Finite-temperature Equation Of State Research Articles

Finite-temperature equations of state of compact stars with hyperons: three-dimensional tables

We construct tables of finite temperature equation of state (EoS) of hypernuclear matter in the range of densities, temperatures, and electron fractions that are needed for numerical simulations of supernovas, proto-neutron stars, and binary neutron star mergers and cast them in the format of CompOSE database. The tables are extracted from a model that is based on covariant density functional (CDF) theory that includes the full JP=1/2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^P=1/2^+$$\\end{document} baryon octet in a manner that is consistent with the current astrophysical and nuclear constraints. We employ a parameterization with three different values of the slope of the symmetry energy Lsym=30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_\ extrm{sym}=30$$\\end{document}, 50 and 70 MeV and fixed skewness Qsat=400\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_\ extrm{sat}= 400$$\\end{document} MeV for above saturation matter. A model for the EoS of inhomogeneous matter is matched at sub-saturation density to the high-density hypernuclear EoS. We discuss the generic features of the resulting EoS and the composition of matter as a function of density, temperature, and electron fraction. The nuclear characteristics and strangeness fraction of these models are compared to the alternatives from the literature. The integral properties of static and rapidly rotating compact stars in the limit of zero temperature are discussed and confronted with the multimessenger astrophysical constraints.

Quantifying uncertainties in general relativistic magnetohydrodynamic codes

In this paper, we show that similar open-source codes for general relativistic magnetohydrodynamic (GRMHD) produce different results for key features of binary neutron star mergers. First, we present a new open-source version of the publicly available IllinoisGRMHD code that provides support for realistic, finite temperature equations of state. After stringent tests of our upgraded code, we perform a code comparison between GRHydro, IllinoisGRMHD, Spritz, and WhiskyTHC, which implement the same physics, but slightly different computational methods. The benefit of the comparison is that all codes are embedded in the EinsteinToolkit suite, hence their only difference is algorithmic. We find similar convergence properties, fluid dynamics, and gravitational waves, but different merger times, remnant lifetimes, and gravitational wave phases. Such differences must be resolved before the post-merger dynamics modeled with such simulations can be reliably used to infer the properties of nuclear matter especially in the era of precision gravitational wave astronomy.

Addition of tabulated equation of state and neutrino leakage support to illinoisgrmhd

We have added support for realistic, microphysical, finite-temperature equations of state (EOS) and neutrino physics via a leakage scheme to illinoisgrmhd, an open-source GRMHD code for dynamical spacetimes in the einstein toolkit. These new features are provided by two new, nrpy+-based codes: nrpyeos, which performs highly efficient EOS table lookups and interpolations, and nrpyleakage, which implements a new, adaptive mesh refinement (AMR)-capable neutrino leakage scheme in the einstein toolkit. We have performed a series of strenuous validation tests that demonstrate the robustness of these new codes, particularly on the Cartesian AMR grids provided by carpet. Furthermore, we show results from fully dynamical GRMHD simulations of single unmagnetized neutron stars, and magnetized binary neutron star mergers. This new version of illinoisgrmhd, as well as nrpyeos and nrpyleakage, is pedagogically documented in jupyter notebooks and fully open source. The codes will be proposed for inclusion in an upcoming version of the einstein toolkit.

GRMHD Simulations of Neutron-star Mergers with Weak Interactions: r-process Nucleosynthesis and Electromagnetic Signatures of Dynamical Ejecta

Fast neutron-rich material ejected dynamically over ≲10 ms during the merger of a binary neutron star (BNS) can give rise to distinctive electromagnetic counterparts to the system’s gravitational-wave emission that serve as a “smoking gun” to distinguish between a BNS and an NS–black hole merger. We present novel ab initio modeling of the kilonova precursor and kilonova afterglow based on 3D general-relativistic magnetohydrodynamic simulations of BNS mergers with nuclear, tabulated, finite-temperature equations of state (EOSs), weak interactions, and approximate neutrino transport. We analyze dynamical mass ejection from 1.35–1.35 M ⊙ binaries, consistent with properties of the first observed BNS merger GW170817, using three nuclear EOSs that span the range of allowed compactness of 1.35 M ⊙-neutron stars. Nuclear reaction network calculations yield a robust second-to-third-peak r-process. We find few ×10−6 M ⊙ of fast (v > 0.6c) ejecta that give rise to broadband synchrotron emission on ∼years timescales, consistent with tentative evidence for excess X-ray/radio emission following GW170817. We find ≈2 × 10−5 M ⊙ of free neutrons that power a kilonova precursor on ≲ hours timescale. A boost in early UV/optical brightness by a factor of a few due to previously neglected relativistic effects, with enhancements up to ≲10 hr post-merger, is promising for future detection with UV/optical telescopes like Swift or ULTRASAT. We find that a recently predicted opacity boost due to highly ionized lanthanides at ≳70,000 K is unlikely to affect the early kilonova based on the obtained ejecta structures. Azimuthal inhomogeneities in dynamical ejecta composition for soft EOSs found here (“lanthanide/actinide pockets”) may have observable consequences for both early kilonova and late-time nebular emission.

