in the intermediate temperature regime. We would also discuss whether the gravitational wave signature of such phase transition is unique and the detector specification needed to detect such signals., Comment: 6 pages, 0 figure, contribution in ConfXIV conference

Quantum Chromodynamics predicts phase transition from hadronic matter to quark matter at high density, which is highly probable in astrophysical systems like binary neutron star mergers. To explore the critical density where such phase transition can occur, we performed numerical relativity simulations of binary neutron star mergers with various masses (equal and unequal binaries). We aim to understand the effect of the onset of phase transition on the merger dynamics and gravitational wave spectra. We generated a set of equations of states by agnostically changing the onset of phase transition, having the hadronic matter part and quark matter part fixed. This particular arrangement of the equation of states explores the scenario of mergers where mixed phases of matter are achieved before or during the merger. Under these circumstances, if the matter properties with hadronic and quark degrees differ significantly, it is reflected in the stability of the final merger product for the intermediate mass binary. We performed a case study on mixed species merger, where one of the binary companions is hybrid star. If quark matter appears at low densities, we observe significant change in post-merger gravitational wave analysis in terms of higher peak frequencies and post-merger frequencies in power spectral density. We report indications expressed as spikes in phase difference plots at merger time for mixed mergers. We found that the expression of phase transition in post-merger gravitational wave signals is more significant for unequal mass binary than for equal mass binary having the same total baryonic mass., Comment: 12 pages, 9 figures (accepted in MNRAS)

Numerical simulation of hydrodynamic equations forms the central part of solving various modern astrophysical problems. In the case of shocks, one can have either dynamical equations or jump conditions (the conservation equations without any time evolution). The solution of the jump condition in curve space-time is derived and analyzed in detail in the present work. We also derive the Taub adiabat or combustion adiabat equation from the jump condition. We have analyzed both time-like and space-like shocks in the present work. We find that the change in entropy for the weak shocks for curved space-time is small similar to that for flat space-time. We also find that for general relativistic space-like shocks, the Chapman-Jouguet point does not necessarily correspond to the sonic point for downstream matter, unlike the relativistic case. To analyze the shock wave solution for the curved space-time, one needs the information of metric potentials describing the space-time, which for the present work is taken to be a neutron star. We assume that a shock wave is generated at the centre of the star and is propagating outward. As the shock wave is propagating outwards, it combusts nuclear matter to quark matter, and we have a combustion scenario. We find that the general relativistic treatment of shock conditions is necessary to study shocks in neutron stars so that the results are consistent with the solution of the TOV equation while calculating the maximum mass for a given equation of state. We also find that with such general relativistic treatment, the combustion process in neutron stars is always a detonation., Comment: 39 pages,16 figures

We have studied the spin-down induced phase transition in cold, isolated neutron stars in this work. After birth, as the star slows down, its central density rises and crosses the critical density of phase transition, and a quark core is seeded inside the star. Intermediate mass stars are more likely to have a quark seeding in their lifetime at birth. Smaller neutron stars do not have a quark core and remain neutron stars throughout their life, whereas in massive stars, a quark core exists at their center from birth. In intermediate and massive stars, the quark core grows further as the star slows down. The appearance of a quark core leads to a sudden change in the moment of inertia of the star in its evolutionary history, and it is also reflected in a sudden discontinuity in the braking index of the star (at the frequency where the quark core first seeds). The energy released during the phase transition process as the quark core is seeded can excite the f-mode oscillation in the star and is emitted in the form of the gravitational wave, which is in the range of detection with present operating detectors; however, future detectors will enable a more clean extraction of this signals. Also, neutrinos and bursts of gamma-rays can originate from phase transition events. The spin-down induced phase transition could be gradual or in the form of subsequent leaps producing persistent or multiple transient emissions., Comment: 12 pages, 8 figures

