Gravitational wave damping of neutron star wobble

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 time scale ${\tau }_{\theta }\sim 2\times {10}^5\mathrm{yr}$ $[{10}^{-7}/(\Delta I_d{/I}_0\left){]}^2\right(\mathrm{kHz}/{\nu }_s{)}^4,$ where ${\nu }_s$ is the spin frequency and $\Delta I_d$ 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, 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 $\sim {10}^5$ for the typical cases of interest and even has the wrong sign for $\Delta I_d$ negative. We show where their calculation went astray.