Equation Of State For Neutron Star Matter Research Articles

Velocity of sound beyond the high-density relativistic limit from lattice simulation of dense two-color QCD

Abstract We obtain the equation of state (EoS) for two-color quantum chromodynamics (QCD) at low temperature and high density from the lattice Monte Carlo simulation. We find that the velocity of sound exceeds the relativistic limit ($c_s^2/c^2=1/3$) after BEC-BCS (Bose-Einstein condensation–Bardeen–Cooper–Schrieffer) crossover in the superfluid phase. Such an excess of the sound velocity is previously unknown from any lattice calculations for QCD-like theories. This finding might have a possible relevance to the EoS of neutron star matter revealed by recent measurements of neutron star masses and radii.

Impact of the equation of state on f - and p - mode oscillations of neutron stars

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $\beta$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $\rho_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $\beta$-equilibrated pressure at density $\rho_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.

Bayesian reconstruction of nuclear matter parameters from the equation of state of neutron star matter

The nuclear matter parameters (NMPs), those underlie in the construction of the equation of state (EoS) of neutron star matter, are not directly accessible. The Bayesian approach is applied to reconstruct the posterior distributions of NMPs from the EoS of neutron star matter. The constraints on lower-order parameters as imposed by the finite nuclei observables are incorporated through appropriately chosen prior distributions. The calculations are performed with two sets of pseudo data on the EoS whose true models are known. The median values of second or higher order NMPs show sizeable deviations from their true values and associated uncertainties are also larger. The sources of these uncertainties are intrinsic in nature, identified as (i) the correlations among various NMPs and (ii) the variations in the EoS of symmetric nuclear matter, symmetry energy, and the neutron-proton asymmetry in such a way that the neutron star matter EoS remain almost unaffected.

Gravitational wave asteroseismology for low-mass neutron stars

The fundamental ($f$-) mode gravitational waves from cold low-mass neutron stars are systematically studied with various equations of state (EOSs) characterized by the nuclear saturation parameters, especially focusing on the phenomena of the avoided crossing with the first pressure ($p_1$-) mode. We find that the $f$-mode frequency and the average density for the neutron star at the avoided crossing can be expressed as a function of the parameter, $\eta$, which is the specific combination of the nuclear saturation parameters. Owing to these relations, we can derive the empirical formula expressing the $f$-mode frequency for a low-mass neutron star, whose central density is larger than that for the neutron star at the avoided crossing, as a function of $\eta$ and the square root of the stellar average density, $x$. On the other hand, we also derive the empirical formula expressing the $f$-mode frequency for a neutron star, whose central density is less than that for the neutron star at the avoided crossing, as a function of $x$ independently of the adopted EOS. Furthermore, adopting the empirical formula of $x$ as a function of $\eta$ and $u_c$, which is the ratio of the stellar central density to the saturation density, we can also rewrite our empirical formula for the $f$-mode frequency to a function of $\eta$ and $u_c$. So, by observing the $f$-mode gravitational wave from a low-mass neutron star, whose mass or gravitational redshift is known, one could evaluate the values of $\eta$ and $u_c$, which enables us to severely constrain the EOS for neutron star matter.

Suitable resolution of EOS tables for neutron star investigations * * Supported by National Natural Science Foundation of China (11722546 and 11275073), Talent Program of South China University of Technology (K5180470), This Project is Sponsored by CSC and has Made Use of NASA's Astrophysics Data System

Inasmuch as the hydrostatic structure of the interior of neutron stars uniquely depends on the equation of state (EOS), the inverse constraints on EOS from astrophysical observations have been an important method for revealing the properties of high density matter. Currently, most EOS for neutron star matter are given in tabular form, but these numerical tables can have quite different resolution. To guarantee both the accuracy and efficiency in computing the Tolman-Oppenheimer-Volkoff equations, a concise standard for generating EOS tables with suitable resolution is investigated. It is shown that EOS tables with 50 points logarithmic-uniformly distributed in the supra-nuclear density segment [ ], where is the nuclear saturation density, correspond to the interpolation induced errors of ~0.02% for the gravitational mass and ~0.2% for the tidal deformability .

Astrophysical constraints on a parametric equation of state for neutron-rich nucleonic matter

Extracting the equation of state (EOS) and symmetry energy of dense neutron-rich matter from astrophysical observations is a long-standing goal of nuclear astrophysics. To facilitate the realization of this goal, the feasibility of using an explicitly isospin-dependent parametric EOS for neutron star matter was investigated recently in [1–3]. In this contribution, in addition to outlining the model framework and summarizing the most important findings from [1–3], we report a few new results regarding constraining parameters characterizing the high-density behavior of nuclear symmetry energy. In particular, the constraints on the pressure of neutron star matter extracted from combining the X-ray observations of the neutron star radius, the minimum–maximum mass $$M=2.01$$ $$\hbox {M}_\odot $$ , and causality condition agree very well with those extracted from analyzing the tidal deformability data by the LIGO + Virgo Collaborations. The limitations of using the radius and/or tidal deformability of neutron stars to constrain the high-density nuclear symmetry energy are discussed.

