Structure Of Neutron Stars Research Articles

Toward Accelerated Nuclear-physics Parameter Estimation from Binary Neutron Star Mergers: Emulators for the Tolman–Oppenheimer–Volkoff Equations

Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman–Oppenheimer–Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: multilayer perceptrons (MLPs), Gaussian processes, and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms, whereas the RBM results in the largest speedup with respect to the full high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.

Impact of dark energy on the structure of neutron stars: The vacuum case

The potential role of a cosmic vacuum dark component in the properties of neutron stars is investigated. It is assumed that the static, spherically symmetric distribution of matter within neutron stars is supported by two distinct components: ordinary matter and a vacuum fluid. For normal matter we use a set of state-of-the-art nuclear matter equations of state, each grounded in nuclear physics experiments. The vacuum energy component is inhomogeneously distributed within the star and obeys the standard equation of state (pv=−εv). This is characterized by an energy density fraction y=εm/(εm+εv), which we model as either a constant or radius-dependent. Our findings reveal that the inclusion of vacuum energy significantly affects the mass-radius relationships in neutron stars, influencing both the maximum achievable masses and the qualitative form of these relationships. Some constraints from current multimessenger observational data limiting the amount of vacuum energy within neutron stars are also discussed. Published by the American Physical Society 2024

Stability analysis of charged neutron stars and Darmois junction conditions

This research article examines the impact of f(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {Q}},{\\mathcal {T}})$$\\end{document} theory on the geometry of charged neutron stars filled with anisotropic matter configuration. Here, Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Q}}$$\\end{document} represents non-metricity and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {T}}$$\\end{document} denotes the trace of energy-momentum tensor. We use a particular functional form of this modified theory to reduce the system’s complexity and derive explicit relations of the energy density and pressure components. Further, we consider viable non-singular solutions to analyze the internal structure of the charged neutron stars. The unspecified parameters in the metric coefficients are evaluated through Darmois junction conditions, which ensures consistency between interior and exterior solutions of the stellar objects. These parameters are then used to explore different physical characteristics such as the behavior of energy density, pressure components, anisotropy, energy bounds, equation of state parameter, compactness and redshift function in the interior of charged neutron stars. The stability and equilibrium states of the charged stellar objects are discussed using the Tolman–Oppenheimer–Volkoff equation and the speed of sound, respectively. Our results suggest that the charged neutron stars are viable and stable in the presence of dark source terms.

Compact stars with non-uniform relativistic polytrope

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman–Oppenheimer–Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation.

Relativistic description of dense matter equation of state and neutron star observables constrained by recent astrophysical observations

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic interaction NL-RS which provides an opportunity to readjust the coupling constants keeping in view the properties of finite nuclei, nuclear matter, PREX-II results for neutron skin thickness in 208Pb and astrophysical observations. The NL-RS model interaction has been proposed by fitting the ground state properties (binding energies and charge radii) of finite nuclei, bulk nuclear matter properties, and PREX-II results for neutron skin thickness of 208Pb. The relativistic interaction has been generated by including nonlinear self-interactions of σ and ω μ -mesons and mixed interactions of ω μ , and ρ μ -meson up to the quartic order. The proposed interaction harmonizes with the finite nuclei, bulk nuclear matter, and neutron star properties. A covariance analysis is performed to assess the statistical uncertainties on the model parameters and nuclear observables of interest along with correlations amongst them. The equation of state (EoS) composed of nucleons and leptons in β-equilibrium is computed with the proposed parameter set and used to study the neutron star structure. The maximum mass of the neutron star by employing the EoS computed with the NL-RS parameter set is 2.04 ± 0.03M ⊙ and the radius of a canonical mass neutron star (R 1.4) comes out to be equal to 13.06 ± 0.16 Km. The value of dimensionless tidal deformability, for canonical mass, is 602.23 ± 33.13 which satisfies the constraints of waveform models analysis of GW170817 within 90% confidence level.

Prospects to study hyperon-nucleon interactions at BESIII* *Supported by the National Natural Science Foundation of China (NSFC) (11935018, 11875054, 12165022), the Chinese Academy of Sciences (CAS) Key Research Program of Frontier Sciences (QYZDJ-SSW-SLH003), and the Fundamental Research Project of Yunnan Province, China (202301AT070162)

The prospects to study hyperon-nucleus/nucleon interactions at BESIII and similar colliders are analyzed in this paper. Utilizing the large quantity of hyperons produced by the decay of 10 billion and 2.7 billion collected at BESIII, the cross sections of several specific elastic and inelastic hyperon-nucleus reactions can be measured via scattering between hyperons and nucleus in the dense objects of the BESIII detector. Subsequently, the cross sections of the corresponding hyperon-nucleon interactions can be extracted from further phenomenological calculations. The interactions between antihyperons and nucleus/nucleon, including scattering and annihilation, can also be studied using the method proposed in this study. The results will definitely benefit the realization of precise probes for hyperon-nuclei/nucleus interactions and establish constraints to study the potential of strong interaction, the origin of color confinement, a unified model for baryon-baryon interactions, and the internal structure of neutron stars. In addition, the desirable prospects of corresponding studies in the future Super Tau-Charm Factory (STCF) are discussed and estimated in this study.

