Non-rotating Neutron Stars Research Articles

Exotic Stable Branches with Efficient TOV Sequences

Modern inference schemes for the neutron star (NS) equation of state (EoS) require large numbers of stellar models constructed with different EoS, and these stellar models must capture all the behavior of stable stars. I introduce termination conditions for sequences of stellar models for cold nonrotating NSs that can identify all stable stellar configurations up to arbitrarily large central pressures along with an efficient algorithm to build accurate interpolators for macroscopic properties. I explore the behavior of stars with both high- and low-central pressures. Interestingly, I find that EoSs with monotonically increasing sound-speed can produce multiple stable branches (twin stars) and that large phase transitions at high densities can produce stable branches at nearly any mass scale, including sub-solar masses while still supporting stars with M > 2 M ⊙. I conclude with some speculation about the astrophysical implications of this behavior.

Calculation of the TOV Limit Based on Neutron Degeneracy Pressure

Original theory on the mass limit beyond which a cold, non-rotating neutron star cannot be formed, instead only stellar black holes will be created, was stipulated by J.R. Oppenheimer and G.M. Volkoff based on R.C. Tolman’s work in 1939. The limit calculated from the equation established by them is known as the TOV limit which is analogous to the Chandrasekhar limit for White Dwarfs. But the results obtained using the formula was found to be not valid today. Subsequent theoretical works place the limit in the range 1.5 to 3 solar masses. There are several basic theories and related formulae for calculating the TOV limit. In this article a different and novel approach has been adopted to calculate the TOV limit using the theory on neutron degeneracy pressure. As per present calculations, the TOV limit is around 2.928 times the solar mass. These calculations also highlight two aspects which are conceptually new; first, a black hole having mass higher than the TOV limit can also become a neutron star and both can coexist concurrently up to a certain limit; and second, that upper limit of star mass beyond which a black hole will explode in supernova before becoming a neutron star is 7.15 times the solar mass as at that stage the gravitational energy of the black hole will be equal or exceed to its nuclear binding energy.

Ray-traced spectra of a hot neutron star for various metallicities

General relativity strongly affects the observed spectra of compact objects. New models of hot nonrotating neutron star (NS) atmospheres are presented for various chemical compositions. We demonstrate the influence of strong gravity on the value of the hardening factor measured by a distant observer. We prepare new xspec fitting packages based on our extended numerical models for hot NS atmospheres in order to use them for a spectral analysis in the X-ray domain. For the Schwarzschild metric, ray-tracing calculations were performed to determine the observational appearance of the continuum emission of an NS. The grid of intensity spectra emerging from the NS surface was computed with the code which solves the model atmosphere equations with an accurate treatment of the Compton scattering of photons on free electrons in fully relativistic thermal motion. For the single value of the surface gravity, $ =14.34$ (cgs), the emerging specific intensity spectra were then ray-traced from the surface to the distant observer with the code across the spacetime of a nonrotating NS obtained using the lo library. The color-correction factors were determined for a large grid of models of different chemical compositions for surface gravities from the critical gravity $ g_ crit $ up to $15.00$ (cgs), and for effective temperatures in the range of $10^ eff $ K. Comptonized spectra seen at the source rest frame display hardening factors in the range from 1.4 up to 2.0 in the case of a highly luminous metal-rich atmosphere. The ratio of the color temperature $T_ c $ to the effective temperature $T_ eff $ for ray-traced spectra is in the range $0.9-1.4$. In the strong gravity regime, the structure of a hot atmosphere strongly depends on the surface gravity, luminosity, and atmospheric metal abundance of the NS. The theoretical hardening factors of the ray-traced spectra are systematically lower then the hardening factors of spectra at the source by about 30<!PCT!> on average.

Thermal evolution and axion emission properties of strongly magnetized neutron stars

Emission properties of compact astrophysical objects such as Neutron stars (NSs) are associated with crucial astronomical observables. In the current work, we obtain the mass, pressure profiles of the non-rotating NSs using the modified Tolman Oppenheimer Volkoff (TOV) system of equations in the presence of intense magnetic field. We obtain the profiles by using a specific distance-dependent magnetic field in the modified TOV equations. We employ three different equations of states (EoS) to solve the TOV equations by assuming the core of NSs comprises a hadronic matter. Employing the above profiles, we determine the cooling rates of spherically symmetric NSs as a function of time with and without including the magnetic field using the NSCool code. We have also determined the cooling rates as a function of radius for three different NSs. Furthermore, we determine the luminosity of neutrinos, axions, and photons emitting from the NSs in the presence and absence of a magnetic field for an axion mass 16 meV and three different EoS. Our comparative study indicates that the cooling rate and luminosities of neutrinos, axions, and photons change significantly due to the impact of the strong magnetic field. We also find that due to the magnetic field, the axion mass bound increases slightly compared to without a magnetic field.

