Mass-radius Curves Research Articles

Exploring the macroscopic properties of proto-neutron stars: Effects of entropy and lepton fraction

Neutron stars (NSs) have generally been considered as cold, zero-temperature entities. Recent progress in computational methods and theoretical modelling has opened up the exploration of finite temperature effects, marking an important research frontier. We examine the macroscopic properties of Proto-Neutron Stars (PNS) using different parametrizations of relativistic mean field (RMF) models. We adopt a constant entropy approach by fixing entropy per baryon, S=1 and 2. Higher S elevates the maximum mass for PNS and flattens the mass-radius curves. The higher lepton fraction (Yl) leads to a decrease in maximum mass and an increase in the canonical radius. Furthermore, both the S and Yl influence the dimensionless tidal deformability (Λ). We note that the f-mode frequencies in PNSs increase as S decreases and the Yl increases at maximum mass. We find that the macroscopic properties of the PNS exhibit the same trend, irrespective of the parameter sets employed for the variation of S and Yl.

Constraining neutron star matter from the slope of the mass-radius curves

Constraining neutron star matter from the slope of the mass-radius curves

Mardigras: A Visualization Tool of Theoretical Mass–Radius Relations in the Context of Planetary Science

Over the past two decades, mass–radius relations have become a crucial tool for inferring the bulk composition of exoplanets using only their measured masses and radii. These relations, often referred to as isocomposition curves, are derived from interior structure models by calculating the theoretical radius as a function of mass for a given fixed planetary composition. Each mass–radius curve can be influenced by a variety of parameters, such as planetary composition, age, and equilibrium temperature. Navigating this parameter space can be cumbersome, particularly when models or their results are not open-source. To address this challenge, I have developed MAss–Radius DIaGRAm with Sliders, a visualization tool that enables simple, fast, and interactive exploration of the parameter space that governs mass–radius relations for any given model.

Effect of decoupling parameters on maximum allowable mass of anisotropic stellar structure constructed by mass constraint approach in f(Q)-gravity

In the present article anisotropic solutions with vanishing complexity in the framework of f(Q) gravity are generated. At first, the field equations in f(Q)-gravity are gravitationally decoupled where the isotropic fluid component corresponds to Vlasenko–Pronin space-time. Then, with a new source, the complete geometric deformation is supplemented to an isotropic component, and the related deformation function is derived by the method known as mimicking of mass constraints. Furthermore, the generated anisotropic solution prevails all the physical tests along with the stability analysis with respect to the decoupling parameter as well as the f(Q) gravity parameter and it accomplishes the physical representation of observational constraint related to stars, namely, SMC X-1, 2 S 0921-630, PSR J0437-4715, Vela X-1, PSR J1748-2021B which are reflected in Mass–Radius curves. Hence, the study comes out to be worthy of the fact that the f(Q) gravity parameter directly influences the maximum mass of a compact stellar configuration for the fixed decoupling parameter in the context of gravitational decoupling where it predicts the star PSR J1748-2021B having highest mass 2.74 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\odot }$$\\end{document}. It is noted that when the decoupling parameter (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) increases, the central value of the adiabatic index value also increases, while the reverse situation occurs when the f(Q)-parameter (β1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _1$$\\end{document}) gets increased. This implies that both the parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and β1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _1$$\\end{document} have the overall controlling power on the stability of the model.

Probing the impact of WIMP dark matter on universal relations, GW170817 posterior, and radial oscillations

ABSTRACT In this study, we investigate the impact of weakly interacting massive particles (WIMPs) dark matter (DM) on C–Λ universal relations, GW170817 posterior, and radial oscillations of neutron stars (NSs) by considering the interactions of uniformly trapped neutralinos as a DM candidate with the hadronic matter through the exchange of the Higgs boson within the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The hadronic equation of state (EOS) is modelled using the relativistic mean-field (RMF) formalism with IOPB-I, G3, and quark–meson coupling (QMC)-RMF series parameter sets. The presence of DM softens the EOS at both the background and the perturbation levels that implies a small shift to the left in the posterior accompanied by a much larger jump in the left of the mass–radius curves with increasing DM mass. It is observed that EOSs with DM also satisfy the C–Λ universality relations among themselves but get slightly shifted to the right in comparison to that without considering DM. Additionally, we find that the inclusion of DM allows the mass–radius (M–R) curves to remain consistent with observational constraints for HESS J1731−347, indicating the possibility of classifying it as a dark matter-admixed neutron star (DMANS). Moreover, we explore the impact of DM on the radial oscillations of pulsating stars and investigate the stability of NSs. The results demonstrate a positive correlation between the mass of DM and the frequencies of radial oscillation modes.

