Nonlinear evolution of r-modes: the role of differential rotation

TL;DR

This paper studies how differential rotation influences the nonlinear evolution of r-modes in newly born neutron stars, showing that it affects mode saturation, star spin-down, and angular momentum transfer.

Contribution

It demonstrates the impact of differential rotation on r-mode saturation amplitude and angular momentum transfer, providing new insights into neutron star spin evolution.

Findings

R-mode amplitude saturates within a few hundred seconds.

Star spins down to initial pulsar rotation rates.

Most initial angular momentum is transferred to the r-mode.

Abstract

Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly rotating neutron star. It is shown that the amplitude of the r-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r-mode and, consequently, almost none is carried away by gravitational radiation.