Equation of state for hot hyperonic neutron star matter

Abstract The FSU2H equation-of-state model, originally developed to describe cold neutron star matter with hyperonic cores, is extended to finite temperature. Results are presented for a wide range of temperatures and lepton fractions, which cover the conditions met in protoneutron star matter, neutron star mergers, and supernova explosions. It is found that the temperature effects on the thermodynamical observables and the composition of the neutron star core are stronger when the hyperonic degrees of freedom are considered. An evaluation of the temperature and density dependence of the thermal index leads to the observation that the so-called Γ law, widely used in neutron star merger simulations, is not appropriate to reproduce the true thermal effects, specially when hyperons start to be abundant in the neutron star core. To make finite temperature equations of state easily accessible, simple parametrizations of the thermal index for nucleonic and hyperonic β-stable neutrino-free matter are provided.

Thermodynamics of Hot Neutron Stars and Universal Relations

Over the last few years, the detection of gravitational waves from binary neutron star systems has rekindled our hopes for a deeper understanding of the unknown nature of ultradense matter. In particular, gravitational wave constraints on the tidal deformability of a neutron star can be translated into constraints on several neutron star properties using a set of universal relations. Apart from binary neutron star mergers, supernova explosions are also important candidates for the detection of multimessenger signals. Such observations may allow us to impose significant constraints on the binding energy of neutron stars. The purpose of the present study is twofold. Firstly, we investigate the agreement of finite temperature equations of state with established universal relations. Secondly, we examine the possible existence of a universal relation between the binding energy and the dimensionless tidal deformability, which are the bulk properties connected to the most promising sources for multimessenger signals. We find that hot equations of state are not always compatible with accepted universal relations. Therefore, the use of such expressions for probing general relativity or imposing constraints on the structure of neutron stars would be inconclusive (when thermal effects are present). Additionally, we show that the binding energy and the dimensionless tidal deformability exhibit a universal trend at least for moderate neutron star masses. The latter allows us to set bounds on the binding energy of a 1.4 M⊙ neutron star using data from the GW170817 event. Finally, we provide a relation between the compactness, the binding energy and the dimensionless tidal deformability of a neutron star that is accurate for cold and hot isentropic equations of state.

Finite-temperature equation of state with hyperons

We present the novel finite-temperature FSU2H* equation-of-state model that covers a wide range of temperatures and lepton fractions for the conditions in proto-neutron stars, neutron star mergers and supernovae. The temperature effects on the thermodynamical observables and the composition of the neutron star core are stronger when the hyperonic degrees of freedom are considered. We pay a special attention to the temperature and density dependence of the thermal index in the presence of hyperons and conclude that the true thermal effects cannot be reproduced with the use of a constant Г law

Impact of the nuclear symmetry energy on the post-merger phase of a binary neutron star coalescence

The nuclear symmetry energy plays a key role in determining the equation of state of dense, neutron-rich matter, which governs the properties of both terrestrial nuclear matter as well as astrophysical neutron stars. A recent measurement of the neutron skin thickness from the PREX Collaboration has lead to new constraints on the slope of the nuclear symmetry energy, $L$, which can be directly compared to inferences from gravitational wave observations of the first binary neutron star merger inspiral, GW170817. In this paper, we explore a new regime for potentially constraining the slope, $L$, of the nuclear symmetry energy with future gravitational wave events: the post-merger phase of a binary neutron star coalescence. In particular, we go beyond the inspiral phase, where imprints of the slope parameter $L$ may be inferred from measurements of the tidal deformability, to consider imprints on the post-merger dynamics, gravitational wave emission, and dynamical mass ejection. To this end, we perform a set of targeted neutron star merger simulations in full general relativity using new finite-temperature equations of state, which systematically vary $L$ while keeping the magnitude of the symmetry energy at the saturation density, $S$, fixed. We find that the post-merger dynamics and gravitational wave emission are mostly insensitive to the slope of the nuclear symmetry energy. In contrast, we find that dynamical mass ejection contains a weak imprint of $L$, with large values of $L$ leading to systematically enhanced ejecta.

