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The Lense-Thirring effect from spinning neutron stars in double neutron star binaries contributes to the periastron advance of the orbit. This extra term involves the moment of inertia of the neutron stars. The moment of inertia, on the other hand, depends on the mass and spin of the neutron star, as well as the equation of state of the matter. If at least one member of the double neutron star binary (better the faster one) is a radio pulsar, then accurate timing analysis might lead to the estimation of the contribution of the Lense-Thirring effect to the periastron advance, which will lead to the measurement of the moment of inertia of the pulsar. The combination of the knowledge on the values of the moment of inertia, the mass and the spin of the pulsar will give a new constraint on the equation of state. Pulsars in double neutron star binaries are the best for this purpose as short orbits and moderately high eccentricities make the Lense-Thirring effect substantial, whereas tidal effects are negligible (unlike pulsars with main sequence or white-dwarf binaries). The most promising pulsars are PSR J0737 − 3039A and PSR J1757 − 1854. The spin-precession of pulsars due to the misalignment between the spin and the orbital angular momentum vectors affect the contribution of the Lense-Thirring effect to the periastron advance. This effect has been explored for both PSR J0737 − 3039A and PSR J1757 − 1854, and as the misalignment angles for both of these pulsars are small, the variation in the Lense-Thirring term is not much. However, to extract the Lense-Thirring effect from the observed rate of the periastron advance, more accurate timing solutions including precise proper motion and distance measurements are essential.

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-\\[\\mu \\]Hz 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 \\[\\mu \\]s 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-\\[\\mu \\]Hz gravitational waves apart from auxiliary pulsar science. Future directions for these experiments are outlined.

We investigate f-mode oscillations of anisotropic quark stars within the framework of full general relativity. We consider two different equations of state (EOSs), one is the MIT bag model EOS and the other is EOS-A. Our study examines the impact of the pressure anisotropy on the equilibrium structure, as well as on the frequencies and damping times of f-mode oscillations. Our results confirm that the f-mode frequency scales linearly with the square root of the average density, with anisotropy influencing both the slope and intercept of this relation. The dependence of the f-mode frequency on total mass reveals distinct trends based on the relative dominance of tangential and radial pressure. When the tangential pressure exceeds the radial pressure, the frequency increases with mass, exhibiting rapid growth for massive quark stars. When the radial pressure dominates, the frequency increases with mass; however, in cases where the radial pressure is significantly greater than the tangential pressure, the frequency decreases as mass increases. For low-mass quark stars, stronger tangential pressure leads to an increase in frequency, while beyond a threshold mass, a further increase in tangential pressure results in a decrease in frequency. For the chosen range of anisotropic strengths, the frequency varies between 1.3 kHz and 2.3 kHz for the MIT bag EOS and between 1.8 kHz and 3.4 kHz for EOS-A. We find that the normalized damping time follows a linear trend with compactness. For a fixed stellar mass, an increase in tangential pressure relative to radial pressure reduces the damping time, whereas a decrease in tangential pressure significantly increases it. The damping time ranges from 83 ms to 900 ms for the MIT bag EOS and from 60 ms to 761 ms for EOS-A. We present semi-empirical expressions for both the frequency and damping time as functions of mass, radius, and anisotropic strength.

The Square Kilometre Array (SKA), when it becomes functional, is expected to enrich Neutron Star (NS) catalogues by at least an order of magnitude over their current state. This includes the discovery of new NS objects leading to better sampling of under-represented NS categories, precision measurements of intrinsic properties such as spin period and magnetic field, as also data on related phenomena such as microstructure, nulling, glitching, etc. This will present a unique opportunity to seek answers to interesting and fundamental questions about the extreme physics underlying these exotic objects in the Universe. In this paper, we first present a meta-analysis (from a methodological viewpoint) of statistical analyses performed using existing NS data, with a two-fold goal. First, this should bring out how statistical models and methods are shaped and dictated by the science problem being addressed. Second, it is hoped that these analyses will provide useful starting points for deeper analyses involving richer data from SKA whenever it becomes available. We also describe a few other areas of NS science which we believe will benefit from SKA which are of interest to the Indian NS community.

It is an exceptionally opportune time for astrophysics when a number of next-generation mega-instruments are poised to observe the Universe across the entire electromagnetic spectrum with unprecedented data quality. The Square Kilometre Array (SKA) is undoubtedly one of the major components of this scenario. In particular, the SKA is expected to discover tens of thousands of new neutron stars giving a major fillip to a wide range of scientific investigations. India has a sizeable community of scientists working on different aspects of neutron star physics with immediate access to both the uGMRT (an SKA pathfinder) and the recently launched X-ray observatory Astrosat. The current interests of the community largely centre around studies of (a) the generation of neutron stars and the SNe connection, (b) the neutron star population and evolutionary pathways, (c) the evolution of neutron stars in binaries and the magnetic fields, (d) the neutron star equation of state, (e) the radio pulsar emission mechanism, and (f) the radio pulsars as probes of gravitational physics. Most of these studies are the main goals of the SKA first phase, which is likely to be operational in the next four years. This article summarizes the science goals of the Indian neutron star community in the SKA era, with significant focus on coordinated efforts among the SKA and other existing/upcoming instruments.

