arXiv subjects

Ritam Mallick

Publications and source records attributed to Ritam Mallick.

At least 19 recordsLinked to original sources

arXiv2026

Relativistic Oblique Shocks at Finite Temperature: Detachment Angle, Shock Polars, and the Turning Parameter

Oblique shocks are ubiquitous in high-energy astrophysical environments, yet a systematic analytical treatment of how finite upstream temperature influences the maximum deflection angle has been lacking. We address this problem by developing a unified thermodynamic framework based on a novel dimensionless quantity, the turning parameter, which encapsulates the equation of state, upstream Mach number, and thermal state of the flow into a single variable. Starting from the relativistic Rankine-Hugoniot conditions and the Taub adiabat, we derive a compact turning relation and a first-order perturbative expansion in the upstream thermal parameter. We show that any finite upstream temperature monotonically suppresses the maximum deflection angle relative to the cold-fluid limit, implying that cold models systematically overestimate shock attachment. In the combined ultra-thermal and ultra-relativistic limit, the turning parameter saturates to a universal value, yielding an asymptotic detachment angle that depends only on the equation of state. Numerical shock-polar calculations validate the analytical results and reveal a non-monotonic dependence of the detachment angle on the Mach number at intermediate temperatures, arising from the competition between thermal pressure and bulk kinetic energy-a distinctly relativistic thermal effect absent in both the cold and ultra-hot limits. As an illustrative astrophysical application, we apply the framework to the Crab pulsar wind nebula, demonstrating how finite-temperature effects modify the termination-shock morphology and the observed torus geometry.

astro-ph.HE↗

arXiv2026

Constraining the High-Density Equation of State with Present and Future NICER Observations Using Physics-Informed Regularized Machine Learning

The precise mass and radius measurements of neutron stars by NICER have significantly advanced our ability to constrain the properties of matter at supranuclear densities. In this work, we develop a physics-informed regularized conditional Invertible Neural Network (cINN) that bijectively maps mass--radius posterior distributions directly onto the corresponding central energy density and pressure, eliminating the need for explicit high-dimensional parameter sampling. The physics-informed regularisation guarantees that all inferred solutions satisfy causality and thermodynamic stability, ensuring physically consistent predictions without explicit forward modelling. We demonstrate that the framework accurately reconstructs central EoS posteriors for NICER-like observations while preserving the mapping between macroscopic stellar observables and the microscopic properties of dense matter. Exploiting the computational efficiency of the cINN, we perform a systematic optimisation study of 62,400 simulated mass--radius observations to identify the most informative targets for constraining the high-density EoS. We find that the constraining power depends strongly on the location of the observation in the mass--radius plane, with an optimal strategy that alternates between compact high-mass stars and extended intermediate-mass stars, reducing the uncertainty in the inferred EoS by up to $\sim 9\%-10\%$ relative to the current NICER baseline. These results establish physics-informed invertible neural networks as a powerful framework for rapid, physically consistent inference of dense-matter properties from present and future multi-messenger observations.

astro-ph.HE↗

arXiv2026

Neutron stars with an agnostic Dark sector: Core and Halo configurations from a two-fluid approach

The study of dark matter admixed neutron stars has the potential to advance our understanding of dark matter particle candidates. However, the large parameter space of dark matter particle masses restricts a systematic, model-independent study. In this analysis, we employ agnostic hadronic and dark matter equations of state to construct dark-matter-admixed neutron stars within a two-fluid formalism. Dark matter is characterised solely by its low-density equation of state and mass, and is modelled as a Fermi gas, while hadronic matter is anchored at low and high densities by chiral effective field theory and perturbative quantum chromodynamics calculations. A speed-of-sound parametrisation covers the intermediate density region for hadronic matter and the high-density region for dark matter, so the dark matter equation of state is constrained only by thermodynamic consistency, free from bias toward a softer or stiffer equation of state. Within this agnostic framework, we find that dark matter does not generically compactify the star: light dark matter forms extended halos that raise the tidal deformability, while heavy dark matter forms compact cores that lower it. Consequently, the dominant observational constraint shifts from gravitational-wave tidal deformability for light, halo-dominated models to NICER mass--radius data for heavy, core-dominated models. Using current data at $1\sigma$, we constrain the dark matter fraction to $f_{\mathrm{DM}} \lesssim 0.11$ for light dark matter. Being almost independent of any assumed dark-sector microphysics, our framework yields conservative, broadly applicable bounds on the dark-matter content of neutron stars. Neutron stars with similar masses but very different tidal deformabilities could be a smoking-gun signature of dark matter in Neutron stars.

