Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XI. Stabilizing neutron stars against a ferromagnetic collapse

We construct a new Hartree-Fock-Bogoliubov (HFB) mass model, labeled HFB-18, with a generalized Skyrme force. The additional terms that we have introduced into the force are density-dependent generalizations of the usual $t_1$ and $t_2$ terms and are chosen in such a way as to avoid the high-density ferromagnetic instability of neutron stars that is a general feature of conventional Skyrme forces, and in particular of the Skyrme forces underlying all the HFB mass models that we have developed in the past. The remaining parameters of the model are then fitted to essentially all the available mass data, an rms deviation $\sigma$ of $0.585$ MeV being obtained. The new model thus gives almost as good a mass fit as our best-fit model HFB-17 ($\sigma =0.581$ MeV) and has the advantage of avoiding the ferromagnetic collapse of neutron stars.

Figure 1

Energy per nucleon ($T=0$) for pure neutron matter (NeuM) with forces BSk17 and SLy4. The squares are the results of the realistic calculations from Friedman and Pandharipande [3].

Figure 2

Neutron polarization $I_{\sigma n}$ for pure neutron matter (NeuM) with force BSk17.

Figure 3

Energy per nucleon ($T=0$) for neutron-star matter (${\mathrm{N}}^{*}\mathrm{M}$) with forces BSk17 and SLy4.

Figure 4

Proton fraction $Y_e$, neutron and proton polarizations $I_{\sigma n}$ and $I_{\sigma p}$, respectively, for neutron-star matter (${\mathrm{N}}^{*}\mathrm{M}$) with force BSk17.

Figure 5

Energy per nucleon ($T=0$) for pure neutron matter (NeuM), polarized and unpolarized, with force BSk18. The squares show the results of the realistic calculations of Friedman and Pandharipande [3].

Figure 6

Energy per nucleon ($T=0$) for neutron-star matter (${\mathrm{N}}^{*}\mathrm{M}$) with force BSk18. The system is stable against polarization in the ground state.

Figure 7

Proton fraction $Y_e$ for neutron-star matter (${\mathrm{N}}^{*}\mathrm{M}$) with force BSk18.

Figure 8

Landau parameter $G_0$ in symmetric nuclear matter for forces BSk17 (dashed line) and BSk18 (solid line).

Figure 9

Landau parameter $G_0^{\text{'}}$ in symmetric nuclear matter for forces BSk17 (dashed line) and BSk18 (solid line).

Figure 10

Velocity of sound $v_s$ (in units of the velocity of light $c$) for pure neutron matter with force BSk18.