We study the effect of light-bending on the signal of a pulsar in binaries with rotating black hole companions, focusing on stellar mass black holes. We show that the impacts of various parameters on the bending delays visually match with those observed for a non-rotating black holes, because the magnitude of the spin as well as the orientation of the spin axis of the black hole introduce changes in the nanosecond order and other parameters do so in the microsecond order. Consequently, the distortion of the beam and the resulting changes in the pulse shape are minimally influenced by spin-related parameters of the black hole. We also investigate the impact of various parameters on the difference of the delays with and without the spin of the black hole and notice nanosecond scale discontinuities at orbital phases where the path of the light ray changes its direction with respect to the direction of the spin of the black hole. Moreover, as in the Schwarzschild case, the bending delays become irregular (on the microsecond scale) near the superior conjunction. We also explore the effect of bending on the pulse profiles and bending delays if the companion of the pulsar is a rotating super-massive black hole. We find significant enhancement and change in the shape of the profiles at and near the superior conjunction in comparison to stellar mass black holes. Moreover, bending delays are about three orders of magnitude higher than those in case of the stellar mass black holes.

The Lense-Thirring effect from spinning neutron stars in double neutron star binaries contribute to the periastron advance of the orbit. This extra term involves the moment of inertia of the neutron stars. Moment of inertia, on the other hand, depends on the mass and spin of the neutron star as well as the equation of state of the matter. If at least one member of the double neutron star binary (better the faster one) is a radio pulsar, then accurate timing analysis might lead to the estimation of the contribution of the Lense-Thirring effect to the periastron advance, which will lead to the measurement of the moment of inertia of the pulsar. Combination of the knowledge on the values of the moment of inertia, the mass, and the spin of the pulsar, will give a new constraint on the equation of state. Pulsars in double neutron star binaries are the best for this purpose as short orbits and moderately high eccentricities make the Lense-Thirring effect substantial, whereas tidal effects are negligible (unlike pulsars with main sequence or white-dwarf binaries). The most promising pulsars are PSR J0737-3039A and PSR J1757-1854. The spin-precession of pulsars due to the misalignment between the spin and the orbital angular momentum vectors affect the contribution of the Lense-Thirring effect to the periastron advance. This effect has been explored for both PSR J0737-3039A and PSR J1757-1854, and as the misalignment angles for both of these pulsars are small, the variation in the Lense-Thirring term is not much. However, to extract the Lense-Thirring effect from the observed rate of the periastron advance, more accurate timing solutions including precise proper motion and distance measurements are essential.

The observed values of the time-derivatives of the spin or orbital frequency of pulsars are affected by their dynamical properties. We derive thorough analytical expressions for such dynamical contributions in terms of the Galactic coordinates, the proper motion, the pulsar distance, and the radial velocity. We find that the effects of the dynamical terms in the second-derivative of frequencies or parameters based on such second derivatives, e.g., braking index, are usually negligible. However, unique pulsars for which the effects of the dynamical terms are significant can exist. In particular, dynamical effects can make the magnitude of the observed value of the braking index to be in the order of thousand while the true value of it is close to the theoretically expected value three, especially if the pulsars lie close to the Galactic centre. Dynamics can also affect the value of the second derivative of the orbital frequency of a binary pulsar at the first decimal place. We also emphasize the fact that our expressions provide more accurate results than pre-existing approximate ones that exclude some of the terms. Comparison with a set of pulsars showed that the median value of the difference between the results obtained by our method and a pre-existing method is about 50 percent.

We investigate f-mode oscillations of static anisotropic stable neutron stars within the framework of full general relativity. We present equations governing unperturbed stellar structures and oscillations with an ansatz to account for the anisotropy. We solve those equations for two different equations of states. We see that, moderately anisotropic neutron stars with the tangential pressure larger than the radial pressure can give more massive neutron stars than the isotropic or very anisotropic ones. We find that the frequency of the f-mode exhibits a linear relationship with the square root of the average density of the stars and the slope of the fit depends on the anisotropic strength. For any given value of the anisotropic strength, the frequency increases with the increase of the mass of the neutron star, linearly for lower masses, and rapidly at higher masses. However, this non-linear rise in the frequency with the mass is not prominent when the radial pressure is larger than the tangential pressure. For a fixed value of a small mass, higher anisotropy leads to a larger value of the frequency, but when the fixed mass is above a threshold value, higher anisotropy leads to a smaller value of the frequency. The nature of the variation in the frequency with the change in the anisotropic strength is similar for the two equations of state, but for a fixed mass and the same amount of the anisotropy, the softer equations of state gives higher frequency. We also find that the damping time of the f-mode oscillation decreases as the mass of the neutron star increases for all values of the anisotropic strength. For a fixed mass of the neutron star and for the same amount of the anisotropy, the value of the damping time is lower for the softer equation of state, but the nature of the variation in the damping time with the change in the anisotropic strength is similar.

The values of the bending delays in the signal of a radio pulsar in a binary with a stellar mass black hole as a companion have been calculated accurately within a full general relativistic framework considering the Schwarzchid spacetime near the companion. The results match with the pre-existing approximate analytical expressions unless both of the orbital inclination angle and the orbital phase are close to \\(90^{\\circ}\\). For such a case, the approximate analytical expressions underestimate the value of the bending delay. On the other hand, for systems like the double pulsar, those expressions are valid throughout the orbital phase, unless its inclination angle is very close to 90 degrees. For a pulsar-black hole binary, the bending phenomenon also increases the strength of the pulse profile and sometimes can lead to a small low intensity tail.