ABSTRACT
Neutron stars in low-mass X-ray binaries are thought to be heated up by accretion-induced exothermic nuclear reactions in the crust. The energy release and the location of the heating ...sources are important ingredients of the thermal evolution models. Here, we present thermodynamically consistent calculations of the energy release in three zones of the stellar crust: at the outer–inner crust interface, in the upper layers of the inner crust (up to the density ρ ≤ 2 × 1012 g cm−3), and in the underlying crustal layers. We consider three representative models of thermonuclear ashes (superburst, extreme rp, and Kepler ashes). The energy release in each zone is parametrized by the pressure at the outer–inner crust interface, Poi, which encodes all uncertainties related to the physics of the deepest inner-crust layers. Our calculations allow us to set new theoretical lower limits on the net energy release (per accreted baryon): Q ≳ 0.28 MeV for extreme rp ashes and Q ≳ 0.43–0.51 MeV for superburst and Kepler ashes. Our results can be directly incorporated into numerical codes and provide an opportunity to constrain Poi by comparing thermal evolution models of accreting neutron stars with observations.
ABSTRACT
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 apply a simplified reaction network to model nuclear evolution of various multi-component thermonuclear burning ashes (superburst, KEPLER, and extreme rp-process ashes) in the outer crust and calculate the deep crustal heating energy release Q, parametrized by the pressure at the outer–inner crust interface, Poi. Using the general thermodynamic arguments, we set a lower limit on Q, Q ≳ 0.13−0.2 MeV per baryon (an actual value depends on the ash composition and the employed mass model).
ABSTRACT
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 ...modelling 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. very well, if one applies the same mass model. However, the composition and the heating power are shown to be sensitive to the mass table used and treatment of mass tables boundary, if one applies several of them in one simulation. In particular, the impurity parameter Qimp at density ρ = 2 × 1012 g cm−3 can differ for a factor of few, and even increase with density increase. The profile of integrated heat release shown to be well confined between results by Fantina et al. and Lau et al.
ABSTRACT
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, 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 by dissipative forces; however, the required diffusion fluxes are of the same order as total baryon flux at Eddington accretion. We argue that redistribution of neutrons in the inner crust should be involved in realistic model of accreted crust.
ABSTRACT
We model the nuclear evolution of an accreted matter as it sinks toward the stellar centre, in order to find its composition and equation of state. To this aim, we developed a simplified ...reaction network that allows for redistribution of free neutrons in the inner crust to satisfy the recently suggested neutron hydrostatic and diffusion equilibrium condition. We analyse the main reaction pathways for the three representative thermonuclear ash compositions: Superburst, Kepler, and Extreme rp. In contrast to the previous results, which neglect redistribution of free (unbound) neutrons in the inner crust, the most significant reactions in our calculations are neutron captures and electron emissions. The pycnonuclear fusion plays some role only for Kepler ashes. For the direct application of our results in astrophysical codes we present profiles of the average charge, 〈Z〉, impurity parameter, Qimp, and equation of state for a set of models, parametrized by the pressure at the outer–inner crust interface. Typically, for Superburst ashes Qimp ≈ 1 − 4, while for Kepler ashes Qimp decreases from ≈23 at the outer–inner crust interface to ≈5 at the end of our simulation (the corresponding density equals ρdc ≈ 2 × 1012 g cm−3). At the same time, for Extreme rp ashes Qimp remains large ≈30 − 35 in the considered inner crust region. Our results are important for modelling the thermal relaxation of transiently accreting neutron stars after the end of the outburst.
Neutron star crust consists of highly neutron excess nuclei, which are inaccessible for laboratory experiments. In the deepest region of the crust (so-called inner crust, located after the neutron ...drip) atomic nuclei are immersed into the sea of degenerate unbound neutrons. Study of the crust structure and equation of state in such conditions relies on the theoretical nuclear mass models. In particular, it is convenient to use the compressible liquid drop model, which contains the surface tension term. A thermodynamically consistent description must take into account adsorption of neutrons on the nucleus surface (neutron skin) and dependence of surface tension on matter properties in two-phase equilibrium. We calculate the surface tension of nuclear matter by the extended Thomas-Fermi approach. For this aim, we parametrize the number density profile of the two-phase system by Fermi-Dirac type functions, totally containing 5 parameters, and minimize the thermodynamic potential Ω to obtain equilibrium configuration. We use Skyrme-type nuclear interactions SLy4 and BSk24, fulfilling experimental data of atomic nuclei, observational constraints on the maximal neutron star mass and theoretical calculations of high-density nuclear matter. The results are presented as a function of neutron chemical potential, which is useful for compressible liquid drop models in the inner crust of a neutron star.
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 if the outer crust has one-component composition, the appearance of free neutrons in the inner crust leads to branching of reaction chains and formation of the multicomponent composition. We apply the compressible liquid drop nuclear model, which includes effects of free neutrons on nuclear energies. It allows us to calculate the composition, the heating profile and the equation of state of matter up to densities ρ ≃ 2 × 1013 g cm−3.
Nuclear pasta phases in the neutron stars mantle can affect the mechanical and transport properties of superdense matter, thus playing an important role in the dynamics and evolution of neutron ...stars. In this paper, we compare results obtained by the Extended Thomas–Fermi (ETF) method with the compressible liquid drop model (CLDM), based on the thermodynamically consistent description of the surface properties calculated for the two-phase plane interface and the same energy-density functional (for numerical illustration, we applied the Skyrme-type functional SLy4). Our ETF calculations found that pasta phases in cylindrical form cover a significant crustal region (both normal and inverse phases, aka spaghetti and bucatini are presented). Meanwhile, within the applied CLDM framework, which includes the thermodynamically required effect of neutron adsorption on the cluster’s surface but neglects curvature corrections, only the spaghetti phase was found to be energetically favorable in the small density range prior to crust–core transition. On the other hand, the recent CLDM of Dinh Thi et al., 2021, which, on the contrary, accounts for curvature term but neglects neutron adsorption, predicts pasta phase onset in better agreement with the ETF. This fact highlights the importance of the curvature effects and allows counting on the potential validity of the CLDMs as a convenient, transparent and accurate tool for investigation of the pasta-phase properties.
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