Astrophysical shocks are very common and are interesting as they are responsible for particle acceleration in supernovas, blazers, and neutron stars. In this work, we study general relativistic shocks from the frame of the front. We derive the jump conditions and the Taub adiabat equation for both the space-like and time-like shocks. We solve these equations in a neutron star system where the shock is followed by a combustion front which is deconfining hadronic matter to quark matter. The maximum mass of the daughter quark star (generated from the combustion of the parent neutron star) is consistent with the maximum mass limit for the EoS sequence. We find that matter velocities for GR shocks under suitable conditions can break the speed of light limit indicating a very fast combustion process. Also, the matter velocities imply that for space-like shocks the combustion process is most probably a deflagration and for time-like shocks, it is a detonation and can even proceed with velocities that are super-luminous., Comment: 12 pages and 9 figures

In this study, we model a pulsar as a general relativistic oblique rotator, where the oblique rotator is a rotationally deformed neutron star whose rotation and magnetic axis are inclined at an angle. The oblique rotator spins down, losing rotational energy through the magnetic poles. The magnetic field is assumed to be dipolar; however, the star has a non-zero azimuthal component due to the misalignment. The magnetic field induces an electric field for a force-free condition. The magnetic field decreases as the misalignment increases and is minimum along the equatorial plane of the star. In contrast, the electric field remains almost constant initially but decreases rapidly at a high misalignment angle. The charge separation at the star surface is qualitatively similar to that of Newtonian calculation. We find that the power loss for a general relativistic rotator is minimum for either an aligned or an orthogonal rotator, which contrasts with Newtonian calculation, where the power loss increases with an increase in the misalignment angle., Comment: 19 page, 10 figures

The occurrence of quark matter at the center of neutron stars is still in debate. This study defines some semi-empirical parameters that quantify the occurrence and the amount of quark matter at star interiors. These parameters show semi-universal relations across all the EoS. One parameter depends on the shifting of the keplerian mass-radius curve from the static one and shows it is a constant across all EoS. The Z-parameter shows how tidal deformability depends on the quark content of the star and the stiffness of the EoS. The quark content of the star also affects the compactness of the star, and its dependence is almost universal. The empirical parameter gives a bound on the quark content of the star and shows that if the amount of the quark content increases, the stars are likely to collapse into a black hole. It is seen that the change in the mass and radius after PT is linearly proportional to the mass of the parent NS. Given a hadronic EoS, bag constant, and quark coupling constant, one can have a critical mass of the neutron star and the maximum mass of the hybrid star for phase transition without any baryonic mass loss., Comment: 6 pages, 3 figures and supplementary file

Aim: To study the multimessenger nature of the signal that can result from the phase transition of a neutron star to a quark star and their corresponding astrophysical observations. Methods: The phase transition process is initiated by the abrupt pressure and density changes at the star center, giving rise to a shock which deconfines matter followed by a weak front converting excess down to strange quarks to attain absolute stability. This process's effects are investigated by understanding how the energy escapes from the star in the form of neutrino-antineutrino annihilation. For such annihilation process, the corresponding energy deposition rate is calculated. Structural changes due to the energy loss have been investigated in the likes of misalignment angle evolution of the star and its astrophysical observation through gravitational waves. Results: The energy and time signature for the neutrino-antineutrino annihilation is compared with the observed isotropic energy for a short gamma-ray burst. The misalignment angle evolves to align the star's tilt axis, which can lead to the sudden increase or decrease of radio intensity from the pulsar. The corresponding gravitational wave emission, both continuous and burst, all lead towards multimessenger signals coming from the phase transition., Comment: 9 pages, 7 figures

