Stability of coalescing binary stars against gravitational collapse: hydrodynamical simulations

TL;DR

This study uses hydrodynamical simulations in post-Newtonian gravity to analyze the stability of relativistic binary stars against gravitational collapse, revealing that tidal interactions can stabilize stars regardless of internal velocity profiles.

Contribution

It provides the first detailed simulation-based analysis of binary star stability against collapse in a relativistic context, highlighting the stabilizing effect of tidal fields.

Findings

Tidal fields stabilize stars against gravitational collapse.

No innermost stable circular orbit exists for the soft equation of state used.

Stability results are consistent across different internal velocity profiles.

Abstract

We perform simulations of relativistic binary stars in post-Newtonian gravity to investigate their dynamical stability prior to merger against gravitational collapse in a tidal field. In general, our equations are only strictly accurate to first post-Newtonian order, but they recover full general relativity for spherical, static stars. We study both corotational and irrotational binary configurations of identical stars in circular orbits. We adopt a soft, adiabatic equation of state with $\Gamma = 1.4$, for which the onset of instability occurs at a sufficiently small value of the compaction $M/R$ that a post-Newtonian approximation is quite accurate. For such a soft equation of state there is no innermost stable circular orbit, so that we can study arbitrarily close binaries. This choice still allows us to study all the qualitative features exhibited by any adiabatic equation of state regarding stability against gravitational collapse. We demonstrate that, independent of the internal stellar velocity profile, the tidal field from a binary companion stabilizes a star against gravitational collapse.