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 τ_θ∼2×10⁵yr [10^-7/(ΔI_d/I₀)]²(kHz/ν_s)⁴, where ν_s is the spin frequency and ΔI_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 τ_θ is too short by a factor of ∼10⁵ for the typical cases of interest and even has the wrong sign for ΔI_d negative. We show where their calculation went astray.