Bayesian analysis of a relativistic hadronic model constrained by recent astrophysical observations

ABSTRACTWe use Bayesian analysis in order to constrain the equation of state for nuclear matter from astrophysical data related to the recent measurements from the NICER mission, LIGO/Virgo collaboration, and probability distributions of mass and radius from other 12 sources, including thermonuclear busters, and quiescent low-mass X-ray binaries. For this purpose, we base our study on a relativistic hadronic mean field model including an ω − ρ interaction. Our results indicate optimal ranges for some bulk parameters at the saturation density, namely, effective mass, incompressibility, and symmetry energy slope (L0). For instance, we find $L_0 = 50.79^{+15.16}_{-9.24}$ MeV (Case 1) and $L_0 = 75.06^{+8.43}_{-4.43}$ MeV (Case 2) in a 68 per cent confidence interval for the two cases analysed (different input ranges for L0 related to the PREX-II data). The respective parametrizations are in agreement with important nuclear matter constraints, as well as observational neutron star data, such as the dimensionless tidal deformability of the GW170817 event. From the mass–radius curves obtained from these best parametrizations, we also find the ranges of 11.97 km ≤ R1.4 ≤ 12.73 km (Case 1) and 12.34 km ≤ R1.4 ≤ 13.06 km (Case 2) for the radius of the $1.4\, \mathrm{M}_\odot$ neutron star.

Nonstrange quark stars within resummed QCD

The recently developed resummation technique known as {\it renormalization group optimized perturbation theory} (RGOPT) is employed in the evaluation of the EoS describing non-strange cold quark matter at NLO. Inspired by recent investigations, which suggest that stable quark matter can be made only of up and down quarks, the mass-radius relation for two flavor pure quark stars is evaluated and compared with the predictions from perturbative QCD (pQCD) at NNLO. This comparison explicitly shows that by being imbued with renormalization group properties, and a variational optimization procedure, the method allows for an efficient resummation of the perturbative series. Remarkably, when the renormalization scale is chosen so as to reproduce maximum mass stars with M=$2-2.3M_\odot$, one obtains a mass-radius curve compatible with the masses and radii of the pulsars PSR J0740+6620, PSR J0030+0451, and the compact object HESS J1731-347. Moreover, the scale dependence of the EoS (and mass-radius relation) obtained with the RGOPT is greatly improved when compared to that of pQCD. This seminal application to the description of quark stars shows that the RGOPT represents a robust alternative to pQCD when describing compressed quark matter.

The Effect of f(R, T) Modified Gravity on the Mass and Radius of Pulsar HerX1

Millisecond pulsars are the perfect testable to examine potential matter-geometry coupling and its physical consequences in the context of the recent Neutron Star Interior Composition Explorer discoveries. We apply the field equations of modified gravity, f(R, T) = R + α T, to a spherically symmetric spacetime, where R is the Ricci scalar, α is a dimensional parameter, and T is the matter of the geometry. Five unknown functions are present in the output system of differential equations, which consists of three equations. To close the system, we make explicit assumptions about the anisotropy and the radial metric potential, g rr . We then solve the output differential equations and derive the explicit forms of the components of the energy-momentum tensor, i.e., density, radial, and tangential pressures. We look into the possibility that all of the physical parameters in the star can be reexpressed in terms of α and the compactness parameters, C = 2 GM Rc−2. We show that, for a given mass, the size permitted by Einstein’s general relativity is less due to the matter-geometry coupling in f(R, T). The validity of the hypothesis was validated by observations from an extra 21 pulsars. To achieve a surface density that is compatible with a neutron core at nuclear saturation density, the mass–radius curve enables masses up to 3.35M ⊙. We emphasize that although there is no assumption of an equation of state, the model fits well with a linear behavior. When comparing the surface densities of these 20 pulsars, we divided them into three groups. We show that these three groups are compatible with neutron cores.

