Cold Neutron Stars Research Articles

Quantum nucleation of up-down quark matter and astrophysical implications

Quark matter with only $u$ and $d$ quarks ($ud$QM) might be the ground state of baryonic matter at large baryon number $A>A_{\rm min}$. With $A_{\rm min}\gtrsim 300$, this has no direct conflict with the stability of ordinary nuclei. An intriguing test of this scenario is to look for quantum nucleation of $ud$QM inside neutron stars due to their large baryon densities. In this paper, we study the transition rate of cold neutron stars to $ud$ quark stars ($ud$QSs) and the astrophysical implications, considering the relevant theoretical uncertainties and observational constraints. It turns out that a large portion of parameter space predicts an instantaneous transition, and so the observed neutron stars are mostly $ud$QSs. We find this possibility still viable under the recent gravitational wave and pulsar observations, although there are debates on its compatibility with some observations that involve complicated structure of quark matter. The tension could be partially relieved in the two-families scenario, where the high-mass stars ($M\gtrsim2 M_{\odot}$) are all $ud$QSs and the low-mass ones ($M\sim1.4\, M_{\odot}$) are mostly hadronic stars. In this case, the slow transition of the low-mass hadronic stars points to a very specific class of hadronic models with moderately stiff EOSs, and $ud$QM properties are also strongly constrained.

Oscillations of Hypermassive Compact Stars with Gravitational Radiation and Viscosity

Abstract Binary neutron star mergers, such as the multimessenger GW170817 event, may produce hypermassive compact objects that are supported against collapse by the internal circulation of the fluid within the star. We compute their unstable modes of oscillations driven by gravitational-wave radiation and shear viscosity, modeling them as triaxial Riemann ellipsoids. We work in a perturbative regime, where the gravitational radiation-reaction force is taken into account at 2.5-post-Newtonian order and find unstable modes with dissipation timescales ≳1 ms that are relevant to the transient state of a hypermassive remnant of a merger. We show that the secular instabilities are dominated by gravitational-wave radiation. If the shear viscosity is included, it can increase the growth times or even stabilize the unstable modes, but it must have values several orders of magnitude larger than predicted for cold neutron stars.

Accuracy of the relativistic Cowling approximation in protoneutron star asteroseismology

The relativistic Cowling approximation, where the metric perturbations are neglected during the fluid oscillations, is often adopted for considering the gravitational waves from the protoneutron stars (PNSs) provided via core-collapse supernova explosions. In this study, we evaluate how the Cowling approximation works well by comparing the frequencies with the Cowling approximation to those without the approximation. Then, we find that the behavior of the frequencies with the approximation is qualitatively the same way as that without the approximation, where the frequencies with the approximation can totally be determined within $\sim 20\%$ accuracy. In particular, the fundamental mode with the Cowling approximation is overestimated. In addition, we also discuss the damping time of various eigenmodes in gravitational waves from the PNSs, where the damping time for the PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite different from that for cold neutron stars, but it is more or less similar to that for cold neutron stars in the later phase. The damping time is long enough compared to the typical time interval of short-Fourier transformation that often used in the analysis, and that ideally guarantees the validity of the transformation.

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.

