Gravitational Wave Damping of Neutron Star Wobble

TL;DR

This paper calculates how gravitational waves damp neutron star wobble, revealing a long damping timescale and correcting previous erroneous results, with implications for neutron star dynamics.

Contribution

It provides a new, accurate calculation of gravitational wave damping timescale for neutron star wobble, correcting past errors and offering two derivations for the result.

Findings

Damping timescale tau_{theta} approx 2 x 10^5 years

Previous calculations by Bertotti and Anile were incorrect by a factor of 10^5

The damping depends on neutron star's spin frequency and inertia tensor component DId.

Abstract

We calculate the effect of gravitational wave (gw) back-reaction on realistic neutron stars (NS's) undergoing torque-free precession. By `realistic' we mean that the NS is treated as a mostly-fluid body with an elastic crust, as opposed to a rigid body. We find that gw's damp NS wobble on a timescale tau_{theta} approx 2 x 10^5 yr [10^{-7}/(DId/I_0)]^2 (kHz/ nu_s)^4, where nu_s is the spin frequency and DId is the piece of the NS's inertia tensor that "follows" the crust's principal axis (as opposed to its spin axis). We give two different derivations of this result: one based solely on energy and angular momentum balance, and another obtained by adding the Burke-Thorne radiation reaction force to the Newtonian equations of motion. This problem was treated long ago by Bertotti and Anile (1973), but their claimed result is wrong. When we convert from their notation to ours, we find that their tau_{theta} is too short by a factor of order 10^5 for typical cases of interest, and even has the wrong sign for DId negative. We show where their calculation went astray.