Framework for phase transitions between the Maxwell and Gibbs constructions

By taking the nucleon-to-quark phase transition within a neutron star as an example, we present a thermodynamically consistent method to calculate the equation of state of ambient matter so that transitions that are intermediate to those of the familiar Maxwell and Gibbs constructions can be described. This method does not address the poorly known surface tension between the two phases microscopically (as, for example, in the calculation of the core pasta phases via the Wigner-Seitz approximation) but instead combines the local and global charge neutrality conditions characteristic of the Maxwell and Gibbs constructions, respectively. Overall charge neutrality is achieved by dividing the leptons to those that obey local charge neutrality (Maxwell) and those that maintain global charge neutrality (Gibbs). The equation of state is obtained by using equilibrium constraints derived from minimizing the total energy density. The results of this minimization are then used to calculate neutron star mass-radius curves, tidal deformabilities, equilibrium and adiabatic sound speeds, and nonradial $g$-mode oscillation frequencies for several intermediate constructions. Various quantities of interest transform smoothly from their Gibbs structures to those of Maxwell as the local-to-total electron ratio $\eta$, introduced to mimic the hadron-to-quark interface tension from $0$ (Gibbs) to $\infty$ (Maxwell), is raised from $0$ to $1$. A notable exception is the $g$-mode frequency for the specific case of $\eta=1$ for which a gap appears between the quark and hadronic branches.

Skyrme Crystals, Nuclear Matter and Compact Stars

A general review of the crystalline solutions of the generalized Skyrmemodel and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrmemodel on the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first-order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass–radius curves already reasonably satisfy current astrophysical constraints.

Kaon condensation in skyrmion matter and compact stars

We address the possibility of the appearance of a charged kaon condensate in neutron star cores described within a generalized Skyrme model. Our treatment of strange degrees of freedom is based on the Bound State Approach by Callan and Klebanov, which allows to obtain an in-medium effective potential for the $s$-wave kaon condensate. We predict the onset of kaon condensation at a certain threshold density - whose value depends on the parameters of the model, and ranges between 1.5 and 2.5 times saturation density -, and obtain both the particle fractions and equation of state for dense matter in the kaon condensed phase. Finally, we discuss the effect of such condensates on the mass-radius curves and other observable properties of neutron stars with kaon condensed cores.

Systematic errors due to quasiuniversal relations in binary neutron stars and their correction for unbiased model selection

Inference of the equation of state (EOS) of dense nuclear matter in neutron-star cores is a principal science goal of x-ray and gravitational-wave observations of neutron stars. In particular, gravitational-wave observations provide an independent probe of the properties of bulk matter in neutron star cores that can then be used to compare with theoretically derived equations of state. In this paper, we quantify the systematic errors arising from the application of EOS-independent quasiuniversal relations in the estimation of neutron star tidal deformabilities and radii from gravitational-wave measurements and introduce a strategy to correct for the systematic biases in the inferred radii. We apply this method to a simulated population of events expected to be observed by future upgrades of current detectors and the next generation of ground-based observatories. We show that our approach can accurately correct for the systematic biases arising from approximate universal relations in the mass-radius curves of neutron stars. Using the posterior distributions of the mass and radius for the simulated population we infer the underlying EOS with a good degree of precision. Our method revives the possibility of using the universal relations for rapid Bayesian model selection of the dense matter EOS in gravitational-wave observations.

Photometric study and evolutionary state for some newly discovered W UMA systems

First orbital solution and photometric study for the newly discovered systems V968 CEP, ET CMI, and ES CMI was carried out by means of WD code (windows interface version) based on model atmosphere provided by Kurucz. Our modelling revealed absolute and physical parameters, which show that the primary components in all systems are hotter and more massive than the secondary components. According to the estimated parameters, the evolutionary statuses for all systems were estimated on theoretical mass-luminosity and mass-radius curves. Spectral types of the systems components were adopted using the estimated temperatures.

Non-trivial class of anisotropic compact stellar model in Rastall gravity

We investigated Rastall gravity, for an anisotropic star with a static spherical symmetry, whereas the matter-geometry coupling as assumed in Rastall Theory (RT) is expected to play a crucial role differentiating RT from General Relativity (GR). Indeed, all the obtained results confirm that RT is not equivalent to GR, however, it produces same amount of anisotropy as GR for static spherically symmetric stellar models. We used the observational constraints on the mass and the radius of the pulsar Her X-1 to determine the model parameters confirming the physical viability of the model. We found that the matter-geometry coupling in RT allows slightly less size than GR for a given mass. We confirmed the model viability via other twenty pulsars’ observations. Utilizing the strong energy condition we determined an upper bound on compactness U_text {max}sim 0.603, in agreement with Buchdahl limit, whereas Rastall parameter epsilon =-0.1. For a surface density compatible with a neutron core at nuclear saturation density the mass-radius curve allows masses up to 3.53 M_odot . We note that there is no equation of state is assumed, however the model fits well with linear behaviour. We split the twenty pulsars into four groups according to the boundary densities. Three groups are compatible with neutron cores while one group fits perfectly with higher boundary density 8times 10^{14}hbox {g/cm}^3 which suggests that those pulsars may have quark-gluon cores.