Delta baryons and diquark formation in the cores of neutron stars

We investigate the hadron-quark phase transition in cold neutron stars in light of (i) the observed limits on the maximum-mass of heavy pulsars, (ii) constraints on the tidal properties inferred from the gravitational waves emitted in binary neutron-star mergers, and (iii) mass and radius constraints derived from the observation of hot spots on neutron star observed with NICER. Special attention is directed to the possible presence of $\Delta(1232)$ baryons in neutron star matter. Our results indicate that this particle could make up a large fraction of the baryons in neutron stars and thus have a significant effect on the properties of such objects, particularly on their radii. This is partially caused by the low density appearance of $\Delta$s for a wide range of theoretically defensible sets of meson-hyperon, SU(3) ESC08 model, and meson-$\Delta$ coupling constants. The transition of hadronic matter to quark matter, treated in the 2SC+s condensation phase, is found to occur only in neutron stars very close to the mass peak. Nevertheless, quark matter may still constitute an appreciable fraction of the stars' total matter if the phase transition is treated as Maxwell-like (sharp), in which case the neutron stars located beyond the gravitational mass peak would remain stable against gravitational collapse. In this case, the instability against gravitational collapse is shifted to a new (terminal) mass different from the maximum-mass of the stellar sequence, giving rise to stable compact objects with the same gravitational masses as those of the neutron stars on the traditional branch, but whose radii are smaller by up to 1 km. All models for the equation of state of our study fall comfortably within the bound established very recently by Annala {\it et al.} (Nature Physics, 2020)

Maximum mass cutoff in the neutron star mass distribution and the prospect of forming supramassive objects in the double neutron star mergers

The sample of neutron stars with a measured mass is growing quickly. With the latest sample, we adopt both a flexible Gaussian mixture model and a Gaussian plus Cauchy-Lorentz component model to infer the mass distribution of neutron stars and use the Bayesian model selection to explore evidence for multimodality and a sharp cutoff in the mass distribution. The two models yield rather similar results. Consistent with previous studies, we find evidence for a bimodal distribution together with a cutoff at a mass of $M_{\rm max}=2.26_{-0.05}^{+0.12}M_\odot$ (68% credible interval; for the Gaussian mixture model). If such a cutoff is interpreted as the maximum gravitational mass of nonrotating cold neutron stars, the prospect of forming supramassive remnants is found to be quite promising for the double neutron star mergers with a total gravitational mass less than or equal to 2.7$M_\odot$ unless the thermal pions could substantially soften the equation of state for the very hot neutron star matter. These supramassive remnants have a typical kinetic rotational energy of approximately $1-2\times 10^{53}$ ergs. Together with a high neutron star merger rate approximately $10^{3}~{\rm Gpc^{-3}~yr^{-3}}$, the neutron star mergers are expected to be significant sources of EeV($10^{18}$eV) cosmic-ray protons.

WITHDRAWN: Towards grounding nuclear physics in QCD

Abstract Exascale computing could soon enable a predictive theory of nuclear structure and reactions rooted in the Standard Model, with quantifiable and systematically improvable uncertainties. Such a predictive theory will help exploit experiments that use nucleons and nuclei as laboratories for testing the Standard Model and its limitations. Examples include direct dark matter detection, neutrinoless double beta decay, and searches for permanent electric dipole moments of the neutron and atoms. It will also help connect QCD to the properties of cold neutron stars and hot supernova cores. We discuss how a quantitative bridge between QCD and the properties of nuclei and nuclear matter will require a synthesis of lattice QCD (especially as applied to two- and three-nucleon interactions), effective field theory, and ab initio methods for solving the nuclear many-body problem. While there are significant challenges that must be addressed in developing this triad of theoretical tools, the rapid advance of computing is accelerating progress. In particular, we focus this review on the anticipated advances from lattice QCD and how these advances will impact few-body effective theories of nuclear physics by providing critical input, such as constraints on unknown low-energy constants of the effective (field) theories. We also review particular challenges that must be overcome for the successful application of lattice QCD for low-energy nuclear physics. We describe progress in developing few-body effective (field) theories of nuclear physics, with an emphasis on HOBET, a non-relativistic effective theory of nuclear physics, which is less common in the literature. We use the examples of neutrinoless double beta decay and the nuclear-matter equation of state to illustrate how the coupling of lattice QCD to effective theory might impact our understanding of symmetries and exotic astrophysical environments.

