We discuss the thermalisation process of the neutron stars crust described by solving the heat transport equation with a microscopic input for the specific heat of baryonic matter. The heat equation is solved with initial conditions specific to a rapid cooling of the core. To calculate the specific heat of inner crust baryonic matter, i.e., nuclear clusters and unbound neutrons, we use the quasiparticle spectrum provided by the Hartree-Fock-Bogoliubov approach at finite temperature. In this framework we analyse the dependence of the crust thermalisation on pairing properties and on cluster structure of inner crust matter. It is shown that the pairing correlations reduce the crust thermalisation time by a very large fraction. The calculations show also that the nuclear clusters have a non-negligible influence on the time evolution of the surface temperature of the neutron star.
The deep crustal heating, associated with exothermal nuclear reactions, is believed to be a key parameter for describing the thermal evolution of accreting neutron stars. In this paper, we present the first thermodynamically consistent calculations of the crustal heating for realistic compositions of thermonuclear ashes. In contrast to previous studies based on the traditional approach, we account for neutron hydrostatic/diffusion (nHD) equilibrium condition imposed by superfluidity of neutrons in a major part of the inner crust and rapid diffusion in the remaining part of the inner crust. We …
The observed thermal relaxation of transiently accreting neutron stars during quiescence periods in low-mass X-ray binaries suggests the existence of unknown heat sources in the shallow layers of neutron-star crust. Making use of existing experimental nuclear data, we estimate the maximum possible amount of heat that can be deposited in the outer crust of an accreting neutron star due to electron captures and pycnonuclear fusion reactions triggered by the burial of X-ray burst ashes.
We present a new mechanism for deep crustal heating in accreting neutron stars. Charged pions ($π^+$) are produced in nuclear collisions on the neutron star surface during active accretion and upon decay they provide a flux of neutrinos into the neutron star crust. For massive and/or compact neutron stars, neutrinos deposit $\approx 1\textrm{--} 2 \, \mathrm{MeV}$ of heat per accreted nucleon into the inner crust. The strength of neutrino heating is comparable to the previously known sources of deep crustal heating, such as from pycnonuclear fusion reactions, and is relevant for studies of coo…
Nuclear reactions heat and cool the crust of accreting neutron stars and need to be understood to interpret observations of X-ray bursts and of long-term cooling in transiently accreting systems. It was recently suggested that previously neglected neutron transfer reactions may play a significant role in the nuclear processes. We present results from full nuclear network calculations that now include these reactions and determine their impact on crust composition, crust impurity, heating, and cooling. We find that a large number of neutron transfer reactions indeed occur and impact crust model…
Observed thermal emission from accreting neutron stars (NSs) in a quiescent state is believed to be powered by nonequilibrium nuclear reactions that heat the stellar crust (deep crustal heating paradigm). We derive a simple universal formula for the heating efficiency, assuming that an NS has a fully accreted crust. We further show that, within the recently proposed thermodynamically consistent approach to the accreted crust, the heat release can be parametrized by the only one parameter -- the pressure $P_{\rm oi}$ at the outer-inner crust interface (as we argue, this pressure should not nece…
Observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreting neutron stars. Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts. The heating is studied using a fully quantum approach taking consistently into account nuclear shell effects. We have followed the evolution of ashes made of $^{56}$Fe employing the nuclear energy-density functional theory. Both the outer and inner crusts are described using the same functional, thus ensuring a unified and thermodynamically consist…
X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the nuclear reactions that heat and cool the crust during accretion, and define its nonequilibrium composition. We identify here in detail the typical nuclear reaction sequences down to a depth in the inner crust where the mass density is 2E12 g/cm^3 using a full nuclear reaction network for a range of initial compositions. The reaction sequences differ…
Neutron stars in low-mass binary systems are subject to accretion. The common assumption in studying the properties of the neutron star crust is the fully accreted crust approximation. However, observations of some X-ray transient sources indicate that the original crust has not been completely replaced by accreted material, but is partly composed of the compressed original crust. A two-part (or hybrid) crust made of the original crust that is compressed and of the accreted material crashing onto it was reconstructed as a function of the accretion stage. The differences in the composition and …
Correct interpretation of X-ray observations of transiently accreting neutron stars requires modeling of nuclear-physical processes in these objects. We consider a chain of nuclear reactions that drives the crust composition in an accreting neutron star and heats up the star. We constructed multicomponent approach with the kinetics of nuclear reactions described in simplified stepwise manner. The redistribution of nucleons between nuclei by emission and capture of neutrons is shown to significantly affect the nuclear reaction chains and the composition of the inner crust. In particular, even i…