General relativistic effects in the spacetime around the massive astrophysical objects can be captured using a spinning test gyro orbiting around the object in a circular geodesic. This article discusses how the tidal disruption due to a companion object affects the precession frequency of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. In this study, the central object is either a neutron star or a white dwarf. The gyro is any planetary or asteroid-like object orbiting the neutron star or a white dwarf. Moreover, the companion object that causes the tidal field can be a neutron star, white dwarf, a black hole, or a main-sequence star. The tidal effect significantly affects the spacetime around the host star, which affects the gyro precession frequency. The gyro's precession frequency increases with the mass of the companion object and decreases as the separation between the host star and the companion star increases. The tidal effect also varies with the stiffness of the equation of state of matter describing the neutron star. We also find that the tidal field affects the spacetime around a white dwarf more than that of the neutron star., Comment: 10 pages, 11 figures

Neural Machine Translation model is a sequence-to-sequence converter based on neural networks. Existing models use recurrent neural networks to construct both the encoder and decoder modules. In alternative research, the recurrent networks were substituted by convolutional neural networks for capturing the syntactic structure in the input sentence and decreasing the processing time. We incorporate the goodness of both approaches by proposing a convolutional-recurrent encoder for capturing the context information as well as the sequential information from the source sentence. Word embedding and position embedding of the source sentence is performed prior to the convolutional encoding layer which is basically a n-gram feature extractor capturing phrase-level context information. The rectified output of the convolutional encoding layer is added to the original embedding vector, and the sum is normalized by layer normalization. The normalized output is given as a sequential input to the recurrent encoding layer that captures the temporal information in the sequence. For the decoder, we use the attention-based recurrent neural network. Translation task on the German-English dataset verifies the efficacy of the proposed approach from the higher BLEU scores achieved as compared to the state of the art., Comment: Accepted in 36th ACM/SIGAPP Symposium On Applied Computing 2021

This article studies the maximum mass limit of the quark star formed after the shock-induced phase transition of a cold neutron star. By employing hadronic and quark equation of state that satisfies the current mass bound, we use combustion adiabat conditions to find such a limit. The combustion adiabat condition results in a local or a global maximum pressure at an intermediate density range. The maximum pressure corresponds to a local or global maximum mass for the phase transformed hybrid star. The phase transition is usually exothermic if we have a local maximum mass. The criteria for exothermic or endothermic phase transition depend on whether the quark pressure/energy ratios to nuclear pressure/energy are smaller or greater than 1. We find that exothermic phase transition in a cold neutron star usually results in hybrid stars whose mass is smaller than a parent neutron star. The phase transition is endothermic for a global maximum pressure; thereby, one gets a global maximum mass. Hybrid stars much massive than phase transformed local maximum mass can be formed, provided there is some external energy source during the phase transition process. However, for some cases, even massive hybrid stars can form with exothermic phase transition for EoSs having global maximum pressure., Comment: 10 pages, 4 figures, 4 tables

Charged particles at the crust of compact stars may be ejected and accelerated by the electric field generated due to the rotation of the magnetized star. For neutron or hybrid stars, the negatively charged particles are usually electrons, and the positively charged particles are mainly protons and Iron. Whereas the existence of strange stars also includes the possibility of ejection of strangelets from the star surface. The flux of such strangelets emitted from all known pulsars is in the range of $10^9-10^{10}$ GeV. Therefore, such massive strangelets can be one of the candidates for the sources of the highest-energy cosmic rays that have still eluded us. Our model proposes a possible origin of these ultra high energy cosmic rays., Comment: 9 pages, 10 figures

Fluctuation at the neutron star center gives rise to a small deconfined quark core very close to the star center. The density discontinuity at the quark-hadron boundary initiates a shock wave, which propagates outwards of the star. The shock has enough energy to combust nuclear matter to 2-flavor quark matter in the star. The 2-flavor quark matter is not stable and settles to a stable 3-flavor matter in the weakly interacting timescale. In this paper, we study the conversion of 2-flavor matter to 3-flavor matter. We set up a differential equation to convert the excess of down quarks to strange quarks involving weak reaction and diffusion of quarks. Calculating the reaction rate, we solve the differential equation to find the velocity of the conversion front. As the conversion front moves out, the density profile changes, bringing about a change in the star's quadrupole moment and thereby emitting gravitational waves. We find that the GW signal depends strongly on the star temperature and mass. The GW amplitude of a colder star is well within present detector capability, but the frequency is slightly on the higher side. Relatively hotter stars are on the boundary of present detectors and easily detectable with future detectors, and their frequency is also within the present detectability range. In comparison, PT from galactic pulsars is easily detectable with present detectors., Comment: 14 pages and 11 figures