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star: Extension to strongly quantizing magnetic fields

The iterative method recently proposed for determining the internal constitution of the outer crust of a nonaccreted neutron star is extended to magnetars by taking into account the Landau-Rabi quantization of electron motion induced by the presence of a very high magnetic field. It is shown that in the strongly quantizing regime, the method can be efficiently implemented using new analytical solutions for the transitions between adjacent crustal layers. Detailed numerical computations are performed to assess the performance and precision of the method.

Cooling of dark-matter admixed neutron stars with density-dependent equation of state

We propose a dark-matter (DM) admixed density-dependent equation of state where the fermionic DM interacts with the nucleons via Higgs portal. Presence of DM can hardly influence the particle distribution inside neutron star (NS) but can significantly affect the structure as well as equation of state (EOS) of NS. Introduction of DM inside NS softens the equation of state. We explored the effect of variation of DM mass and DM Fermi momentum on the NS EOS. Moreover, DM-Higgs coupling is constrained using dark matter direct detection experiments. Then, we studied cooling of normal NSs using APR and DD2 EOSs and DM admixed NSs using dark-matter modified DD2 with varying DM mass and Fermi momentum. We have done our analysis by considering different NS masses. Also DM mass and DM Fermi momentum are varied for fixed NS mass and DM-Higgs coupling. We calculated the variations of luminosity and temperature of NS with time for all EOSs considered in our work and then compared our calculations with the observed astronomical cooling data of pulsars namely Cas A, RX J0822-43, 1E 1207-52, RX J0002+62, XMMU J17328, PSR B1706-44, Vela, PSR B2334+61, PSR B0656+14, Geminga, PSR B1055-52 and RX J0720.4-3125. It is found that APR EOS agrees well with the pulsar data for lighter and medium mass NSs but cooling is very fast for heavier NS. For DM admixed DD2 EOS, it is found that for all considered NS masses, all chosen DM masses and Fermi momenta agree well with the observational data of PSR B0656+14, Geminga, Vela, PSR B1706-44 and PSR B2334+61. Cooling becomes faster as compared to normal NSs in case of increasing DM mass and Fermi momenta. It is infered from the calculations that if low mass super cold NSs are observed in future that may support the fact that heavier WIMP can be present inside neutron stars.

Coordinate-space solver for finite-temperature Hartree-Fock-Bogoliubov calculations using the shifted Krylov method

In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dimensional (3D) coordinate-space representation. Recently, an efficient method based on the contour integral of Green's function with the shifted conjugate-orthogonal conjugate-gradient method has been proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to the finite temperature, using the shifted conjugate-orthogonal conjugate-residual method. We benchmark the 3D coordinate-space solver of the FT-HFB calculation for hot isolated nuclei and fcc phase in the inner crust of neutron stars at finite temperature. The computational performance of the present method is demonstrated. Different critical temperatures of the quadrupole and the octupole deformations are confirmed for $^{146}$Ba. The robustness of the shape coexistence feature in $^{184}$Hg is examined. For the neutron-star crust, the deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at the nucleon density of 0.045 fm$^{-3}$ and the temperature of $k_B T=200$ keV. The efficiency of the developed solver is demonstrated for nuclei and inhomogeneous nuclear matter at finite temperature. It may provide a standard tool for nuclear physics, especially for the structure of the hot and cold neutron-star matters.

Towards the Keplerian sequence: Realistic equations of state in rapidly rotating neutron stars

Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. In the present work, we investigate the Keplerian (mass-shedding) sequence of rotating neutron stars by employing realistic equations of state based on various theoretical nuclear models. In particular, we compute the moment of inertia and angular momentum of neutron stars against mass-shedding and secular axisymmetric instability. We mainly focus on the dependence of these properties from the bulk properties of neutron stars. Another property that studied in detail, is the dimensionless spin parameter (kerr parameter) of rotating neutron stars at the mass-shedding limit. In addition, supramassive time evolutionary rest mass sequences, which have their origin in general relativity, are explored. Supramassive sequences have masses exceeding the maximum mass of a non-rotating neutron star and evolve toward catastrophic collapse to a black hole. Important information can be gained from the astrophysical meaning of the kerr parameter and the supramassive sequences in neutron stars. Finally, the effects of the Keplerian sequence, in connection with the latter, may provide us constraints on the high density part of the equation of state of cold neutron star matter.

