Rotational Instabilities and Centrifugal Hangup

TL;DR

This paper investigates rotational instabilities in astrophysical objects through simulations, revealing conditions for bar and $m$=1 instabilities that produce detectable gravitational waves.

Contribution

It provides new simulation results on dynamical instabilities in differentially rotating polytropes with implications for gravitational wave detection.

Findings

Bar instability at T/|W| > 0.27 in n=1.5 polytropes

Persistent bar-like structures emit long-lived gravitational waves

Instability at T/|W| > 0.14 in n=3.33 polytropes with m=1 mode

Abstract

One interesting class of gravitational radiation sources includes rapidly rotating astrophysical objects that encounter dynamical instabilities. We have carried out a set of simulations of rotationally induced instabilities in differentially rotating polytropes. An $n$=1.5 polytrope with the Maclaurin rotation law will encounter the $m$=2 bar instability at $T/|W| \gtrsim 0.27$. Our results indicate that the remnant of this instability is a persistent bar-like structure that emits a long-lived gravitational radiation signal. Furthermore, dynamical instability is shown to occur in $n$=3.33 polytropes with the $j$-constant rotation law at $T/|W| \gtrsim 0.14$. In this case, the dominant mode of instability is $m$=1. Such instability may allow a centrifugally-hung core to begin collapsing to neutron star densities on a dynamical timescale. If it occurs in a supermassive star, it may produce gravitational radiation detectable by LISA.