The densest part of neutron star crusts may contain very exotic nuclear configurations, so-called nuclear pasta. We investigate the effect of nuclear symmetry energy on the existence of such phases ...in cold non-accreting neutron stars. For this purpose, we apply three Brussels–Montreal functionals based on generalized Skyrme effective interactions, whose parameters were accurately calibrated to reproduce both experimental data on nuclei and realistic neutron-matter equations of state. These functionals differ in their predictions for the density dependence of the symmetry energy. Within the fourth-order extended Thomas–Fermi method, we find that pasta occupies a wider region of the crust for models with a lower slope of the symmetry energy (and higher symmetry energy at relevant densities) in agreement with previous studies based on pure Thomas–Fermi approximation and compressible liquid-drop models. However, the incorporation of microscopic corrections consistently calculated with the Strutinsky integral method leads to a significant shift of the onset of the pasta phases to higher densities due to the enhanced stability of spherical clusters. As a result, the pasta region shrinks substantially and the role of symmetry energy weakens. This study sheds light on the importance of quantum effects for reliably describing pasta phases in neutron stars.
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 method (ETF). 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.
We previously studied the inner crust and the pasta mantle of a neutron star within the 4th-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 quasi-spherical clusters. However, the two new parametrizations lead to a different mantle structure at mean baryon densities above about 0.07 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.
We model the nuclear evolution of an accreted matter as it sinks toward the stellar center, 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, \(\langle Z\rangle\), impurity parameter, \(Q_\mathrm{imp}\) and equation of state for a set of models, parametrized by the pressure at the outer-inner crust interface. Typically, for Superburst ashes \(Q_\mathrm{imp}\approx 1-4\), while for Kepler ashes \(Q_\mathrm{imp}\) decreases from \(\approx23\) at the outer-inner crust interface to \(\approx5\) at the end of our simulation (the corresponding density equals \(\rho_\mathrm{dc}\approx2\times 10^{12}\) g cm\(^{-3}\)). At the same time, for Extreme rp ashes \(Q_\mathrm{imp}\) remains large \(\approx 30-35\) in the considered inner crust region. Our results are important for modeling the thermal relaxation of transiently accreting neutron stars after the end of the outburst.
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 \(\rho \leq 2\times 10^{12}\) 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, which encodes all uncertainties related to the physics of the deepest inner-crust layers. Our calculations allow us, in particular, to set new lower limits on the net energy release (per accreted baryon): \(Q\gtrsim0.28\) MeV for Extreme rp ashes and Q~0.43-0.51 MeV for Superburst and Kepler ashes.
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 \rho ~ 2 \times 10^{13} g cm^{-3}.
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 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 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 \(Q_\mathrm{imp}\) at density \(\rho=2\times 10^{12}\) g cm\(^{-3}\) can differ for a factor of few, and even increase with density increase. The profile of integrated heat realize shown to be well confined between results by Fantina et al. (2018) and Lau et al. (2018).