On the Maximum Mass and Oblateness of Rotating Neutron Stars with Generic Equations of State

A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than 106 generic EOSs, we assess the validity of quasi-universal relations of neutron-star properties for a broad range of rotation rates, from slow rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modeling of the X-ray emission from the surface of rotating stars.

Measuring Mass and Radius of the Maximum-mass Nonrotating Neutron Star

The mass (M TOV) and radius (R TOV) of the maximum-mass nonrotating neutron star (NS) play a crucial role in constraining the elusive equation of state of cold dense matter and in predicting the fate of remnants from binary neutron star (BNS) mergers. In this study, we introduce a novel method to deduce these parameters by examining the mergers of second-generation (2G) black holes (BHs) with NSs. These 2G BHs are assumed to originate from supramassive neutron stars (SMNSs) formed in BNS mergers. Since the properties of the remnant BHs arising from the collapse of SMNSs follow a universal relation governed by M TOV and R TOV, we anticipate that by analyzing a series (∼100 detections) of mass and spin measurements of the 2G BHs using the third-generation ground-based gravitational-wave detectors, M TOV and R TOV can be determined with a precision of ∼0.01M ⊙ and ∼0.6 km, respectively.

Nonparametric Representation of Neutron Star Equation of State Using Variational Autoencoder

We introduce a new nonparametric representation of the neutron star (NS) equation of state (EOS) by using the variational autoencoder (VAE). As a deep neural network, the VAE is frequently used for dimensionality reduction since it can compress input data to a low-dimensional latent space using the encoder component and then reconstruct the data using the decoder component. Once a VAE is trained, one can take the decoder of the VAE as a generator. We employ 100,000 EOSs that are generated using the nonparametric representation method based on Han et al. as the training set and try different settings of the neural network, then we get an EOS generator (the trained VAE’s decoder) with four parameters. We use the mass–tidal-deformability data of binary NS merger event GW170817, the mass–radius data of PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, and 4U 1702-429, and the nuclear constraints to perform the Bayesian inference. The overall results of the analysis that includes all the observations are , , and (90% credible levels), where R 1.4/Λ1.4 are the radius/tidal deformability of a canonical 1.4 M ⊙ NS, and is the maximum mass of a nonrotating NS. The results indicate that the implementation of these VAE techniques can obtain reasonable results, while accelerating calculation by a factor of ∼3–10 or more, compared with the original method.

Radial Oscillations in Neutron Stars from Unified Hadronic and Quarkyonic Equation of States

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M⊙ star criterion. We solve the Sturm–Liouville problem to compute the 20 lowest radial oscillation modes and their eigenfunctions for a neutron star modeled with eight selected unified EoSs from distinct Skyrme–Hartree–Fock, relativistic mean field and quarkyonic models. We compare the behavior of the computed eigenfrequency for an NS modeled with hadronic to one with quarkyonic EoSs while varying the central densities. The lowest-order f-mode frequency varies substantially between the two classes of the EoS at 1.4 M⊙ but vanishes at their respective maximum masses, consistent with the stability criterion ∂M/∂ρc>0. Moreover, we also compute large frequency separation and discover that higher-order mode frequencies are significantly reduced by incorporating a crust in the EoS.

Oscillations of highly magnetized non-rotating neutron stars

Highly magnetized neutron stars are promising candidates to explain some of the most peculiar astronomical phenomena, for instance, fast radio bursts, gamma-ray bursts, and superluminous supernovae. Pulsations of these highly magnetized neutron stars are also speculated to produce detectable gravitational waves. In addition, pulsations are important probes of the structure and equation of state of the neutron stars. The major challenge in studying the pulsations of highly magnetized neutron stars is the demanding numerical cost of consistently solving the nonlinear Einstein and Maxwell equations under minimum assumptions. With the recent breakthroughs in numerical solvers, we investigate pulsation modes of non-rotating neutron stars which harbour strong purely toroidal magnetic fields of 1015−17 G through two-dimensional axisymmetric general-relativistic magnetohydrodynamics simulations. We show that stellar oscillations are insensitive to magnetization effects until the magnetic to binding energy ratio goes beyond 10%, where the pulsation mode frequencies are strongly suppressed. We further show that this is the direct consequence of the decrease in stellar compactness when the extreme magnetic fields introduce strong deformations of the neutron stars.

