Unified equations of state for cold non-accreting neutron stars with Brussels-Montreal functionals. II. Pasta phases in semi-classical approximation

We generalize our earlier work on neutron stars (arXiv:1903.04981), which assumed spherical Wigner-Seitz cells in the inner crust, to admit the possibility of pasta phases, i.e., non-spherical cell shapes. Full fourth-order extended Thomas-Fermi calculations using the density functional BSk24 are performed for cylindrical and plate-like cells. Unlike in our spherical-cell calculations, we do not include shell and pairing corrections, but there are grounds for expecting these corrections for pasta to be significantly smaller. It is therefore meaningful to compare the ETF pasta results with the full spherical-cell results, i.e., with shell and pairing corrections included. However, in view of the many previous studies in which shell and pairing corrections were omitted entirely, it is of interest to compare our pasta results with the ETF part of the corresponding spherical calculations. Making this latter comparison we find that as the density increases the cell shapes pass through the usual sequence sphere $\to$ cylinder $\to$ plate before the transition to the homogeneous core. The filling fractions found at the phase transitions are in close agreement with expectations based on the liquid-drop model. On the other hand, when we compare with the full spherical-cell results, we find the sequence to be sphere $\to$ cylinder $\to$ sphere $\to$ cylinder $\to$ plate. In neither case do any "inverted", i.e., bubble-like, configurations appear. We provide accurate fitting formulas to all our essential numerical results for each of the three phases, designed especially for the density range where the nonspherical shapes are expected, which enable one to capture not only the general behavior of the fitted functions, but also the differences between them in different phases.