On Massive Neutron Cores

TLDR

When stellar matter pressure rises sufficiently, a new neutron phase is predicted to form. The paper aims to study the gravitational equilibrium of neutron masses using a cold Fermi gas equation of state and general relativity. The authors model neutron cores by applying the cold Fermi gas EOS within general relativity to analyze equilibrium solutions. For masses below one‑third solar mass only a single stable equilibrium exists; between one‑third and three‑quarters solar masses two solutions appear—one stable and quasi‑Newtonian, the other unstable and more condensed; above three‑quarters solar mass no static equilibrium exists, confirming Tolman’s analytic solutions and implying that sufficiently massive neutron cores will collapse indefinitely.

Abstract

It has been suggested that, when the pressure within stellar matter becomes high enough, a new phase consisting of neutrons will be formed. In this paper we study the gravitational equilibrium of masses of neutrons, using the equation of state for a cold Fermi gas, and general relativity. For masses under $\frac{1}{3}\ensuremath{\bigodot}$ only one equilibrium solution exists, which is approximately described by the nonrelativistic Fermi equation of state and Newtonian gravitational theory. For masses $\frac{1}{3}\ensuremath{\bigodot}<m<\frac{3}{4}\ensuremath{\bigodot}$ two solutions exist, one stable and quasi-Newtonian, one more condensed, and unstable. For masses greater than $\frac{3}{4}\ensuremath{\bigodot}$ there are no static equilibrium solutions. These results are qualitatively confirmed by comparison with suitably chosen special cases of the analytic solutions recently discovered by Tolman. A discussion of the probable effect of deviations from the Fermi equation of state suggests that actual stellar matter after the exhaustion of thermonuclear sources of energy will, if massive enough, contract indefinitely, although more and more slowly, never reaching true equilibrium.