A new statistical method for the structure of the inner crust of neutron stars

Abstract

We investigated the structure of the low density regions of the inner crust of neutron stars using the Hartree-Fock-Bogoliubov (HFB) model to predict the proton content Z of the nuclear clusters and, together with the lattice spacing, the proton content of the crust as a function of the total baryonic density ρ b . The exploration of the energy surface in the (Z, ρ b ) configuration space and the search for the local minima require thousands of calculations. Each of them implies an HFB calculation in a box with a large number of particles, thus making the whole process very demanding. In this work, we apply a statistical model based on a Gaussian Process Emulator that makes the exploration of the energy surface ten times faster. We also present a novel treatment of the HFB equations that leads to an uncertainty on the total energy of ≈ 4 keV per particle. Such a high precision is necessary to distinguish neighbour configurations around the energy minima.

Systematic analysis of inner crust composition using the extended Thomas-Fermi approximation with pairing correlations

“…[40,42] now allow the inclusion of pairing correlations for both protons and neutrons. The resulting ETFSI+pairing model leads to results that agree well with the most accurate HFB results currently available [31]. At the interface region between the outer and the inner crust, a non-negligible discrepancy was observed [42], but this concerns a very limited density region and it will not modify the conclusions of this article.…”

Superfluidity in nuclear systems and neutron stars

“…The lattice formed by these nuclei may not be perfect and may contain nuclei with mass numbers different from those predicted for the ground state. Nucleonic superfluidity in the outer crust exists inside the individual bound finite nuclei and can be described using standard methods, such as Hartree-Fock plus BCS or Hartree-Fock-Bogolyubov theories [47,261,[305][306][307].…”

Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations

“…In the case of vanishing pairing, these equations reduce to the Hartree-Fock (HF) one. For more details on the numerical methods used to solve these equations we refer to references [28,29,38,42]. The most relevant point for the following discussion is the choice of the boundary conditions used to solve Equation (4).…”

“…The downsides of the HFB method are its computational cost and the possible numerical inaccuracies related to the boundary conditions adopted in the calculation [26][27][28]. We refer to reference [29] for a more detailed discussion. More recently, the HFB method has been used to investigate heating of the crust [30] and the crust-core transition [31], though these are not systematic studies of the crust.…”