We study the overall spin precession frequency of a test gyroscope around a neutron star. The precession of the test gyroscope gives the signatures of the general relativistic effects that are present in the region of strong gravity of an NS. Using a numerical code, we find the precession of the test gyroscope for a rotating and a strongly magnetized neutron star. The magnetic field distribution inside the neutron star is assumed either to be poloidal or toroidal. The overall spin precession rate is obtained by setting the orbital frequency of the gyroscope to a non-zero value but restricted to a time-like observer. The gyro frequency differs depending on the central object being a black hole or a neutron star. For neutron star, the gyro precession can even be calculated inside the star. We find that the gyroscope precession frequency depends on the stars mass, rotation rate, and magnetic field configuration., Comment: 12 pages, 14 figures

In this article, we perform a 2-d simulation of combustion of neutron star (NS) to hybrid star (HS). We assume that a sudden density fluctuation at the center of the NS initiates a shock discontinuity near the center of the star. This shock discontinuity deconfines NM to 2-f QM, initiating combustion of the star. This combustion front propagates from the center to the surface converting NM to 2-f QM. This combustion stops at a radius of $6 km$ inside the star, as at this density the NM is much stable than QM. Beyond $6 km$ although the combustion stops but the shock wave propagates to the surface. We study the gravitational wave signal for such a PT of NS to HS. We find that such PT has unique GW strain of amplitude $10^{-22}$. These signals last for few tens of $\mu s$ and shows small oscillating behaviour. The power spectrum consists of peaks and at fairly high frequency range. The conversion to NS to HS has a unique signature which would help in defining the PT and the fate of the NS., Comment: 13 pages, 13 figures and 2 Tables

Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodesic of a particle near the star's surface. The polar frame-dragging velocity makes the particle orbit non-planar, and the particle moves both along the azimuthal and polar direction for a fixed radial distance. The extent of particle deviation from planar orbit depends on the magnetic field strength and the misalignment angle. We find that the continuous gravitational wave emitted from such obliquely rotating axisymmetric star is non zero, and for small misalignment angle, the gravitational wave amplitude depends more on the azimuthal frame-dragging velocity. In contrast, for a large misalignment angle, the polar frame-dragging velocity dominates. The energy loss from such a misaligned rotator depends more significantly on the polar frame-dragging velocity and therefore, can significantly affect the magnetosphere around a magnetar., Comment: 17 pages, 7 figures

In this study we derive the magnetized Taub adiabat equations from the hydrodynamic conservation conditions. We employ the magnetized taub adiabat equations to study the evolution of a magnetized neutron star to magnetized quark star. The pressure of the burnt quark matter has a maximum which indicates a bound on the maximum mass of the quark star. The central density of the neutron star and the angle between the rotation axis and the magnetic axis (defined as the tilt angle) are seen to be significant in determining the magnetic field, and the tilt of the quark star. The magnetic field and the tilt of the quark star can have a observational significance and can help in understanding the physics at high density and strong magnetic field., Comment: 7 pages, 7 figures. Comments are welcome

We study the effect of magnetic field in an implosion process achieved by radiation. A time-varying sinusoidal magnetic field is seen to affect the continuous transition of space-like detonation to time-like detonation at the core of implosion region. The oscillating varying magnetic field has a significant effect in increasing the volume of the time-like detonation of the core of implosion and also modify the time of the implosion process. This transition can have significant outcome both theoretically and experimentally in the areas of high energy hadronization of quark-gluon plasma (QGP) matter and Inertial Confinement Fusion efforts of fuels., Comment: 9 pages, 8 figures