astro-ph.HE↗

arXiv2026

Semantic Retrieval for Product Search in E-Commerce

Semantic retrieval in e-commerce must handle short, noisy, and colloquial queries over large product catalogs with fine-grained attribute distinctions. We present a Siamese LLM dual-encoder trained through a two-stage pipeline: contrastive learning with a false-negative margin mask to prevent penalization of near-duplicate products, followed by Relative Odds Alignment for Retrieval (ROAR), a preference optimization objective that extends Bradley-Terry to variable-sized graded relevance groups via consecutive odds-ratio margins. The training corpus mirrors this progression - substitute query-product pairs provide coarse semantic supervision in Stage 1 and graded relevance annotations drive fine-grained ranking in Stage 2. The resulting system accurately retrieves exact matches while correctly ordering substitutes and complementary products, with gains confirmed across query-frequency strata and business verticals, and statistical significance validated through live A/B deployment at scale.

cs.IR↗

arXiv2026

A geometric physics-informed machine learning inference for the neutron star maximum mass and the inverse problem

The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. The study addresses these problems with a physics-informed machine learning approach, guided by astrophysical observations. The Transformer model is trained on an agnostically generated ensemble of equations of state. Two geometric parameters are defined on the mass-radius sequence of a neutron star--the front bending and the back bending. The transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. Second, it predicts the square of the sound speed profile, completing the inverse mapping. The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. The maximum mass for a neutron star predicted by the astrophysical constrained transformer model is $2.477$ solar masses, and a minimum radius of about $11.498$ km for a neutron star of $1.4$ solar masses.

astro-ph.HE↗

arXiv2026

Dynamical response of twin stars to perturbations

If a strong first-order phase transition takes place at sufficiently high rest-mass densities in the equation of state (EOS) modelling compact stars, a new branch will appear in the mass-radius sequence of stable equilibria. This branch will be populated by stars comprising a quark-matter core and a hadronic-matter envelope, i.e., hybrid stars, which represent ``twin-star'' solutions to equilibria having the same mass but a fully hadronic EOS. While both branches are stable to linear perturbations, it is unclear which of the twin solutions is the ``favoured'' one, that is, which of the two configurations is expected to be found in nature. We assess this point by performing a large campaign of general-relativistic simulations aimed at assessing the response of compact stars on the two branches to perturbations of various strength. In this way, we find that, independently of whether the stars populate the hadronic or the twin branch, their response is characterised by a critical-perturbation strength such that the star will oscillate on the original branch for subcritical perturbations and migrate to the neighbouring branch for supercritical perturbations while conserving rest-mass. Because the critical values are different for stars with the same rest-mass but sitting on either branch, it is possible to define as favoured the part of the branch that has the largest critical perturbation, thus correcting the common wisdom that stellar models on the twin branch are the favoured ones. Interestingly, we show that the binding energies on the two branches can be used to deduce without simulations which of the stellar configurations is more likely to be found in nature.

gr-qc↗

arXiv2026

Investigating Twin Star Equation of States in Light of Recent Astrophysical Observations

Twin stars are predicted to exist in nature if the hadron-to-quark phase transition is strong enough to form a new branch of hybrid stars, separated from the branch of neutron stars. We adopt an agnostic approach, using transition energy density, transition pressure, the discontinuity strength, and a constant speed of sound for quark matter as our parameter space to construct a large possibility of hybrid equations of state, and thereby encapsulating a comprehensive picture of the twin star scenario. First, we report the complete conditions on our parameter space imposed by the general relativistic hydrostatic equilibrium solutions. For a fixed transition energy density and speed of sound for quark matter, we define distinct ranges of transition pressures based on the allowed strengths of discontinuity. Below a maximum transition pressure, a range of discontinuity exists that increases as the transition pressure decreases. Thereby, we identify the loci of the limits on discontinuities as the `witch-hat' curves. Based on the causality limit, the witch-hat curves can be punctured or incomplete. Strong constraints on this picture are drawn from the inferences from GW170817 and the NICER measurements. We computed the maximum mass for twin stars to be $2.05~M_\odot$, the allowed strongest discontinuity in rest-mass density to be $7.76\rho_\mathrm{sat}$, and the upper bound on transition rest-mass density to be $4.03\rho_\mathrm{sat}$. Subsequently, we compute the implications of the stiffness of the quark matter equation of state on this picture. Different confidence levels for observational inferences are considered to assess the extent of inclusion (and rejection) of hybrid equations of state and, consequently, their effects on the limits of the maximum mass of twin stars and phase transition properties.