Impact of large-mass constraints on the properties of neutron stars

ABSTRACT The maximum mass of a non-rotating neutron star, MTOV, plays a very important role in deciphering the structure and composition of neutron stars and in revealing the equation of state (EOS) of nuclear matter. Although with a large-error bar, the recent mass estimate for the black-widow binary pulsar PSR J0952–0607, i.e. M = 2.35 ± 0.17 M⊙, provides the strongest lower bound on MTOV and suggests that neutron stars with very large masses can, in principle, be observed. Adopting an agnostic modelling of the EOS, we study the impact that large masses have on the neutron-star properties. In particular, we show that assuming $M_{\rm TOV}\gtrsim 2.35\, {\rm M_\odot}$ constrains tightly the behaviour of the pressure as a function of the energy density and moves the lower bounds for the stellar radii to values that are significantly larger than those constrained by the NICER measurements, rendering the latter ineffective in constraining the EOS. We also provide updated analytic expressions for the lower bound on the binary tidal deformability in terms of the chirp mass and show how larger bounds on MTOV lead to tighter constraints for this quantity. In addition, we point out a novel quasi-universal relation for the pressure profile inside neutron stars that is only weakly dependent on the EOS and the maximum-mass constraint. Finally, we study how the sound speed and the conformal anomaly are distributed inside neutron stars and show how these quantities depend on the imposed maximum-mass constraints.

A hybrid GNA instability

A semi-analytic admixed model formalism to study the stability effects of the inner crust regions against the local collective perturbations in non-rotating neutron stars is proposed. It consists of the viscoelastic heavy neutron-rich nuclei, superfluid neutrons, and degenerate quantum electrons. A normal spherical mode analysis yields a generalized linear dispersion relation multiparametrically mimicking the inner crust features of neutron stars. A hybrid gravito-nucleo-acoustic (GNA) instability mode is found to be excited. It is demonstrated that the electron density and the inner crust curvature act as its accelerating and antidispersive agents. In contrast, the heavy neutron-rich nucleus and neutron densities act as decelerating factors. The heavy nucleus density, electron density, and geometric curvature act as its destabilizers. It is only the neutron density that acts as the GNA stabilizing agent. The heavy neutron-rich nucleus and neutron densities are found to act as dispersive broadening factors to it. The high-K regions are the more unstable spectral windows indicating that the GNA mode plays a dominant role in the inner crust zone towards the local stability. Its fair reliability is indicated in light of the recent astronomic observed scenarios. It could be useful to explore acoustic mode signatures in non-rotating neutron stars and similar other compact astroobjects.

Angular-momentum Transport in Proto-neutron Stars and the Fate of Neutron Star Merger Remnants

Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes (viscosity) have key implications for the remnant’s long-term stability and the NS equation of state (EOS). Guided by a nonrotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular-velocity profile Ω(r). Although the magneto-rotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Tayler–Spruit dynamo dominate in the core of merger remnants where dΩ/dr ≥ 0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid-body rotation will be enforced faster than matter is accreted from rotationally supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2 M TOV for forming a stable solid-body rotating NS remnant (where M TOV is the maximum nonrotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multimessenger constraints on the NS EOS.

GRMHD simulations of accreting neutron stars I: Non-rotating dipoles

ABSTRACT We study the general-relativistic dynamics of matter being accreted on to and ejected by a magnetized and non-rotating neutron star. The dynamics is followed in the framework of fully general relativistic magnetohydrodynamics (GRMHD) within the ideal-MHD limit and in two spatial dimensions. More specifically, making use of the numerical code BHAC, we follow the evolution of a geometrically thick matter torus driven into accretion by the development of a magnetorotational instability. By making use of a number of simulations in which we vary the strength of the stellar dipolar magnetic field, we can determine self-consistently the location of the magnetospheric (or Alfvén) radius rmsph and study how it depends on the magnetic moment μ and on the accretion rate. Overall, we recover the analytic Newtonian scaling relation, i.e. rmsph ∝ B4/7, but also find that the dependence on the accretion rate is very weak. Furthermore, we find that the material torque correlates linearly with the mass-accretion rate, although both of them exhibit rapid fluctuations. Interestingly, the total torque fluctuates drastically in strong magnetic field simulations and these unsteady torques observed in the simulations could be associated with the spin fluctuations observed in X-ray pulsars.