We solve the Combustion adiabat (CA) or the Chapman-Jouget adiabat equation to study the phase transition (PT) of a neutron star (NS) to a quark star (QS). The hadronic matter and quark matter equation of states are used to calculate the matter velocities on either side of the shock front. The CA with the hadronic matter as an input is solved to obtain the corresponding quark matter values. The maximum of the quark pressure is reflected in the retracing of the path in the CA curve. The downstream quark pressure maximum implies towards a maximum mass limit of a phase transformed QS which is different from the regular mass limit of an ordinary QS. Further, the characterization of velocities suggest that the PT from NS to QS is not always feasible from the center of the star. The possible mode of combustion in NSs is likely to be a slow deflagration in most of the low and intermediate density range. The result is crucial and emphasizes on the fact that PT in NSs does not always starts from the center and sometimes a NS does not suffers a PT at all., Comment: 10 pages, 8 figures (updated according to the online published version)

In this work, we have studied the dynamical evolution of the shock front in a neutron star. The shock wave is expected to possess enough strength to ignite the nuclear matter thereby converting it to quark matter. The conversion of nuclear to quark matter is assumed to take place at the shock discontinuity. The density and pressure discontinuity is studied both spatially and temporally as it starts near the center of the star and moves towards the surface. Polytropic equations of state which mimics real original nuclear matter and quark matter equations of state are used to study such dynamical phase transition. Solving relativistic hydrodynamic equations for a spherically symmetric star we have studied the phase transition assuming a considerable density discontinuity near the center. We find that as the shock wave propagates outwards, its intensity decreases with time, however the shock velocity peaks up and reaches a value close to that of light. Such fast shock velocity indicates rapid phase transition in neutron star taking place on a timescale of some tens of microseconds. Such a result is quite an interesting one, and it differs from previous calculations that the phase transition in neutron stars takes at least some tens of milliseconds. Rapid phase transition can have significant observational significance because such fast phase transition would imply quite strong gravitational wave signals but very short lived. Such short-lived gravitational wave signals would be accompanied with short-lived gamma-ray bursts and neutrino signals originating from the neutrino and gamma-ray generation from the phase transition of nuclear matter to quark matter., Comment: 10 figures, 25 pages

In this article, we present the effect of a strong magnetic field in the burning of a neutron star (NS). We have used relativistic magneto-hydrostatic (MHS) conservation equations for studying the PT from nuclear matter (NM) to quark matter (QM). We found that the shock-induced phase transition (PT) is likely if the density of the star core is more than three times nuclear saturation ($\rho_s$) density. The conversion process from NS to quark star (QS) is found to be an exothermic process beyond such densities. The burning process at the star center most likely starts as a deflagration process. However, there can be a small window at lower densities where the process can be a detonation one. At small enough infalling matter velocities the resultant magnetic field of the QS is lower than that of the NS. However, for a higher value of infalling matter velocities, the magnetic field of QM becomes larger. Therefore, depending on the initial density fluctuation and on whether the PT is a violent one or not the QS could be more magnetic or less magnetic. The PT also have a considerable effect on the tilt of the magnetic axis of the star. For smaller velocities and densities the magnetic angle are not affected much but for higher infalling velocities tilt of the magnetic axis changes suddenly. The magnetic field strength and the change in the tilt axis can have a significant effect on the observational aspect of the magnetars., Comment: 16 pages, 12 figures. Updated to match the printed version

In this letter we study the dynamics of a first order phase transition from nucleonic to quark matter in neutron stars. Using standard equations of state for these two phases we find the density range where such a transition is possible. Then we study the transformation of the star assuming that the quark core is formed via a spherical shock wave. The thermodynamical conditions in the quark core are found from the conservation laws across the transition region. Their dependence on the density and velocity of the incoming nuclear matter are studied. It is found that the shock is especially violent in the beginning of the conversion process when the velocity of the infalling matter is especially high. As the shock propagates further from the center the front velocity first increases and reaches a maximum value when the incoming velocity is around $0.2$. Finally, the front velocity quickly goes to zero when incoming matter velocity approaches zero. We have shown that the density and pressure jumps are especially large in the begining of the transition process., Comment: 5 pages, 7 figures