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star

A very fast iterative method is presented to calculate the internal constitution of the outer crust of a cold nonaccreted neutron star, making use of very accurate analytical formulas for the transition pressures between adjacent crustal layers and their density. In addition to the composition of the different crustal layers, their depth and their baryonic mass content can be simultaneously estimated using an approximate solution of Einstein's general relativistic equations. The overall computing time is drastically reduced compared to the traditional approach, thus opening the door to large-scale statistical studies and sensitivity analyses.

Neutrino signal from proto-neutron star evolution: Effects of opacities from charged-current–neutrino interactions and inverse neutron decay

We investigate the impact of charged current neutrino processes on the formation and evolution of neutrino spectra during the deleptonization of proto-neutron stars. To this end we develop the full kinematics of these reaction rates consistent with the nuclear equation of state, including weak magnetism contributions. This allows us to systematically study the impact of inelastic contributions and weak magnetism on the $\nu_e$ and $\bar\nu_e$ luminosities and average energies. Furthermore, we explore the role of the inverse neutron decay, also known as the direct Urca process, on the emitted spectra of $\bar\nu_e$. This process is commonly considered in the cooling scenario of cold neutron stars but has so far been neglected in the evolution of hot proto-neutron stars. We find that the inverse neutron decay becomes the dominating opacity source for low-energy $\bar\nu_e$. Accurate three-flavor Boltzmann neutrino transport enables us to relate the magnitude of neutrino fluxes and spectra to details of the treatment of weak processes. This allows us to quantify the corresponding impact on the conditions relevant for the nucleosynthesis in the neutrino-driven wind, which is ejected from the proto-neutron star surface during the deleptonization phase.

Role of the crust in the tidal deformability of a neutron star within a unified treatment of dense matter

The role of the crust on the tidal deformability of a cold nonaccreted neutron star is studied using the recent unified equation of state BSk24. This equation of state, which is based on the nuclear-energy density functional theory, provides a thermodynamically consistent description of all stellar regions. Results obtained with this equation of state are compared to those calculated for a putative neutron star made entirely of homogeneous matter. The presence of the crustal layers is thus found to significantly reduce the Love number $k_2$, especially for low-mass stars. However, this reduction mainly arises from the increase in the stellar radius almost independently of the equation of state. This allows for a simple analytic estimate of $k_2$ for realistic neutron stars using the equation of state of homogeneous matter only.

Force on a neutron quantized vortex pinned to proton fluxoids in the superfluid core of cold neutron stars

ABSTRACT The superfluid and superconducting core of a cold rotating neutron star (NS) is expected to be threaded by a tremendous number of neutron quantized vortices and proton fluxoids. Their interactions are unavoidable and may have important astrophysical implications. In this paper, the various contributions to the force acting on a single vortex to which fluxoids are pinned are clarified. The general expression of the force is derived by applying the variational multifluid formalism developed by Carter and collaborators. Pinning to fluxoids leads to an additional Magnus type force due to proton circulation around the vortex. Pinning in the core of an NS may thus have a dramatic impact on the vortex dynamics, and therefore on the magnetorotational evolution of the star.

