We study the effect of titled magnetic axis in a slowly rotating magnetar. We present our problem... more We study the effect of titled magnetic axis in a slowly rotating magnetar. We present our problem in a GR framework and solve it using a perturbative approach. We assume that the magnetar's rotational speed is small and had neglected rotational distortion. We consider a strong poloidal magnetic field in the star which imparts considerable distortion along the magnetic axis. The frame dragging due to the rotation of such a magnetar arises both from the $\theta$ and $\phi$ direction. We solve the Einstein equation up to 1st order perturbation in rotation and second-order perturbation in the magnetic field to obtain the equation of motion. Solving the equation of motion, we find the geodesic of a particle near the surface of the star, and we find that the path of the particle bends southwards due to the $\theta$ contribution. The bending of the path of the particle depends both on the magnetic field strength and also on the extent of misalignment of the magnetic and rotational axis.
Aims. To study the multimessenger nature of the signal that can result from the phase transition ... more Aims. 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...
The occurrence of quark matter at the center of neutron stars is still in debate. This study defi... more 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 c...
Monthly Notices of the Royal Astronomical Society, 2015
We study the possibility of vector (ρ −) meson condensation in dense matter subject to strong mag... more We study the possibility of vector (ρ −) meson condensation in dense matter subject to strong magnetic fields. For this purpose, we adopt a standard relativistic equation of state (GM3). We find that rho-meson condensates can appear in the core of the neutron star as the rho mass decreases with density and magnetic field. For reasonable values of the parameters, the rho condensate can appear in a neutron star at 4.4 times the normal nuclear matter density. This number guarantees a sizeable portion of the star to have a ρ-condensed phase.
Monthly Notices of the Royal Astronomical Society, 2021
This paper studies the maximum mass limit of the hybrid star formed after the shock-induced phase... more This paper studies the maximum mass limit of the hybrid 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 ma...
Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magneti... more 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.
Journal of Physics G: Nuclear and Particle Physics, 2020
Charged particles at the crust of compact stars may be ejected and accelerated by the electric fi... more 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.
In this study we derive the magnetized Taub adiabat equations from the hydrodynamic conservation ... more 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.
Monthly Notices of the Royal Astronomical Society, 2019
We solve the Combustion adiabat (CA) or the Chapman-Jouget adiabat equation to study the phase tr... more 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 centre 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 centre and sometimes an NS does not suffers a PT at all.
In this paper, we present the effect of a strong magnetic field in the burning of a neutron star ... more In this paper, 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 ([Formula: see text]) 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 th...
Neutron stars feature extremely high magnetic fields with deduced field strengths of $10^{15}$ G ... more Neutron stars feature extremely high magnetic fields with deduced field strengths of $10^{15}$ G in the case of magnetars and potentially much higher values inside of the star. In this context we consider the appearance of $\rho^-$ meson condensation taking into account the effect of the magnetic field. The results show that, depending on parameters, such a condensation in magnetized neutron stars might (just) occur.
Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavi... more Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavior 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 $\ensuremath{\gamma}$-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 impact 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 a normal incidence frame.
We investigate the General Relativistic (GR) effects on the conversion from nuclear to two-flavou... more 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.
We study the effect of titled magnetic axis in a slowly rotating magnetar. We present our problem... more We study the effect of titled magnetic axis in a slowly rotating magnetar. We present our problem in a GR framework and solve it using a perturbative approach. We assume that the magnetar's rotational speed is small and had neglected rotational distortion. We consider a strong poloidal magnetic field in the star which imparts considerable distortion along the magnetic axis. The frame dragging due to the rotation of such a magnetar arises both from the $\theta$ and $\phi$ direction. We solve the Einstein equation up to 1st order perturbation in rotation and second-order perturbation in the magnetic field to obtain the equation of motion. Solving the equation of motion, we find the geodesic of a particle near the surface of the star, and we find that the path of the particle bends southwards due to the $\theta$ contribution. The bending of the path of the particle depends both on the magnetic field strength and also on the extent of misalignment of the magnetic and rotational axis.
Aims. To study the multimessenger nature of the signal that can result from the phase transition ... more Aims. 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...
The occurrence of quark matter at the center of neutron stars is still in debate. This study defi... more 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 c...
Monthly Notices of the Royal Astronomical Society, 2015
We study the possibility of vector (ρ −) meson condensation in dense matter subject to strong mag... more We study the possibility of vector (ρ −) meson condensation in dense matter subject to strong magnetic fields. For this purpose, we adopt a standard relativistic equation of state (GM3). We find that rho-meson condensates can appear in the core of the neutron star as the rho mass decreases with density and magnetic field. For reasonable values of the parameters, the rho condensate can appear in a neutron star at 4.4 times the normal nuclear matter density. This number guarantees a sizeable portion of the star to have a ρ-condensed phase.
Monthly Notices of the Royal Astronomical Society, 2021
This paper studies the maximum mass limit of the hybrid star formed after the shock-induced phase... more This paper studies the maximum mass limit of the hybrid 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 ma...
Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magneti... more 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.
Journal of Physics G: Nuclear and Particle Physics, 2020
Charged particles at the crust of compact stars may be ejected and accelerated by the electric fi... more 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.
In this study we derive the magnetized Taub adiabat equations from the hydrodynamic conservation ... more 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.
Monthly Notices of the Royal Astronomical Society, 2019
We solve the Combustion adiabat (CA) or the Chapman-Jouget adiabat equation to study the phase tr... more 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 centre 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 centre and sometimes an NS does not suffers a PT at all.
In this paper, we present the effect of a strong magnetic field in the burning of a neutron star ... more In this paper, 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 ([Formula: see text]) 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 th...
Neutron stars feature extremely high magnetic fields with deduced field strengths of $10^{15}$ G ... more Neutron stars feature extremely high magnetic fields with deduced field strengths of $10^{15}$ G in the case of magnetars and potentially much higher values inside of the star. In this context we consider the appearance of $\rho^-$ meson condensation taking into account the effect of the magnetic field. The results show that, depending on parameters, such a condensation in magnetized neutron stars might (just) occur.
Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavi... more Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavior 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 $\ensuremath{\gamma}$-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 impact 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 a normal incidence frame.
We investigate the General Relativistic (GR) effects on the conversion from nuclear to two-flavou... more 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.
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Papers by RITAM MALLICK