Relativistic mean field model parametrizations in the light of GW170817, GW190814, and PSR J0740+6620

Three parametrizations DOPS1, DOPS2, and DOPS3 (named after the Department of Physics Shimla) of the relativistic mean field model have been proposed with the inclusion of all possible self and mixed interactions between the scalar-isoscalar ($\ensuremath{\sigma}$), vector-isoscalar ($\ensuremath{\omega}$), and vector-isovector ($\ensuremath{\rho}$) mesons up to quartic order. The generated parameter sets are in harmony with the finite and bulk nuclear matter properties. A set of equations of state (EOSs) composed of pure hadronic (nucleonic) matter and nucleonic with quark matter (hybrid EOSs) for superdense hadron-quark matter in $\ensuremath{\beta}$ equilibrium is obtained. The quark matter phase is calculated by using the three-flavor Nambu-Jona-Lasinio (NJL) model. The maximum mass of a nonrotating neutron star with DOPS1 parametrization is found to be around $2.6M\ensuremath{\bigodot}$ for the pure nucleonic matter, which satisfies the recent gravitational wave analysis of GW190814 [Abbott et al., Astrophys. J. Lett. 896, L44 (2020)] with possible maximum mass constraint indicating that the secondary component of GW190814 could be a nonrotating heaviest neutron star composed of pure nucleonic matter. EOSs computed with the DOPS2 and DOPS3 parametrizations satisfy the x-ray observational data [Steiner et al., Astrophys. J. 722, 33 (2010)] and the recent observations of GW170817 maximum mass constraint of a stable nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04--2.16\ifmmode\pm\else\textpm\fi{}0.03M\ensuremath{\bigodot}$ [Rezzolla et al., Astrophys. J. Lett. 852, L25 (2018)] and also in good agreement with constraints on mass and radius measurement for PSR $\mathrm{J}0740+6620$ (NICER) [Riley et al., Astrophys. J. Lett. 918, L27 (2021); Miller et al., Astrophys. J. Lett. 918, L28 (2021)]. The hybrid EOSs obtained with the NJL model also satisfy astrophysical constraints on the maximum mass of a neutron star from PSR J1614-2230 [Demorest et al., Nature (London) 467, 1081 (2010)]. We also present the results for dimensionless tidal deformability, $\mathrm{\ensuremath{\Lambda}}$ which are consistent with the waveform models analysis of GW170817.

Constraining neutron star properties with a new equation of state insensitive approach

Instead of parameterizing the pressure-density relation of a neutron star (NS), one can parameterize its macroscopic properties such as mass ($M$), radius ($R$), and dimensionless tidal deformability ($\Lambda$) to infer the equation of state (EoS) combining electromagnetic and gravitational wave (GW) observations. We present a new method to parameterize $R(M)$ and $\Lambda(M)$ relations, which approximate the candidate EoSs with accuracy better than 5\% for all masses and span a broad region of $M-R-\Lambda$ plane. Using this method we combine the $M-\Lambda$ measurement from GW170817 and GW190425, and simultaneous $M-R$ measurement of PSR J0030+0451 and PSR J0740+6620 to place joint constraints on NS properties. At 90 \% confidence, we infer $R_{1.4}=12.05_{-0.87}^{+0.98}$ km and $\Lambda_{1.4}=372_{-150}^{+220}$ for a $1.4 M_{\odot}$ NS, and $R_{2.08}=12.65_{-1.46}^{+1.36}$ km for a $2.08 M_{\odot}$ NS. Furthermore, we use the inferred values of the maximum mass of a nonrotating NS $M_{\rm max}=2.52_{-0.29}^{+0.33} M_{\odot}$ to investigate the nature of the secondary objects in three potential neutron star-black hole merger (NSBH) system.

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.

