2025MNRAS.537..650D

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.