Spin Wandering of an Accreting Neutron Star near Torque Balance: Implications for Gravitational-wave Searches

Abstract Torque balance between gravitational radiation reaction and magnetocentrifugal accretion is one reason why accreting neutron stars rotate slower than centrifugal breakup. Random processes in the accretion disk, such as Rayleigh–Taylor instabilities and flicker noise, drive the spin frequency f * and gravitational wave frequency f gw ∝ f * to wander stochastically around their torque balance values. Here it is shown theoretically, in terms of an idealized Ornstein–Uhlenbeck model, that the standard deviation of f gw is given by σ f gw ( h 0 ) ∝ f gw h 0 D β T 1 / 2 , or equivalently σ f gw ( F X ) ∝ f gw 1 / 2 F X 1 / 2 D β T 1 / 2 , where h 0 is the characteristic wave strain, F X is the X-ray flux, D is the source distance, and β and T are the fractional amplitude and autocorrelation timescale of the stochastic torque. One can use σ f gw ( h 0 ) and σ f gw ( F X