Gravitational waves from <i>r</i>-mode oscillations of stochastically accreting neutron stars

ABSTRACT r-mode oscillations in rotating neutron stars are a source of continuous gravitational radiation. We investigate the excitation of r-modes by the mechanical impact on the neutron star surface of stochastically accreted clumps of matter, assuming that the Chandrasekhar–Friedman–Schutz instability is not triggered. The star is idealized as a slowly rotating, unmagnetized, one-component fluid with a barotropic equation of state in Newtonian gravity. It is found that the r-mode amplitude depends weakly on the equation of state but sensitively on the rotation frequency $\nu _{\rm s}$. The gravitational wave strain implicitly depends on the equation of state through the damping time-scale. The root-mean-square strain is $h_{\rm rms} \approx 10^{-35} (\nu _{\rm s}/ 10\, {\rm Hz})^{2} (R_*/10\, {\rm km})^2 (\Delta t_{\rm acc}/1\, {\rm yr})^{1/2} (f_{\rm acc}/1\, {\rm kHz})^{-1/2} (\dot{M}/10^{-8}\text{M}_{\odot } \, \text{yr}^{-1}) (v/0.4c) (d/1\, {\rm kpc})^{-1}$, which is comparable to the strain from g-, p-, and f-modes excited by stochastic accretion, where $R_*$ is the radius of the star, $\Delta t_{\rm acc}$ is the uninterrupted duration of an accretion episode, $f_{\rm acc}$ is the mean clump impact frequency, $\dot{M}$ is the accretion rate, v is the impact speed, and d is the distance of the star from the Earth. An observational test is proposed, based on the temporal autocorrelation function of the gravitational wave signal, to discern whether the Chandrasekhar–Friedman–Schutz instability switches on and coexists with impact-excited r-modes before or during a gravitational wave observation.