Our previous investigation of neutron-star crusts, based on the functional BSk24, led to a substantial reduction of the pasta mantle when Strutinsky integral and pairing corrections were added on top of the fourth-order extended Thomas-Fermi (ETF) method. Here, our earlier calculations are widened to a larger set of functionals within the same family and we find that the microscopic corrections weaken significantly the influence of the symmetry energy. In particular, the correlation observed at the pure ETF level between the density for the onset of pasta formation and the symmetry energy vanishes, not only for the $L$ coefficient but also for the symmetry-energy values at the relevant densities. Moreover, the inclusion of microscopic corrections results in a much lower abundance of pasta for all functionals.

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, P_oi. 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).

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.

We previously studied the inner crust and the pasta mantle of a neutron star within the fourth-order extended Thomas-Fermi (ETF) approach with consistent proton shell corrections added perturbatively via the Strutinsky integral (SI) theorem together with the contribution due to pairing. To speed up the computations and avoid numerical problems, we adopted parametrized nucleon density distributions. However, the errors incurred by the choice of the parametrization are expected to become more significant as the mean baryon number density is increased, especially in the pasta mantle where the differences in the energy per nucleon of the different phases are very small, typically a few keV. To improve the description of these exotic structures, we discuss the important features that a nuclear profile should fulfill and introduce two new parametrizations. Performing calculations using the BSk24 functional, we find that these parametrizations lead to lower ETF energy solutions for all pasta phases than the parametrization we adopted before and more accurately reproduce the exact equilibrium nucleon density distributions obtained from unconstrained variational calculations. Within the ETFSI method, all parametrizations predict the same composition in the region with quasispherical clusters. However, the two new parametrizations lead to a different mantle structure at mean baryon densities above about $0.07{\mathrm{fm}}^{-3}$, at which point lasagna is energetically favored. Interestingly, spherical clusters reappear in the pasta region. The inverted pasta phases such as bucatini and Swiss cheese are still found in the densest region above the core in all cases.

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, P_oi, 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 P_oi by comparing thermal evolution models of accreting neutron stars with observations.