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.

Bayesian analysis of nontrivial features in the speed of sound inside neutron stars in light of astrophysical and pQCD constraints

Functional forms of the neutron star Equation of State (EoS) are required to extract the viable EoS band from neutron star observations. Realistic nuclear EoS, containing deconfined quarks or hyperons, present nontrivial features in the speed of sound such as bumps, kinks, and plateaus. Using modified Gaussian processes to model EoS with nontrivial features, we show in a fully Bayesian analysis incorporating measurements from X-ray sources, gravitational wave observations, and perturbative QCD results that these features are compatible with current constraints. We find that nontrivial behavior in the EoS plays a role in understanding the possible phase structure of neutron stars at densities around 2 nsat.

Constraints on Neutron Star Structure from the Clocked X-Ray Burster 1RXS J180408.9−342058

Type I X-ray bursts are rapid-brightening transient phenomena on the surfaces of accreting neutron stars (NSs). Some X-ray bursts, called clocked bursters, exhibit regular behavior with similar light-curve profiles in their burst sequences. The periodic nature of clocked bursters has the advantage of constraining X-ray binary parameters and physics inside the NS. In the present study, we compute numerical models, based on different equations of state and NS masses, which are compared with the observations of a recently identified clocked burster, 1RXS J180408.9−342058. We find that the relation between the accretion rate and the recurrence time is highly sensitive to the NS mass and radius. We determine, in particular, that 1RXS J180408.9−342058 appears to possess a mass less than 1.7M ⊙ and favors a stiffer nuclear equation of state (with an NS radius ≳12.7 km). Consequently, the observations of this new clocked burster may provide additional constraints for probing the structure of NSs.

Bounding the QCD Equation of State with the Lattice

The equation of state of QCD matter at high densities is relevant for neutron star structure and for neutron star mergers and has been a focus of recent work. We show how lattice QCD simulations, free of sign problems, can provide an upper bound on the pressure as a function of quark chemical potentials. We show that at large chemical potentials this bound should become quite sharp; the difference between the upper bound on the pressure PPQ and the true pressure P is of order PPQ− P = O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αs3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_{\ extrm{s}}^3 $$\\end{document}P). The corrections arise from a single Feynman diagram; its calculation would render remaining corrections O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αs4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_{\ extrm{s}}^4 $$\\end{document}P).

Compact stars in scalar–tensor theories with a single-well potential and the corresponding [formula omitted] theory

The macroscopic properties of compact stars in modified gravity theories can be significantly different from the general relativistic (GR) predictions. Within the gravitational context of scalar–tensor theories, with a scalar field ϕ and coupling function Φ(ϕ)=exp[2ϕ/3], we investigate the hydrostatic equilibrium structure of neutron stars for the simple potential V(ϕ)=ωϕ2/2 defined in the Einstein frame (EF). From the scalar field in the EF, we also interpret such theories as f(R) gravity in the corresponding Jordan frame (JF). The mass–radius relations, proper mass, and binding energy are obtained for a polytropic equation of state (EoS) in the JF. Our results reveal that the maximum-mass values increase substantially as ω gets smaller, while the radius and mass decrease in the low-central-density region as we move further away from the pure GR scenario. Furthermore, a cusp is formed when the binding energy is plotted as a function of the proper mass, which indicates the appearance of instability. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to dM/dρcJ=0 on the M(ρcJ)-curve.

Constraining self-interacting fermionic dark matter in admixed neutron stars using multimessenger astronomy

ABSTRACT We investigate the structure of admixed neutron stars with a regular hadronic component and a fraction of fermionic self-interacting dark matter. Using two limiting equations of state for the dense baryonic interior, constructed from piecewise generalized polytropes, and an asymmetric self-interacting fermionic dark component, we analyse different scenarios of admixed neutron stars depending on the mass of dark fermions mχ, interaction mediators mϕ, and self-interacting strengths g. We find that the contribution of dark matter to the masses and radii of neutron stars leads to tension with mass estimates of the pulsar J0453+1559, the least massive neutron star, and with the constraints coming from the GW170817 event. We discuss the possibilities of constraining dark matter model parameters g and y ≡ mχ/mϕ, using current existing knowledge on neutron star estimations of mass, radius, and tidal deformability, along with the accepted cosmological dark matter freeze-out values and self-interaction cross-section to mass ratio, σSI/mχ, fitted to explain Bullet, Abell, and dwarf galaxy cluster dynamics. By assuming the most restrictive upper limit, σSI/mχ < 0.1 cm2 g−1, along with dark matter freeze-out range values, the allowed g–y region is 0.01 ≲ g ≲ 0.1, with 0.5 ≲ y ≲ 200. For the first time, the combination of updated complementary restrictions is used to set constraints on self-interacting dark matter.