Numerical relativity simulations of prompt collapse mergers: Threshold mass and phenomenological constraints on neutron star properties after GW170817

We determine the threshold mass for prompt (no bounce) black hole formation in equal-mass neutron star (NS) mergers using a new set of 227 numerical relativity simulations. We consider 23 phenomenological and microphysical finite-temperature equations of state (EOS), including models with hyperons and first-order phase transitions to deconfined quarks. We confirm the existence of EOS-insensitive relations between the threshold mass, binary tidal parameter at the threshold (${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{th}}$), maximum mass of nonrotating NSs, and radii of reference mass NSs. We combine the EOS-insensitive relations, phenomenological constraints on NS properties, and observational data from GW170817 to derive an improved lower limit on radii of maximum mass and a $1.6\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ NS of 9.81 and 10.90 km, respectively. We also constrain the radius and quadrupolar tidal deformability ($\mathrm{\ensuremath{\Lambda}}$) of a $1.4\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ NS to be larger than 10.74 km and 172, respectively. We consider uncertainties in all independent parameters---fitting coefficients as well as GW170817 masses while reporting the range of radii constraints. We discuss an approach to constrain the upper as well as lower limit of NS maximum mass using future binary NS detections and their identification as prompt or delayed collapse. With future observations, it will be possible to derive even tighter constraints on the properties of matter at and above nuclear density using the method proposed in this work.

Constraints on the Maximum Densities of Neutron Stars from Postmerger Gravitational Waves with Third-Generation Observations.

Using data from 289 numerical relativity simulations of binary neutron star mergers, we identify, for the first time, a robust quasiuniversal relation connecting the postmerger peak gravitational-wave frequency and the value of the density at the center of the maximum mass nonrotating neutron star. This relation offers a new possibility for precision equation-of-state constraints with next-generation ground-based gravitational-wave interferometers. Mock Einstein Telescope observations of fiducial events indicate that Bayesian inferences can constrain the maximum density to ∼15% (90% credibility level) for a single signal at the minimum sensitivity threshold for a detection. If the postmerger signal is included in a full-spectrum (inspiral-merger-postmerger) analysis of such a signal, the pressure-density function can be tightly constrained up to the maximum density, and the maximum neutron star mass can be measured with an accuracy better than 12% (90% credibility level).

Realistic neutron star models in f(T) gravity

We investigate the nonrotating neutron stars in f(T) gravity with f(T)=T+alpha {T}^2, where T is the torsion scalar in the teleparallel formalism of gravity. In particular, we utilize the SLy and BSk family of equations of state for perfect fluid to describe the neutron stellar matter and search for the effects of the f(T) modification on the models of neutron stars. For positive alpha , the modification results in a smaller stellar mass in comparison to general relativity, while the neutron stars will contain larger amount of matter for negative alpha . Moreover, there seems to be an upper limit for the central density of the neutron stars with alpha >0, beyond which the effective f(T) fluid would have a steplike phase transition in density and pressure profiles, collapsing the numerical system. We obtain the mass–radius relations of the realistic models of neutron stars and subject them to the joint constraints from the observed massive pulsars PSR J0030+0451, PSR J0740+6620, and PSR J2215+5135, and gravitational wave events GW170817 and GW190814. For the neutron star model in f(T) gravity to be able to accommodate all the mentioned data, the model parameter alpha needs to be smaller than -,4.295, -,6.476, -,4.4, and -,2.12 (in the unit of {G}^2M_odot ^2/c^4) for SLy, BSk19, BSk20, and BSk21 equations of state, respectively. If one considers the unknown compact object in the event GW190814 not to be a neutron star and hence excludes this dataset, the constraints can be loosened to alpha <-,0.594, -,3.5, 0.4 and 1.9 (in the unit of {G}^2M_odot ^2/c^4), respectively.

A look into the mass–radius relation of the neutron star in modified Chaplygin gas background

Motivated by the work of Astashenok et al. [Causal limit of neutron star maximum mass in f(R) gravity in view of GW190814, Phys. Lett. B 816 (2021) 136222], the present work aims at studying the behavior of f in f(R) gravity and attempts to study the causal mass–radius relation of a massive neutron star. To initiate the study, the background evolution is taken as of modified Chaplygin gas. We observed the positive behavior of f. The Tolman–Oppenheimer–Volkoff equation has been taken into consideration which states the spherical stellar structure of non-rotating neutron stars. We also observed that the mass–radius relationship is close to the Tolman–Oppenheimer–Volkoff limit. The change of density of neutron stars with respect to the radius clearly manifests the actual variation of density from the core to the surface of a neutron star in the background evolution of modified Chaplygin gas, which can unify the early inflation with the late time acceleration of the universe.