Jacobi-like bar mode instability of relativistic rotating bodies

TL;DR

This study numerically investigates how general relativity influences the secular triaxial instability of rotating fluid bodies, finding that relativity slightly stabilizes the system but the effect remains modest.

Contribution

It provides the first detailed numerical analysis of relativistic effects on the Jacobi-like bar mode instability in homogeneous rotating bodies.

Findings

Relativity weakens the instability but only slightly.

The critical T/|W| ratio increases by about 30% at high compaction.

Eccentricity at instability onset varies weakly with relativity.

Abstract

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.