Dynamical Rotational Instability at Low $T/W$

TL;DR

This paper demonstrates that differentially rotating polytropes with specific parameters exhibit dynamical instabilities, which could lead to neutron star formation and produce detectable gravitational waves for current and future observatories.

Contribution

It identifies the conditions under which dynamical rotational instability occurs in differentially rotating polytropes and discusses potential gravitational wave signals.

Findings

Instability occurs at T/|W| ≳ 0.14 for N=3.33 polytropes.

Strong m=1 mode dominates the instability.

Potential gravitational wave detection by LIGO II and LISA.

Abstract

Dynamical instability is shown to occur in differentially rotating polytropes with N = 3.33 and $T/|W| \gtrsim 0.14$. This instability has a strong m=1 mode, although the m=2, 3, and 4 modes also appear. Such instability may allow a centrifugally-hung core to begin collapsing to neutron star densities on a dynamical timescale. The gravitational radiation emitted by such unstable cores may be detectable with advanced ground-based detectors, such as LIGO II. If the instability occurs in a supermassive star, it may produce gravitational radiation detectable by the space-based detector LISA.