On the neutronization radius of magnetic neutron stars: The field and temperature dependences of the chemical potential and minimum number density of a degenerate magnetized electron gas

Abstract

The temperature and field dependences of the chemical potential and the field dependence of the Fermi energy for a degenerate relativistic electron gas in a magnetic field have been analyzed by numerical and analytical methods. An analytical expression has been derived for the dependence of the minimum electron number density and the corresponding neutronization radius on the magnetic field strength in a collapsing star upon its subsequent transformation into a neutron one. We believe that a similar relation also holds for the equilibrium neutron star radius. Our results refine the conclusions reached previously [1] in the case of a nonzero temperature and the influence of the star’s proton component on the neutronization process as well as confirm and generalize them in terms of a significant (by an order of magnitude or severalfold) decrease in the equilibrium radius of a neutron star in a superstrong (1014–1017 G) magnetic field compared to the case where there is no such field. We point out that there may exist a separate class of stellar objects—very small magnetar neutron stars that we propose to name “minimagnetars”. We hypothesize that they can be the final evolutionary stage of stars before their collapse into a black hole.