Moments of inertia of neutron stars in relativistic mean field theory: The role of the isovector scalar channel

With the inclusion of the isovector scalar channel in the meson-nucleon couplings, taking DD-ME$\delta$ as an effective interaction, the moments of inertia of neutron stars possessing various stellar masses are studied within the density dependent relativistic mean field (RMF) theory. The isovector scalar channel contributes to the softening of the neutron-star matter equation of state (EOS) and therefore the reduction of the maximum mass and radius of neutron stars. Smaller values of the total moment of inertia $I$ and the crustal moment of inertia $\Delta{I}$ are then obtained in DD-ME$\delta$ via numerical procedure in comparison with those in other selected RMF functionals. In addition, the involvement of the isovector scalar channel lowers the thickness of the neutron star crust and its mass fraction as well. The sensitivity to both the crustal mass and stellar radius causes the crustal moment of inertia to be more obviously reduced than the total one, eventually leading to a suppression on the fraction of crustal moment of inertia $\Delta{I}/I$ in DD-ME$\delta$. The results indicate the crustal moment of inertia as a more sensitive probe of the neutron-star matter EOS than the total one, and demonstrate that the isovector scalar meson-nucleon couplings in the RMF theory could exert influence over the physics of pulsar glitches.

Neutron stars including the effects of chaotic magnetic fields and anomalous magnetic moments**Supported by National Natural Science Foundation of China (11535004, 11375086, 11120101005, 11175085, 11235001), 973 National Major State Basic Research and Development of China (2013CB834400), and Science and Technology Development Fund of Macau (068/2011/A)

The relativistic mean field (RMF) FSUGold model extended to include hyperons is employed to study the properties of neutron stars with strong magnetic fields. The chaotic magnetic field approximation is utilized. The effect of anomalous magnetic moments (AMMs) is also investigated. It is shown that the equation of state (EOS) of neutron star matter is stiffened by the presence of the magnetic field, which increases the maximum mass of a neutron star by around 6%. The AMMs only have a small influence on the EOS of neutron star matter, and increase the maximum mass of a neutron star by 0.02Msun. Neutral particles are spin polarized due to the presence of the AMMs.

Magnetic field and EoS of neutron star matter at finite temperature

In this paper, magnetic field and equation of state (EoS) of neutron star matter are studied under relativistic mean field theory. A nonzero mass term of magnetic field in the Lagrangian is introduced, which depends on baryon density of charged particles. The magnetic field has not been treated as external as usual and the calculations of magnetic field strength at finite temperature reveal the existence of inflection points in certain densities.

Equation of State for Nucleonic Matter and its Quark Mass Dependence from the Nuclear Force in Lattice QCD

Quark mass dependence of the equation of state (EOS) for nucleonic matter is investigated, on the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon interaction extracted from lattice QCD simulations. We observe saturation of nuclear matter at the lightest available quark mass corresponding to the pseudoscalar meson mass ≃469 MeV. Mass-radius relation of the neutron stars is also studied with the EOS for neutron-star matter from the same nuclear force in lattice QCD. We observe that the EOS becomes stiffer and thus the maximum mass of neutron star increases as the quark mass decreases toward the physical point.

A two-solar-mass neutron star measured using Shapiro delay

Neutron stars are composed of the densest form of matter known to exist in our Universe, the composition and properties of which are still theoretically uncertain. Measurements of the masses or radii of these objects can strongly constrain the neutron star matter equation of state and rule out theoretical models of their composition. The observed range of neutron star masses, however, has hitherto been too narrow to rule out many predictions of 'exotic' non-nucleonic components. The Shapiro delay is a general-relativistic increase in light travel time through the curved space-time near a massive body. For highly inclined (nearly edge-on) binary millisecond radio pulsar systems, this effect allows us to infer the masses of both the neutron star and its binary companion to high precision. Here we present radio timing observations of the binary millisecond pulsar J1614-2230 that show a strong Shapiro delay signature. We calculate the pulsar mass to be (1.97 ± 0.04)M(⊙), which rules out almost all currently proposed hyperon or boson condensate equations of state (M(⊙), solar mass). Quark matter can support a star this massive only if the quarks are strongly interacting and are therefore not 'free' quarks.