From masses and radii of neutron stars to EOS of nuclear matter through neural network* *Supported by the National Natural Science Foundation of China (12375144, 11975101), and the Natural Science Foundation of Guangdong Province, China (2022A1515011552, 2020A151501820)

The equation of state (EOS) of dense nuclear matter is a key factor for determining the internal structure and properties of neutron stars. However, the EOS of high-density nuclear matter has great uncertainty, mainly because terrestrial nuclear experiments cannot reproduce matter as dense as that in the inner core of a neutron star. Fortunately, continuous improvements in astronomical observations of neutron stars provide the opportunity to inversely constrain the EOS of high-density nuclear matter. Several methods have been proposed to implement this inverse constraint, including the Bayesian analysis algorithm, the Lindblom's approach, and so on. Neural network algorithm is an effective method developed in recent years. By employing a set of isospin-dependent parametric EOSs as the training sample of a neural network algorithm, we set up an effective way to reconstruct the EOS with relative accuracy using a few mass-radius data. Based on the obtained neural network algorithms and according to the NICER observations on masses and radii of neutron stars with assumed precision, we obtain the inversely constrained EOS and further calculate the corresponding macroscopic properties of the neutron star. The results are basically consistent with the constraint on EOS in Huth et al. [Nature 606, 276 (2022)] based on Bayesian analysis. Moreover, the results show that even though the neural network algorithm was obtained using the finite parameterized EOS as the training set, it is valid for any rational parameter combination of the parameterized EOS model.

Phase diagram determination at fivefold nuclear compression

In the standard model of particle physics, the strong force is characterized by the theory of quantum chromodynamics (QCD). It is commonly understood from QCD properties that hadrons, at sufficiently high temperatures or densities, melt into their constituent quarks, thereby undergoing a deconfinement transition to a new phase of quarks and gluons, often referred to as quark matter or quark-gluon plasma (QGP) [1,2]. Although QGP has been observed in relativistic heavy-ion collisions [3,4], uncertainties remain about when the onset of deconfinement occurs. After comparing simulations from a reliable hadron and quark relativistic transport model with recent data from the STAR experiment, we determined that the onset of the hadron-quark phase transition occurs at about five times nuclear compression, corresponding to temperature T∼ 112 MeV and baryon chemical potential μB∼ 586 MeV, in the nuclear matter phase diagram. This discovery has significant implications for the studies of both the early and present universe [5], including the fraction of dark matter formed in the early universe [6–8] and the structure and dynamics of neutron stars and their mergers [9].

Tabulated equations of state from models informed by chiral effective field theory

Abstract We construct four equation of state (EoS) tables, tabulated over a range of temperatures, densities, and charge fractions, relevant for neutron star applications such as simulations of neutron star mergers. The EoS are computed from a relativistic mean-field theory constrained by the pure neutron matter EoS from chiral effective field theory, inferred properties of isospin-symmetric nuclear matter, and astrophysical observations of neutron star structure. To model nuclear matter at low densities, we attach an EoS that models inhomogeneous nuclear matter at arbitrary temperatures and charge fractions. The four EoS tables we develop are available from the CompOSE EoS repository https://compose.obspm.fr/eos/297 and gitlab.com/ahaber/qmc-rmf-tables.

Neutron star characteristics from the neutron structure

We draw insight into the neutron star structure and characteristics from the neutron structure. The eigenvectors of the special unitary group, SU(3), describing baryons, imply that neutron quarks reside on three faces of a tetrahedron. The tetrahedral structure accounts for the neutron magnetic moment and mass. Thus, we reason that neutrons precipitate with aligned magnetic moments into the triakis truncated tetrahedron tessellation under immense gravitational pressure. As the particle’s tetrahedral symmetry does not match the crystal’s rhombic symmetry, the total magnetic moment invariably misaligns with the star’s spinning axis. We infer further from the neutron structure that with increasing gravitational pressure, two neutrons condense into the same tetrahedron. Due to doubling density, the contracting star spins up abruptly but then settles down slowly as the gradients in density smoothen. As down quarks are positioned for pairwise fusions into anti-up quarks in the dineutron, we reason that tetraquark indeed forms as gravitational pressure increases further. The star balances the accompanying loss of mass by spinning down suddenly but recovers as the gradients in density smoothen again. Ultimately, when gravitational pressure increases even more, the anti-up quarks will annihilate with up quarks. As the core becomes ever more structured, such high-energy events fade out, and eventually, only magnetic field-collimated radio-frequency dissipation drives the spin down. The nuclear moments manifest fully in a magnetar, free from floating, hence counteraligning baryonic matter. In conclusion, the neutron structure makes sense of the neutron star density, magnetism, beams at an angle to the spinning axis, and pulsing transients, and paves the way for making sense of reactions in a black hole.