Equation of State and Composition of Proto-Neutron Stars and Merger Remnants with Hyperons

Finite-temperature equation of state (EoS) and the composition of dense nuclear and hypernuclear matter under conditions characteristic of neutron star binary merger remnants and supernovas are discussed. We consider both neutrino free-streaming and trapped regimes which are separated by a temperature of a few MeV. The formalism is based on covariant density functional (CDF) theory for the full baryon octet with density-dependent couplings, suitably adjusted in the hypernuclear sector. The softening of the EoS with the introduction of the hyperons is quantified under various conditions of lepton fractions and temperatures. We find that Λ, Ξ−, and Ξ0 hyperons appear in the given order with a sharp density increase at zero temperature at the threshold being replaced by an extended increment over a wide density range at high temperatures. The Λ hyperon survives in the deep subnuclear regime. The triplet of Σs is suppressed in cold hypernuclear matter up to around seven times the nuclear saturation density, but appears in significant fractions at higher temperatures, T≥20 MeV, in both supernova and merger remnant matter. We point out that a special isospin degeneracy point exists where the baryon abundances within each of the three isospin multiplets are equal to each other as a result of (approximate) isospin symmetry. At that point, the charge chemical potential of the system vanishes. We find that under the merger remnant conditions, the fractions of electron and μ-on neutrinos are close and are about 1%, whereas in the supernova case, we only find a significant fraction (∼10%) of electron neutrinos, given that in this case, the μ-on lepton number is zero.

HARM3D+NUC: A New Method for Simulating the Post-merger Phase of Binary Neutron Star Mergers with GRMHD, Tabulated EOS, and Neutrino Leakage

Abstract The first binary neutron star merger has already been detected in gravitational waves. The signal was accompanied by an electromagnetic counterpart including a kilonova component powered by the decay of radioactive nuclei, as well as a short γ-ray burst. In order to understand the radioactively powered signal, it is necessary to simulate the outflows and their nucleosynthesis from the post-merger disk. Simulating the disk and predicting the composition of the outflows requires general relativistic magnetohydrodynamical (GRMHD) simulations that include a realistic, finite-temperature equation of state (EOS) and self-consistently calculating the impact of neutrinos. In this work, we detail the implementation of a finite-temperature EOS and the treatment of neutrinos in the GRMHD code HARM3D+NUC, based on HARM3D. We include formal tests of both the finite-temperature EOS and the neutrino-leakage scheme. We further test the code by showing that, given conditions similar to those of published remnant disks following neutron star mergers, it reproduces both recombination of free nucleons to a neutron-rich composition and excitation of a thermal wind.

On accretion discs formed in MHD simulations of black hole–neutron star mergers with accurate microphysics

ABSTRACT Remnant accretion discs formed in compact object mergers are an important ingredient in the understanding of electromagnetic afterglows of multimessenger gravitational-wave events. Due to magnetically and neutrino-driven winds, a significant fraction of the disc mass will eventually become unbound and undergo r-process nucleosynthesis. While this process has been studied in some detail, previous studies have typically used approximate initial conditions for the accretion discs, or started from purely hydrodynamical simulations. In this work, we analyse the properties of accretion discs formed from near equal-mass black hole–neutron star mergers simulated in general-relativistic magnetohydrodynamics in dynamical spacetimes with an accurate microphysical description. The post-merger systems were evolved until $120\, {\rm ms}$ for different finite-temperature equations of state and black hole spins. We present a detailed analysis of the fluid properties and of the magnetic-field topology. In particular, we provide analytic fits of the magnetic-field strength and specific entropy as a function of the rest-mass density, which can be used for the construction of equilibrium disc models. Finally, we evolve one of the systems for a total of $350\, \rm ms$ after merger and study the prospect for eventual jet launching. While our simulations do not reach this stage, we find clear evidence of continued funnel magnetization and clearing, a prerequisite for any jet-launching mechanism.