Sensitivity of the moment of inertia of neutron stars to the equation of state of neutron-rich matter

The sensitivity of the stellar moment of inertia to the neutron-star matter equation of state is examined using accurately-calibrated relativistic mean-field models. We probe this sensitivity by tuning both the density dependence of the symmetry energy and the high density component of the equation of state, properties that are at present poorly constrained by existing laboratory data. Particularly attractive is the study of the fraction of the moment of inertia contained in the solid crust. Analytic treatments of the crustal moment of inertia reveal a high sensitivity to the transition pressure at the core-crust interface. This may suggest the existence of a strong correlation between the density dependence of the symmetry energy and the crustal moment of inertia. However, no correlation was found. We conclude that constraining the density dependence of the symmetry energy - through, for example, the measurement of the neutron skin thickness in 208Pb - will place no significant bound on either the transition pressure or the crustal moment of inertia.

Relativistic models of the neutron-star matter equation of state

Motivated by a recent astrophysical measurement of the pressure of cold matter above nuclear-matter saturation density, we compute the equation of state of neutron star matter using accurately calibrated relativistic models. The uniform stellar core is assumed to consist of nucleons and leptons in beta equilibrium; no exotic degrees of freedom are included. We found the predictions of these models to be in fairly good agreement with the measured equation of state. Yet the Mass-vs-Radius relations predicted by these same models display radii that are consistently larger than the observations.

Λhypernuclei and neutron star matter in a chiral SU(3) relativistic mean field model with a logarithmic potential

We develop a chiral SU($3$) symmetric relativistic mean field model with a logarithmic potential of scalar condensates. Experimental and empirical data of symmetric nuclear matter saturation properties, bulk properties of normal nuclei, and separation energies of single- and double-$\ensuremath{\Lambda}$ hypernuclei are well explained. The nuclear matter equation of state (EOS) is found to be softened by $\ensuremath{\sigma}\ensuremath{\zeta}$ mixing which comes from determinant interaction. The neutron star matter EOS is further softened by $\ensuremath{\Lambda}$ hyperons.

THE EFFECT OF THE SCALAR-ISOVECTOR MESON FIELD ON HYPERON-RICH NEUTRON STAR MATTER

We investigate the effect of the scalar-isovector δ-meson field on the equation of state (EOS) and composition of hyperonic neutron star matter, and the properties of hyperonic neutron stars within the framework of the relativistic mean field theory. The influence of the δ-field turns out to be quite different and generally weaker for hyperonic neutron star matter as compared to that for npeμ neutron star matter. We find that inclusion of the δ-field enhances the strangeness content slightly and consequently moderately softens the EOS of neutron star matter in its hyperonic phase. As for the composition of hyperonic star matter, the effect of the δ-field is shown to shift the onset of the negatively-charged (positively-charged) hyperons to slightly lower (higher) densities and to enhance (reduce) their abundances. The influence of the δ-field on the maximum mass of hyperonic neutron stars is found to be fairly weak, whereas inclusion of the δ-field turns out to enhance sizably both the radii and the moments of inertia of neutron stars with given masses. It is also shown that the effects of the δ-field on the properties of hyperonic neutron stars remain similar in the case of switching off the Σ hyperons.

Relativistic equation of state for supernova and neutron star

We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for use in supernova simulations. The properties of nuclear matter with both uniform and non-uniform distributions are studied consistently. We tabulate the outcome in terms of the pressure, free energy, entropy, etc. at a sufficiently large number of mesh points in the density range ϱ B = 10 5.1 ∼ 10 15.4g/cm 3, the temperature range T = 0 ∼ 100 MeV and the proton fraction range Y p = 0 ∼ 0.56 to be used for supernova simulations. We also discuss the EOS of neutron star matter at zero temperature in a wide density range including hyperons.

Neutron star profiles in the relativistic Brueckner-Hartree-Fock theory

Abstract We study the properties of neutron star matter and neutron stars in the relativistic Brueckner-Hartree-Fock (RBHF) theory. Adopting the equation of state (EOS) in the RBHF theory, we calculate the properties of neutron star matter under the beta equilibrium condition in a wide range of density. We perform the Thomas-Fermi calculation of neutron star matter in the crust region taking into account the change of nuclear shapes around the density, ϱ ∼ 10 14 g/cm 3 . We compare the results with the properties of dense matter in the non-relativistic many body theory. The qualitative feature of neutron star matter in the crust is consistent with previous works. The relativistic EOS of neutron star matter is found to be stiffer than the non-relativistic EOSs characteristically. We found that the proton fraction of neutron star matter in the high density region in the RBHF theory is quite large as compared with those found in the non-relativistic calculations and allow the direct Urca process, which is crucial for the rapid cooling of neutron stars, for relatively massive neutron stars.