The possibility of meson condensation in stars and in heavy-ion collisions has been discussed in the past. Here, we study whether rho meson condensation ($\rho^{-}$) can occur in very dense matter and determine the effect of strong magnetic fields on this condensation. We find that rho meson condensates can appear in the core of the neutron star assuming a rho mass which is reduced due to in-medium effects. We find that the magnetic field has a non-negligible effect in triggering condensation., Comment: 10 pages, 3 figures

Shock waves constitute discontinuities in matter which are relevant in studying the plasma behaviour in astrophysical scenarios and in heavy-ion collision. They can produce conical emission in relativistic collisions and are also thought to be the mechanism behind the acceleration of energetic particles in active galactic nuclei and gamma ray bursts. The shocks are mostly hydrodynamic shocks. In a magnetic background they become magnetohydrodynamic (MHD) shocks. For that reason we study the space-like and time-like shock discontinuity in a magnetic plasma. The shocks induce a phase transition in the plasma, here assuming a transition from hadron to quarks. The MHD conservation conditions are derived across the shock. The conservation conditions are solved for downstream velocities and flow angles for given upstream variables. The shock conditions are solved at different baryon densities. For the space-like shocks the anisotropy in the downstream velocity arises due to the magnetic field. The downstream velocity vector always points downward with respect to the shock normal. With the increase in density the anisotropy is somewhat reduced. The magnetic field has effectively no effect on time-like shocks. The slight anisotropy in the downstream flow velocities is caused by the boosting that brings the quantities from the fluid frame to normal incidence (NI) frame., Comment: 20 pages, 6 figures

Magnetars are compact stars which are observationally determined to have very strong surface magnetic fields of the order of $10^{14}-10^{15}$G. The centre of the star can potentially have a magnetic field several orders of magnitude larger. We study the effect of the field on the mass and shape of such a star. In general, we assume a non-uniform magnetic field inside the star which varies with density. The magnetic energy and pressure as well as the metric are expanded as multipoles in spherical harmonics up to the quadrupole term. Solving the Einstein equations for the gravitational potential, one obtains the correction terms as functions of the magnetic field. Using a nonlinear model for the hadronic EoS the excess mass and change in equatorial radius of the star due to the magnetic field are quite significant if the surface field is $10^{15}$G and the central field is about $10^{18}$ G. For a value of the central magnetic field strength of $1.75\times10^{18}$ G, we find that both the excess mass and the equatorial radius of the star changes by about $3-4\%$ compared to the spherical solution., Comment: 16 pages, 4 figures

The phase transition from normal hadronic matter to quark matter in neutron stars (NS) could give rise to several interesting phenomena. Compact stars can have such exotic states up to their surface (called strange stars (SS)) or they can have quark core surrounded by hadronic matter, known as hybrid stars (HS). As the state of matter of the resultant SS/HS is different from the initial hadronic matter, their masses also differ. Therefore, such conversion leads to huge energy release, sometimes of the order of $10^{53}$ ergs. In the present work we study the qualitative energy released by such conversion. Recent observations reveal huge surface magnetic field in certain stars, termed magnetars. Such huge magnetic fields can modify the equations of state (EOS) of the matter describing the star. Therefore, the mass of magnetars are different from normal NS. The energy released during the conversion process from neutron magnetar (NM) to strange magnetar/hybrid magnetar (SS/HS) is different from normal NS to SS/HS conversion. In this work we calculate the energy release during the phase transition in magnetars. The energy released during NS to SS/HS conversion exceeds the energy released during NM to SM/HM conversion. The energy released during the conversion of NS to SS is always of the order of $10^{53}$ ergs. The amount of energy released during such conversion can only be compared to the energy observed during the gamma ray bursts (GRB). The energy liberated during NM to HM conversion is few times lesser, and is not likely to power GRB at cosmological distances. However, the magnetars are more likely to lose their energy from the magnetic poles and can produce giant flares, which are usually associated with magnetars., Comment: 14 pages, 4 figures, 4 tables

