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 } \sim 2 \times 10 ^ { 5 } yr [ 10 ^ { -7 } / ( \Delta I _ { d } / I _ { 0 } ) ] ^ { 2 } ( { 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 ( 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 \sim 10 ^ { 5 } for typical cases of interest , and even has the wrong sign for \Delta I _ { d } negative .
We show where their calculation went astray .