Nuclear statistical equilibrium equation of state with a parametrized Dirac–Brückner Hartree–Fock calculation

Abstract We calculate new equations of state (EOSs) for astrophysical simulations in the framework of the extended nuclear statistical equilibrium, in which we minimize the free energy density for the full ensemble of nuclei in a hot and dense stellar environment. To evaluate bulk and surface energies of heavy nuclei and free energies of uniformly distributed nucleons, we use fitting formulae for the interaction energies and single-nucleon potentials at zero temperature of a Dirac–Brückner Hartree–Fock (DBHF) theory, one of the modern approaches to describe homogeneous nuclear matter. We find that the DBHF EOS exhibits larger mass fractions for medium-mass nuclei and smaller mass fractions for the other nuclei than the EOS obtained using the variational method (VM), another modern model for homogeneous nuclear matter. This effect is due to the more deeply bound energy for symmetric nuclear matter and the larger symmetry energy encoded in the DBHF EOS. At supra-nuclear densities, the DBHF EOS exhibits characteristics of a larger free energy, a higher pressure, and a larger neutron chemical potential of neutron-rich matter, which lead to a larger radius of cold neutron stars than that obtained by the VM EOS.

Influence of Density Dependence of Symmetry Energy in Hot and Dense Matter for Supernova Simulations

Abstract We study the influence of density-dependent symmetry energy at high densities in simulations of core-collapse supernovae, black hole formation, and proto–neutron star cooling by extending the relativistic mean field (RMF) theory used for the Shen equation-of-state (EOS) table. We adopt the extended RMF theory to examine the density dependence of the symmetry energy with a small value of the slope parameter L, while the original properties of the symmetric nuclear matter are unchanged. In order to assess matter effects at high densities, we perform numerical simulations of gravitational collapse of massive stars adopting the EOS table at high densities beyond 1014 g cm−3 with the small L value, which is in accord with the experimental and observational constraints, and compare them with the results obtained by using the Shen EOS. Numerical results for 11.2 and 15 M ⊙ stars exhibit minor effects around the core bounce and in the following evolution for 200 ms. Numerical results for 40 and 50 M ⊙ stars reveal a shorter duration toward the black hole formation with a smaller maximum mass for the small-L case. Numerical simulations of proto–neutron star cooling over 10 s through neutrino emissions demonstrate increasing effects of the symmetry energy at high densities. Neutrino cooling drastically proceeds in a relatively long timescale with high luminosities and average energies with the small symmetry energy. Evolution toward the cold neutron star is affected because of the different behavior of neutron-rich matter, while supernova dynamics around core bounce remains similar in less neutron-rich environments.

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.

Contraction of cold neutron star due to in the presence a quark core

Motivated by importance of the existence of quark matter on structure of neutron star. For this purpose, we use a suitable equation of state (EoS) which include three different parts: (i) a layer of hadronic matter, (ii) a mixed phase of quarks and hadrons, and, (iii) a strange quark matter in the core. For this system, in order to do more investigation of the EoS, we evaluate energy, Le Chatelier’s principle and stability conditions. Our results show that the EoS satisfies these conditions. Considering this EoS, we study the effect of quark matter on the structure of neutron stars such as maximum mass and the corresponding radius, average density, compactness, Kretschmann scalar, Schwarzschild radius, gravitational redshift and dynamical stability. Also, considering the mentioned EoS in this paper, we find that the maximum mass of hybrid stars is a little smaller than that of the corresponding pure neutron star. Indeed the maximum mass of hybrid stars can be quite close to the pure neutron stars. Our calculations about the dynamical stability show that these stars are stable against the radial adiabatic infinitesimal perturbations. In addition, our analyze indicates that neutron stars are under a contraction due to the existence of quark core.

Role of the symmetry energy and the neutron-matter stiffness on the tidal deformability of a neutron star with unified equations of state

The role of the symmetry energy and the neutron-matter stiffness on the tidal deformability of a cold nonaccreted neutron star is studied using a set of unified equations of state. Based on the nuclear energy-density functional theory, these equations of state provide a thermodynamically consistent treatment of all regions of the star and were calculated using functionals that were precision fitted to experimental and theoretical nuclear data. Predictions are compared to constraints inferred from the recent detection of the gravitational-wave signal GW170817 from a binary neutron-star merger and from observations of the electromagnetic counterparts.