Maximum mass of compact stars from gravitational wave events with finite-temperature equations of state

We conjecture and verify a set of relations between global parameters of hot and fast-rotating compact stars which do not depend on the equation of state, including a relation connecting the masses of the mass-shedding (Kepler) and static configurations. We apply these relations to the GW170817 event by adopting the scenario in which a hypermassive compact star remnant formed in a merger evolves into a supramassive compact star that collapses into a black hole once the stability line for such stars is crossed. We deduce an upper limit on the maximum mass of static, cold neutron stars $2.{15}_{\ensuremath{-}0.17}^{+0.18}\ensuremath{\le}{M}_{\mathrm{TOV}}^{★}/{M}_{\ensuremath{\bigodot}}\ensuremath{\le}2.{24}_{\ensuremath{-}0.44}^{+0.45}$ for the typical range of entropy per baryon, $2\ensuremath{\le}S/A\ensuremath{\le}3$, and electron fraction ${Y}_{e}=0.1$ characterizing the hot hypermassive star. Our result implies that accounting for the finite temperature of the merger remnant relaxes previously derived constraints on the value of the maximum mass of a cold, static compact star.

Accretion-induced prompt black hole formation in asymmetric neutron star mergers, dynamical ejecta, and kilonova signals

ABSTRACT We present new numerical relativity results of neutron star (NS) mergers with chirp mass 1.188 M⊙ and mass ratios q = 1.67 and q = 1.8 using finite-temperature equations of state (EOS), approximate neutrino transport, and a subgrid model for magnetohydrodynamics-induced turbulent viscosity. The EOS are compatible with nuclear and astrophysical constraints and include a new microphysical model derived from ab initio calculations based on the Brueckner–Hartree–Fock approach. We report for the first time evidence for accretion-induced prompt collapse in high-mass-ratio mergers, in which the tidal disruption of the companion and its accretion on to the primary star determine prompt black hole (BH) formation. As a result of the tidal disruption, an accretion disc of neutron-rich and cold matter forms with baryon masses ∼0.15 M⊙, and it is significantly heavier than the remnant discs in equal-masses prompt-collapse mergers. Massive dynamical ejecta of the order of ∼0.01 M⊙ also originate from the tidal disruption. They are neutron-rich and expand from the orbital plane with a crescent-like geometry. Consequently, bright, red, and temporally extended kilonova emission is predicted from these mergers. Our results show that prompt BH mergers can power bright electromagnetic counterparts for high-mass-ratio binaries, and that the binary mass ratio can be, in principle, constrained from multimessenger observations.

Spritz: a new fully general-relativistic magnetohydrodynamic code

The new era of multimessenger astrophysics requires the capability of studying different aspects of the evolution of compact objects. In particular, the merger of neutron star binaries is a strong source of gravitational waves and electromagnetic radiation, from radio to γ-rays, as demonstrated by the detection of GW170817 and its electromagnetic counterparts. In order to understand the physical mechanisms involved in such systems, it is necessary to employ fully general relativistic magnetohydrodynamic (GRMHD) simulations able to include the effects of a composition and temperature dependent equation of state describing neutron star matter as well as neutrino emission and reabsorption. Here, we present our new code named Spritz that solves the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime. The code can support tabulated equations of state, taking into account finite temperature effects and allowing for the inclusion of neutrino radiation. In this first paper, we present the general features of the code and a series of tests performed in special and general relativity to assess the robustness of the basic GRMHD algorithms implemented. Among these tests, we also present the first comparison between a non-staggered and a staggered formulation of the vector potential evolution, which is used to guarantee the divergence-less character of the magnetic field. With respect to other publicly available GRMHD codes, Spritz combines the robust approach of a staggered formulation of the vector potential together with the use of an equation of state driver (EOS_Omni) that can allow the code to use finite temperature equations of state. A next version of the code will fully test the EOS_Omni driver by coupling it with a neutrino leakage scheme.