Universal Relations for the Increase in the Mass and Radius of a Rotating Neutron Star

Rotation causes an increase in a neutron star’s mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOSs to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for nonrotating neutron stars. The correction factors depend only on the nonrotating star’s mass and radius and are almost independent of the EOS. This makes it computationally inexpensive to include observations of rotating neutron stars in EOS inference codes. We also construct a mapping from the measured mass and radius of a rotating neutron star to a corresponding nonrotating star. The mapping makes it possible to construct a zero-spin mass–radius curve if the masses and radii of many neutron stars with different spins are measured. We show that the changes in polar and equatorial radii are symmetric, in that the polar radius shrinks at the same rate in which the equatorial radius grows. This symmetry is related to the observation that the equatorial compactness (the ratio of mass to radius) is almost constant on one of the constant-density sequences.

Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers

The postmerger gravitational wave (GW) emission from a binary neutron star merger is expected to provide exciting new constraints on the dense-matter equation of state (EoS). Such constraints rely, by and large, on the existence of quasi-universal relations, which relate the peak frequencies of the postmerger GW spectrum to properties of the neutron star structure in a model-independent way. In this work, we report on violations of existing quasi-universal relations between the peak spectral frequency, f 2, and the stellar radius, for EoS models with backwards-bending slopes in their mass–radius relations (such that the radius increases at high masses). The violations are extreme, with variations in f 2 of up to ∼600 Hz between EoSs that predict the same radius for a 1.4 M ⊙ neutron star but that have significantly different radii at higher masses. Quasi-universality can be restored by adding in a second parameter to the fitting formulae that depends on the slope of the mass–radius curve. We further find strong evidence that quasi-universality is better maintained for the radii of very massive stars (with masses 2 M ⊙). Both statements imply that f 2 is mainly sensitive to the high-density EoS. Combined with observations of the binary neutron star inspiral, these generalized quasi-universal relations can be used to simultaneously infer the characteristic radius and slope of the neutron star mass–radius relation.

Structure and density of silicon carbide to 1.5 TPa and implications for extrasolar planets.

There has been considerable recent interest in the high-pressure behavior of silicon carbide, a potential major constituent of carbon-rich exoplanets. In this work, the atomic-level structure of SiC was determined through in situ X-ray diffraction under laser-driven ramp compression up to 1.5 TPa; stresses more than seven times greater than previous static and shock data. Here we show that the B1-type structure persists over this stress range and we have constrained its equation of state (EOS). Using this data we have determined the first experimentally based mass-radius curves for a hypothetical pure SiC planet. Interior structure models are constructed for planets consisting of a SiC-rich mantle and iron-rich core. Carbide planets are found to be ~10% less dense than corresponding terrestrial planets.

Determination of the symmetry energy from the neutron star equation of state

We analyze the uncertainties introduced in the determination of the neutron star matter proton fraction, in a range of densities close to the saturation density, if the cold $\ensuremath{\beta}$-equilibrium neutron star matter equation of state (EOS) is known. In particular, we discuss the effect of neglecting the muon contribution and of considering that the energy density of nuclear matter is well described by taking only terms until second order in the proton-neutron asymmetry. It is shown that two types of uncertainties may be associated with the extraction of the symmetry energy from the $\ensuremath{\beta}$-equilibrium EOS: an overestimation if terms above the parabolic approximation on the asymmetry parameter are neglected, or an underestimation if the muon contribution is not considered. The effect of the uncertainty on the symmetric nuclear matter EOS on the determination of the proton fraction is discussed. It could be shown that the neutron star mass-radius curve is sensitive to the parabolic approximation on the asymmetry parameter.

Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars

AbstractWe consider stability of nonrotating gaseous stars modeled by the Euler‐Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (TPP) that the stability of the stars is entirely determined by the mass–radius curve parametrized by the center density. In particular, the stability can only change at extrema (i.e., local maximum or minimum points) of the total mass. For a very general equations of state, TPP implies that for increasing center density the stars are stable up to the first mass maximum and unstable beyond this point until the next mass extremum (a minimum). Moreover, we get a precise counting of unstable modes and exponential trichotomy estimates for the linearized Euler‐Poisson system. To prove these results, we develop a general framework of separable Hamiltonian PDEs. The general approach is flexible and can be used for many other problems, including stability of rotating and magnetic stars, relativistic stars, and galaxies. © 2021 Wiley Periodicals LLC.

Turning Point Principle for Relativistic Stars

Upon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960’s Zel’dovich (Voprosy Kosmogonii 9:157–170, 1963) and Harrison et al. (Gravitation Theory and Gravitational Collapse. The University of Chicago press, Chicago, 1965) formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.