The persistent thermal luminosity of magnetars and their outbursts suggest the existence of some internal heat sources located in their outer crust. The compression of matter accompanying the decay of the magnetic field may trigger exothermic electron captures and, possibly, pycnonuclear fusions of light elements that may have been accreted onto the surface from the fallback of supernova debris, from a disk or from the interstellar medium. This scenario bears some resemblance to deep crustal heating in accreting neutron stars, although the matter composition and the thermodynamic conditions ar…
Few unified equations of state for neutron star matter where core and crust are described using the same nuclear model are available. However the use of non-unified equations of state with a simplified matching between the crust and the core has been shown to introduce uncertainties in the radius determination which can be larger than the expected precision of the next generation of X-ray satellites. We aim at eliminating the dependence of the radius and mass of neutron staron the detailed model for the crust and on the crust-core matching procedure. We solve the approximate equations of the h…
Observed temperatures of transiently accreting neutron stars in the quiescent state are generally believed to be supported by deep crustal heating, associated with non-equilibrium exothermic reactions in the crust. Traditionally, these reactions are studied by considering nuclear evolution governed by compression of the accreted matter. Here we show that this approach has a basic weakness, that is that in some regions of the inner crust the conservative forces, applied for matter components (nuclei and neutrons), are not in mechanical equilibrium. In principle the force balance can be restored…
Transiently accreting neutron stars in low mass X-ray binaries are generally believed to be heated up by nuclear reactions in accreted matter during hydrostatic compression. Detailed modeling of these reactions is required for the correct interpretation of observations. In this paper, we construct a simplified reaction network, which can be easily implemented and depends mainly on atomic mass tables as nuclear physics input. We show that it reproduces results of the detailed network by Lau et al. (2018) very well, if one applies the same mass model. However, the composition and the heating pow…
We performed a Penning trap mass measurement of $^{61}{\rm Zn}$ at the National Superconducting Cyclotron Laboratory and NuShellX calculations of the $^{61}{\rm Zn}$ and $^{62}{\rm Ga}$ structure using the GXPF1A Hamiltonian to obtain improved estimates of the $^{61}{\rm Zn}(p,γ)^{62}{\rm Ga}$ and $^{60}{\rm Cu}(p,γ)^{61}{\rm Zn}$ reaction rates. Surveying astrophysical conditions for type-I X-ray bursts with the code MESA, implementing our improved reaction rates, and taking into account updated nuclear masses for $^{61}{\rm V}$ and $^{61}{\rm Cr}$ from the recent literature, we refine the ne…
Spin-Down of Neutron Stars and Compositional Transitions in the Cold Crustal Matter
本文研究了零温下恒星自旋下降引起的中子星壳核成分的变化。我们建立了一个可压缩的液滴模型的能量的原子核浸没在中子气体中，包括配对和壳修正项，在参考的已知属性的基态的物质以上的中子滴密度，$4.3 \times 10^{11} g cm^{-3}$。最近的实验值和核质量的外推用于描述密度低于中子滴的物质。考虑到缓慢均匀旋转的相对论性中子星的壳层结构，计算了由于恒星自旋下降引起的壳层物质压力的变化。如果初始旋转周期为$\sim$ ms，这些变化会导致最初处于质量密度约为$3 \times 10^{13} g cm^{-3}$的基态物质中的原子核在物质经历压缩的赤道区域吸收中子，并在物质经历减压的旋转轴附近发射中子。通过这些过程产生的热量被发现有显着的影响，旧的中子星的热演化与低磁场的表面发射预测从这种加热相比，$ROSAT$观测的X射线发射毫秒双星，并被证明是不足以解释所观察到的X射线光度。
We study the long-wavelength excitations of the inner crust of neutron stars, considering three phases: cubic crystal at low densities, rods and plates near the core-crust transition. To describe the phonons, we write an effective Lagrangian density in terms of the coarse-grained phase of the neutron superfluid gap and of the average displacement field of the clusters. The kinetic energy, including the entrainment of the neutron gas by the clusters, is obtained within a superfluid hydrodynamics approach. The potential energy is determined from a model where clusters and neutron gas are conside…
We investigate the nuclear pasta phases in neutron star crusts by conducting a large number of three-dimensional Hartree-Fock+BCS calculations at densities leading to the crust-core transition. We survey the shape parameter space of pasta at constant pressure. Spaghetti, waffles, lasagna, bi-continuous phases and cylindrical holes occupy local minima in the resulting Gibbs energy surfaces. The bi-continuous phase, in which both the neutron gas and nuclear matter extend continuously in all dimensions and therefore protons are delocalized, appears over a large range of depths. Our results suppor…
Collective excitations in the inner crust of neutron stars : supergiant resonances
本文研究了中子气体中含有核团簇的Wigner-Seitz盒的核集体激发。这种重子非均匀系统是中子星壳内物质结构所特有的。在坐标表象下的球Hartree-Fock-Bogoliubov +准粒子随机相位近似框架下研究了集体激发。对重子密度分别为0.02 fm $^{-3}$和0.08 fm $^{-3}$的两个有代表性的Wigner-Seitz盒进行了计算。结果表明，低多极性的激发几乎完全集中在一个强集体模式，耗尽了很大一部分的能量加权和规则。由于这些集体模与标准核的巨共振相比处于非常低的能量，它们可能会显著影响中子星重子内壳物质的比热。
We have studied systematically microscopic properties of a quantum vortex in neutron matter at finite temperatures and densities corresponding to different layers of the inner crust of a neutron star. To this end and in preparation of future simulations of the vortex dynamics, we have carried out fully self-consistent 3D Hartree-Fock-Bogoliubov calculations, using one of the latest nuclear energy-density functionals from the Brussels-Montreal family, which has been developed specifically for applications to neutron superfluidity in neutron-star crusts. By analyzing the flow around the vortex, …
The accretion of matter onto the surface of a neutron star in a low-mass X-ray binary triggers X-ray bursts, whose ashes are buried and further processed thus altering the composition and the properties of the stellar crust. In this second paper of a series, the impact of accretion on the equation of state and on the global properties of neutron stars is studied in the framework of the nuclear energy-density functional theory. Considering ashes made of $^{56}$Fe, we calculated the equations of state using the same Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21, as…