Equation of state effects in the core collapse of a 20−M⊙ star

Uncertainties in our knowledge of the properties of dense matter near and above nuclear saturation density are among the main sources of variations in multi-messenger signatures predicted for core-collapse supernovae (CCSNe) and the properties of neutron stars (NSs). We construct 97 new finite-temperature equations of state (EOSs) of dense matter that obey current experimental, observational, and theoretical constraints and discuss how systematic variations in the EOS parameters affect the properties of cold nonrotating NSs and the core collapse of a $20\,M_\odot$ progenitor star. The core collapse of the $20\,M_\odot$ progenitor star is simulated in spherical symmetry using the general-relativistic radiation-hydrodynamics code GR1D where neutrino interactions are computed for each EOS using the NuLib library. We conclude that the effective mass of nucleons at densities above nuclear saturation density is the largest source of uncertainty in the CCSN neutrino signal and dynamics even though it plays a subdominant role in most properties of cold NS matter. Meanwhile, changes in other observables affect the properties of cold NSs, while having little effect in CCSNe. To strengthen our conclusions, we perform six octant three-dimensional CCSN simulations varying the effective mass of nucleons at nuclear saturation density. We conclude that neutrino heating and, thus, the likelihood of explosion is significantly increased for EOSs where the effective mass of nucleons at nuclear saturation density is large.

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures $T$, we demonstrate that the coefficient in $T^2$ expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly-interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-{\it ansatz} equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in details. At $T=0$ we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.

Low mass binary neutron star mergers: Gravitational waves and neutrino emission

Neutron star mergers are among the most promising sources of gravitational waves for advanced ground-based detectors. These mergers are also expected to power bright electromagnetic signals, in the form of short gamma-ray bursts, infrared/optical transients, and radio emission. Simulations of these mergers with fully general relativistic codes are critical to understand the merger and post-merger gravitational wave signals and their neutrinos and electromagnetic counterparts. In this paper, we employ the SpEC code to simulate the merger of low-mass neutron star binaries (two $1.2M_\odot$ neutron stars) for a set of three nuclear-theory based, finite temperature equations of state. We show that the frequency peaks of the post-merger gravitational wave signal are in good agreement with predictions obtained from simulations using a simpler treatment of gravity. We find, however, that only the fundamental mode of the remnant is excited for long periods of time: emission at the secondary peaks is damped on a millisecond timescale in the simulated binaries. For such low-mass systems, the remnant is a massive neutron star which, depending on the equation of state, is either permanently stable or long-lived. We observe strong excitations of l=2, m=2 modes, both in the massive neutron star and in the form of hot, shocked tidal arms in the surrounding accretion torus. We estimate the neutrino emission of the remnant using a neutrino leakage scheme and, in one case, compare these results with a gray two-moment neutrino transport scheme. We confirm the complex geometry of the neutrino emission, also observed in previous simulations with neutrino leakage, and show explicitly the presence of important differences in the neutrino luminosity, disk composition, and outflow properties between the neutrino leakage and transport schemes.

Rotating protoneutron stars: Spin evolution, maximum mass, and I-Love-Q relations

Shortly after its birth in a gravitational collapse, a proto-neutron star enters in a phase of quasi-stationary evolution characterized by large gradients of the thermodynamical variables and intense neutrino emission. In few tens of seconds the gradients smooth out while the star contracts and cools down, until it becomes a neutron star. In this paper we study this phase of the proto-neutron star life including rotation, and employing finite temperature equations of state. We model the evolution of the rotation rate, and determine the relevant quantities characterizing the star. Our results show that an isolated neutron star cannot reach, at the end of the evolution, the maximum values of mass and rotation rate allowed by the zero-temperature equation of state. Moreover, a mature neutron star evolved in isolation cannot rotate too rapidly, even if it is born from a proto-neutron star rotating at the mass-shedding limit. We also show that the I-Love-Q relations are violated in the first second of life, but they are satisfied as soon as the entropy gradients smooth out.

Determination of the finite temperature equation of state of dense matter

The equation of state is calculated for temperatures less than 30 MeV and densities less than four times the saturation density of nuclear matter using a combined analysis of Auxiliarly Fields Diffusion Monte Carlo and Fermi Hypernetted Change methods.

Finite-Temperature Equation of State with Three-Body ForceCorrelations

The equation of state of asymmetric nuclear matter atfinite temperature is studied in the framework of theBrueckner–Hartree–Fock approximation which is extended to includethree-body force correlations. Due to the additional repulsion producedby three-body force contribution, the proton or neutron potentialenergy and effective mass are correspondingly enhanced. The symmetryenergy gradually becomes more sensitive to the temperature with theincreasing density compared with the result that only includes the twohole-line contribution. The asymmetry parameter dependence of symmetryenergy is also indicated. It is shown that there is the same linearrelation between symmetry energy and β2 as the zerotemperature case with β being the asymmetry parameter.