astro-ph.HE↗

arXiv2026

Curvature Effect on the Speed of Sound

The speed of sound refers to the rate at which information travels from one point to another. It is a positive quantity and bounded by causality. It is defined as the rate of change of pressure with respect to the system's density. In this article, we derive a covariant equation for the sound wave and demonstrate how the wave equation is modified in the general relativistic formalism. One can then define an effective speed of sound by attenuating the usual definition of sound speed with the gravitational metric potential. The general relativistic curvature effect is observed to reduce the speed of sound when computed inside a neutron star. This effectively makes the star relatively softer (according to the equation of state). The change in the effective sound speed can be easily visualised if one redefines the non-radial modes in terms of it. The modes do not change, but the space-time curvature reduces the amplitude of the oscillation modes. The formalism is suited for studying astrophysical compact objects.

astro-ph.HE↗

arXiv2025

Are NICER and GW170817 constraints suggesting a compactified scenario for Neutron stars?

Astrophysical observations from NICER and gravitational wave data constrain the properties of matter at the cores of neutron stars, enabling us to probe high-density matter with greater accuracy. To understand its implications for neutron stars, three distinct class-agnostic equation-of-state ensembles are constructed using the speed-of-sound parametrisation, which can describe matter in neutron-star cores. Bayesian analysis is employed to constrain the parameters, namely, the squared speed of sound and chemical potential, using the observational data. The Bayesian inference shows that the observations effectively constrain the low-density region of the equation of state. The astrophysical bound favours a softer, low-density equation of state in which the phase transition occurs at intermediate densities, thereby reducing the upper mass bounds for neutron stars. For the equation of state with density discontinuity, the discontinuities are preferably small. The equation of state with maximum mass configuration shows considerable stiffening from very low density, providing pressure support to generate maximum mass. In contrast, the equation of state with the maximum compact stellar configuration has a softer low-density equation of state, followed by pronounced stiffening, yielding the maximum compact configuration. The observationally favoured EoS shares the same qualitative structure as the maximum-compactness EoS: relative softness at intermediate densities transitioning to stiffness at high densities, a configuration gravity naturally favours.

astro-ph.HE↗

arXiv2025

Imprints of Non-Symmetric Dark Matter Halos on Magnetars: A Two-Fluid Perspective

In this study, we investigate the impact of dark matter on the structure and deformation of magnetars. We assume a perturbative approach for the magnetic field deformation and that the dark matter only interacts gravitationally with hadronic matter. Assuming that dark matter is significantly softer than hadronic matter, we find that the magnetic field can affect dark matter through the deformation of space-time. The number of stars having a dark matter halo outside the visible surface of the star increases with an increase in dark matter fraction and the stiffness of the dark matter equation of state. As the magnetic field deforms the stars from sphericity, we can have a situation where we have a non-symmetric dark matter halo outside the star. The deformation of the dark matter halo gives rise to the discrepancies in the observed period $P$ (and period derivative $\dot{P}$) and gravitational wave signatures. The observed visible surfaces predict a lower period and gravitational wave strain than that with a dark matter halo. This can have interesting observational gravitational signatures unique to magnetars having a dark matter halo.

astro-ph.HE↗

arXiv2025

Distinct Signatures of the Nature of Phase Transition in Binary Neutron Star Mergers