Compact stars can have either hadronic matter or can have exotic states of matter like strange quark matter or color superconducting matter. Stars also can have a quark core surrounded by hadronic matter, known as hybrid stars (HS). The HS is likely to have a mixed phase in between the hadron and quark phase. Observational results suggest huge surface magnetic field in certain neutron stars (NS) called magnetars. Here we study the effect of strong magnetic field on the respective EOS of matter under extreme conditions. We further study the hadron-quark phase transition in the interiors of NS giving rise to hybrid stars (HS) in presence of strong magnetic field. The hadronic matter EOS is described based on relativistic mean field theory and we include the effect of strong magnetic fields leading to Landau quantization of the charged particles. For the quark phase we use the simple MIT bag model. We assume density dependent bag pressure and magnetic field. The magnetic field strength increases going from the surface to the center of the star. We construct the intermediate mixed phase using Glendenning conjecture. The magnetic field softens the EOS of both the matter phases. The effect of magnetic field is insignificant unless the field strength is above $10^{14}$G. A varying magnetic field, with surface field strength of $10^{14}$G and the central field strength of the order of $10^{17}$G has significant effect on both the stiffness and the mixed phase regime of the EOS. We finally study the mass-radius relationship for such type of mixed HS, calculating their maximum mass, and compare them with the recent observation of pulsar PSR J1614-2230, which is about 2 solar mass. The observations puts a severe constraint on the EOS of matter at extreme conditions. The maximum mass with our EOS can reach the limit set by the observation., Comment: 26 pages, 19 figures, typos corrected and new citation added. arXiv admin note: text overlap with arXiv:1207.4872

Recent observation of pulsar PSR J1614-2230 with mass about 2 solar masses poses a severe constraint on the equations of state (EOS) of matter describing stars under extreme conditions. Neutron stars (NS) can reach the mass limits set by PSR J1614-2230. But stars having hyperons or quark stars (QS) having boson condensates, with softer EOS can barely reach such limits and are ruled out. QS with pure strange matter also cannot have such high mass unless the effect of strong coupling constant or colour superconductivity are taken into account. In this work I try to calculate the upper mass limit for a hybrid stars (HS) having a quark-hadron mixed phase. The hadronic matter (having hyperons) EOS is described by relativistic mean field theory and for the quark phase I use the simple MIT bag model. I construct the intermediate mixed phase using Glendenning construction. HS with a mixed phase cannot reach the mass limit set by PSR J1614-2230 unless I assume a density dependent bag constant. For such case the mixed phase region is small. The maximum mass of a mixed hybrid star obtained with such mixed phase region is $2.01 M_{\odot}$., Comment: 14 pages, 7 figures, typos corrected and citation added

Recent results and data suggests that high magnetic field in neutron stars (NS) strongly affects the characteristic (radius, mass) of the star. They are even separated as a class known as magnetars, for whom the surface magnetic field are greater than $10^{14}$ G. In this work we discuss the effect of such high magnetic field on the phase transition of NS to quark star (QS). We study the effect of magnetic field on the transition from NS to QS including the magnetic field effect in equation of state (EoS). The inclusion of the magnetic field increases the range of baryon number density, for which the flow velocities of the matter in the respective phase are finite. The magnetic field helps in initiation of the conversion process. The velocity of the conversion front however decreases due to the presence of magnetic field, as the presence of magnetic field reduces the effective pressure (P). The magnetic field of the star gets decreased by the conversion process, and the resultant QS has lower magnetic field than that of the initial NS., Comment: 8 pages, 9 figures; accepted to be published in MNRAS

