Inner crust of neutron stars with mass-fitted Skyrme functionals

Abstract

The equation of state and composition of the inner crust of neutron stars at zero temperature are calculated, using the T = 0 version of the TETFSI (temperature-dependent extended Thomas-Fermi plus Strutinsky integral) method, for each of a family of three functionals based on Skyrme-type forces BSk19, BSk20 and BSk21, which are characterized by different degrees of symmetry-energy stiffness, and also for the SLy4 functional. We also solve the Tolman-Oppenheimer-Volkoff equations to calculate the distribution of mass within the inner crust. Qualitatively similar results are found for all four functionals, and in particular the number of protons per Wigner-Seitz cell is in all cases equal to 40 throughout the inner crust.Comment: 35 pages, 13 figures, accepted for publication in Physical Review

Neutron Stars—Cooling and Transport

“…Thermodynamic stability of the pasta phase state and, therefore, the existence of the mantle depends on the model of nuclear interactions. Lorenz et al (1993) demonstrated stability of the pasta phases at ρ 10 14 g cm −3 for the FPS EoS model of Pandharipande and Ravenhall (1989), but they were not found to be stable in modern EoS models SLy (Douchin and Haensel 2001) and BSk (Pearson et al 2012).…”

“…The EoS models that avoid this problem by describing the core and the crust in frames of the same physical model are called unified. Examples of the unified EoSs are the FPS (Pandharipande and Ravenhall 1989;Lorenz et al 1993), SLy (Douchin and Haensel 2001), and BSk (Goriely et al 2010;Pearson et al 2011Pearson et al , 2012 EoS families. All of them are based on effective Skyrme-like energy density functionals.…”

“…For comparison, an older fit to Q (brems) ν (Kaminker et al 1999) is plotted by the dotted line. The ground-state composition and the nuclear size are described by the BSk21 model (Goriely et al 2010;Pearson et al 2012, as fitted by ). The accreted composition is taken from Haensel and Zdunik (1990); in this case the approximation by Itoh and Kohyama (1983) is used for the nuclear size.…”

“…We have chosen ρ b = 10 10 g cm −3 and used the BSk21 EoS (Pearson et al 2012) in the parametrized form . The numerical data have been produced with the 2D code of for 5 values of internal temperature T b from 10 7 K to 10 9 K, 5 values of the magnetic field at the pole B p from 10 11 G to 10 15 G, and 20 values of magnetic colatitude θ at the surface of the neutron star from 0 to π/2.…”

“…1 shows the density dependence of the total heat capacity, normalized per one nucleon, c v /n b , throughout the neutron star from the ocean to the core, and partial contributions to c v /n b . Different particle fractions are adopted from the BSk21 model (Goriely et al 2010;Pearson et al 2011Pearson et al , 2012, as fitted by . Here, we have mostly neglected the effects of nucleon superfluidity to be discussed in Sect.…”