Binary neutron-star mergers offer crucial insights into the matter properties of neutron stars. We present the possible imprints in the gravitational wave signal from the nature of phase transition from such events. Our study employs a one-parameter family of equation of states built using a polytropic approach with a control parameter $\Delta p$ surveying the features of hadron-quark phase transition, from Maxwell construction to the Gibbs construction. It allows us to explore the extent of mixed phases and analyse their direct impact on merger dynamics. Post-merger gravitational wave emissions reveal the expression of specific signatures in the spectrogram and power spectral density, serving as a distinct signature of equations of state with mixed phases. We found additional peaks in power spectral density that are exclusively generated from the post-merger remnant experiencing a phase transition. Additionally, the nature of phase transition leaves specific imprints on the spectrogram, leading to a two-folded signature from gravitational wave analysis. Furthermore, we establish the first correlation between $\Delta p$ and the threshold mass for prompt collapse. Our analysis shows that $\Delta p \lesssim 0.04$ is required if GW170817 formed a long-lived remnant or has experienced a delayed collapse into a black hole.

astro-ph.HE↗

arXiv2025

Probing the Internal Structure of Neutron Stars: A Comparative Analysis of Three Different Classes of Equations of State

Sound speed can be an important tool in unraveling the nature of matter that exists at the cores of neutron stars. In this study, we investigate three major classes of equations of state; monotonous, non-monotonous and discontinuous depending on the nature of the sound speed in neutron stars. The monotonous EoS refers to hadronic models, the non-monotonous refers to the quarkyonic or smooth crossover models and discontinuous refers to discontinuous first-order phase transition models. We generate a large ensemble of EoS for three classes with the model agnostic speed of sound interpolation approach. Our main aim is to check which class of EoS is most favoured by present astrophysical bounds. It is seen that although non-monotonous and discontinuous is favoured thermodynamically, the usual neutron star observations like mass-radius, and f-mode oscillation fail to provide a satisfactory result. The universal relations are also seen to be futile as they show considerable spread and significant overlaps among the different classes. The Bayesian analysis shows slight bias towards the non-monotonous model but fails to provide a decisive answer.

astro-ph.HE↗

arXiv2025

Comparison of Equations of State for Neutron Stars with First-Order Phase Transitions: A Qualitative Study

The equation of state is fundamental in describing matter under the extreme conditions characteristic of neutron stars and is central to advancing our understanding of dense matter physics. A critical challenge, however, lies in accurately modelling first-order phase transitions while ensuring thermodynamic consistency and aligning with astrophysical observations. This study explores two frameworks for constructing EoSs with first-order phase transitions: the polytropic interpolation method and the randomized speed-of-sound interpolation approach. It is found that the mass-radius relation and pressure vs. energy density relation are blind towards the thermodynamic consistency check. The polytropic interpolation method can exhibit discontinuities in the chemical potential for first-order phase transition, raising concerns regarding potential causality violations and thermodynamic inconsistencies. In contrast, the speed of sound interpolation approach ensures continuity in the chemical potential, offering a more thermodynamically consistent and reliable framework. Moreover, the sound speed method effectively captures the softer segment of the mass-radius spectrum, a capability not achieved by the consistent piecewise-polytropic approach due to its monotonic stiffness constraints. The speed of sound definition involving number density and chemical potential reveals the thermodynamic inconsistency, making it a more consistent and robust definition. These findings underscore the importance of thermodynamic consistency in EoS construction and highlight the advantages of the randomized speed-of-sound method for modelling phase transitions in dense matter.

astro-ph.HE↗

arXiv2024

Causality for first-order phase transition and its implication on the maximum mass of neutron stars

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.

astro-ph.HE↗

arXiv2024

Analyzing the dense matter equation of states in the light of the compact object HESS J1731-347

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 prefer the hybrid equation of states the most.

astro-ph.HE↗

arXiv2024

Modification of the universal relation between mass, radius and nonradial $f$-mode oscillation in proto-neutron stars

Neutron stars are usually assumed to be cold; however, in certain dynamical astrophysical scenarios such as newly born neutron stars or binary star mergers, the temperature effects play a non-negligible role. We systematically derive the equation of state at finite-temperature within a relativistic mean-field hadronic model applicable to such proto-neutron stars. The equation of state so derived considerably affects the mass-radius curve, thereby affecting the nonradial quadruple $f$-mode oscillation frequencies.} Temperature effectively makes the equation of state stiffer at relatively low and intermediate densities, thereby making the star less compact and flattening the mass-radius curve. 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 nonlinearly 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.

astro-ph.HE↗

arXiv2024

The prospect of confining the equation of state of neutron star with future mass and radius measurement

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.

astro-ph.SR↗

arXiv2024

Prospect of unraveling the first-order phase transition in neutron stars with $f$ and $p_1$ modes

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.

gr-qc↗