Hadronic to quark matter phase transition may occur inside neutron stars (NS) having central densities of the order of 3-10 times normal nuclear matter saturation density ($n_0$). The transition is expected to be a two-step process; transition from hadronic to 2-flavour matter and two-flavour to $\beta$ equilibrated charge neutral three-flavour matter. In this paper we concentrate on the first step process and solve the relativistic hydrodynamic equations for the conversion front in presence of high magnetic field. Lorentz force due to magnetic field is included in the energy momentum tensor by averaging over the polar angles. We find that for an initial dipole configuration of the magnetic field with a sufficiently high value at the surface, velocity of the front increases considerably., Comment: 16 pages, 4 figures, same as published version of JPG, J. Phys. G: Nucl. Part. Phys. 39 (2012) 095201

Rankine-Hugoniot condition has been solved to study phase transition in astrophysical scenario mainly in the case of phase transition from neutron star (NS) to quark star (QS). The phase transition is brought about by a combustion front, which travels from the center to the surface. The equations of state and temperature plays a huge role in determining the nature of the front propagation, which brings about the phase transition in neutron stars (NSs). Magnetic field has been introduced and the modified conservation condition for the perpendicular and oblique shocks is obtained. Numerical solution of the perpendicular shock has been shown in the figures, which finds that the magnetic field helps in shock generation. It indirectly hints at the instability of the matter and thereby the NS for very high magnetic field, implying that NSs can only support finite magnetic field strength., Comment: 16 pages, 8 figures

The estimate of the energy deposition rate (EDR) for neutrino pair annihilation has been carried out. The EDR for the neutrinos coming from the equatorial plane of a rotating neutron star is calculated along the rotation axis using the Cook-Shapiro-Teukolsky (CST) metric. The neutrino trajectories and hence the neutrino emitted from the disk is affected by the redshift due to disk rotation and gravitation. The EDR is very sensitive to the value of the temperature and its variation along the disk. The rotation of the star has a negative effect on the EDR; it decreases with increase in rotational velocity., Comment: 17 pages, 5 figures

Neutron stars provide a natural laboratory to test some unique implications of Quantum Chromodynamics (QCD)- the underlying theory of strong interactions- at extreme conditions of very high baryon density. It has been suggested that the true ground state of QCD is strange quark matter, and, consequently, neutron stars should convert to strange quark stars under suitable conditions. Substantial efforts have been, and are being, spent in studying the details of such conversion. In this letter, we show that the presence of high magnetic field, an essential feature of neutron stars, strongly inhibits the conversion of neutron stars to bare quark stars., Comment: 9 pages, 4 figures

A detailed general relativistic (GR) calculation of the neutrino path for a general metric describing a rotating star is studied. We have calculated the neutrino path along a plane, with the consideration that the neutrino does not at any time leave the plane. The expression for the minimum photosphere radius (MPR) is obtained and matched with the Schwarzschild limit. The MPR is calculated for the stars with two different equations of state (EOS) each rotating with two different velocities. The results shows that the MPR for the hadronic star is much greater than the quark star and the MPR increases as the rotational velocity of the star decreases. The MPR along the polar plane is larger than that along the equatorial plane., Comment: 13 pages, 5 figures and 1 table

The conversion of neutron star to strange star is argued to be a two step process. The first process involves the deconfinement of nuclear to two-flavour quark matter. The GR results shows that the propagating front breaks up into fragments which propagate with different velocities along different directions. The time taken for this conversion to happen is of the order of few $ms$. This calculation indicates the inadequacy of non-relativistic (NR) or even Special Relativistic (SR) treatments for these cases., Comment: 4 pages, 4 figures

We investigate the General Relativistic (GR) effects on the conversion from nuclear to two-flavour quark matter in compact stars, both static as well as rotating. We find that GR effects lead to qualitative differences in rotating stars, indicating the inadequacy of non-relativistic (NR) or even Special Relativistic (SR) treatments for these cases., Comment: 4 pages, 4 figures