Nuclear physics inputs for dense-matter modelling in neutron stars. The nuclear equation of state

In this contribution, we briefly present the equation-of-state modelling for application to neutron stars and discuss current constraints coming from nuclear physics theory and experiments. To assess the impact of model uncertainties, we employ a nucleonic meta-modelling approach and perform a Bayesian analysis to generate posterior distributions for the equation of state with filters accounting for both our present low-density nuclear physics knowledge and high-density neutron-star physics constraints. The global structure of neutron stars thus predicted is discussed in connection with recent astrophysical observations.

Neutron Star Phase Transition as the Origin for the Fast Radio Bursts and Soft Gamma-Ray Repeaters of SGR J1935 + 2154

Magnetars are believed to be neutron stars (NSs) with strong magnetic fields. X-ray flares and fast radio bursts (FRBs) have been observed from the magnetar (soft gamma-ray repeater, SGR J1935+2154). We propose that the phase transition of the NS can power the FRBs and SGRs. Based on the equation of state provided by the MIT bag model and the mean field approximation, we solve the Tolman–Oppenheimer–Volkoff equations to get the NS structure. With the spin-down of the NS, the hadronic shell gradually transfers to the quark shell. The gravitational potential energy released by one time of the phase transition can be achieved. The released energy, time interval between two successive phase transitions, and glitch are all consistent with the observations of the FRBs and the X-ray flares from SGR J1935 + 2154. We conclude that the phase transition of an NS is a plausible mechanism to power the SGRs as well as the repeating FRBs.

The Impacts of Neutron Star Structure and Base Heating on Type I X-Ray Bursts and Code Comparison

Type I X-ray bursts are rapidly brightening phenomena triggered by thermonuclear burning on the accreting layers of a neutron star (NS). The light curves represent the physical properties of NSs and the nuclear reactions on the proton-rich nuclei. The numerical treatments of the accreting NS and physics of the NS interior are not established, which shows uncertainty in modeling for observed X-ray light curves. In this study, we investigate theoretical X-ray burst models compared with burst light curves with GS 1826-24 observations. We focus on the impacts of the NS mass and radius and base heating on the NS surface using the MESA code. We find a monotonic correlation between the NS mass and the parameters of the light curve. The higher the mass, the longer the recurrence time and the greater the peak luminosity. While the larger the radius, the longer the recurrence time, the peak luminosity remains nearly constant. In the case of increasing base heating, both the recurrence time and peak luminosity decrease. We also examine the above results with a different numerical code, HERES, based on general relativity and consider the central NS. We find that the burst rate, energy, and strength are almost the same in two X-ray burst codes by adjusting the base heat parameter in MESA (the relative errors ≲5%), while the duration and rise times are significantly different between (the relative error is possibly ∼50%). The peak luminosity and the e-folding time change irregularly between two codes for different accretion rates.

Probing strong field f(R) gravity and ultradense matter with the structure and thermal evolution of neutron stars

Thermal evolution of neutron stars is studied in the $f(R)=R+\ensuremath{\alpha}{R}^{2}$ theory of gravity. We first review the equations of stellar structure and evolution for a spherically symmetric spacetime plus a perfect fluid at rest. We then present numerical results for the structure of neutron stars using four nucleonic dense matter equations of state and a series of gravity theories for $\ensuremath{\alpha}$ ranging from zero, i.e., general relativity, up to $\ensuremath{\alpha}\ensuremath{\approx}{10}^{16}\text{ }\text{ }{\mathrm{cm}}^{2}$. We emphasize properties of these neutron star models that are of relevance for their thermal evolution as the threshold masses for enhanced neutrino emission by the direct Urca process, the proper volume of the stellar cores where this neutrino emission is allowed, the crust thickness, and the surface gravitational acceleration that directly impact the observable effective temperature. Finally, we numerically solve the equations of thermal evolution and explicitly analyze the effects of altering gravity. We find that uncertainties in the dense matter microphysics, such as the core chemical composition and superfluidity/superconductivity properties, as well as the astrophysical uncertainties on the chemical composition of the surface layers, have a much stronger impact than possible modifications of gravity within the studied family of $f(R)$ theories. We conclude that within this family of gravity theories, conclusions from previous studies of neutron star thermal evolution are not significantly altered by modification of gravity theory. Conversely, this implies that neutron star cooling modeling may not be a useful tool to constrain deviations of gravity from Einstein theory unless these are much more radical than in the $f(R)=R+\ensuremath{\alpha}{R}^{2}$ framework.