Gravitational waves from nonradial oscillations of stochastically accreting neutron stars

Oscillating neutron stars are sources of continuous gravitational waves. We study analytically the excitation of stellar oscillations by the mechanical impact on the stellar surface of ''clumps'' of stochastically accreted matter. We calculate the waveform and spectrum of the gravitational wave signal emitted by the accretion-driven pulsations. Results are generated for an idealised model of a nonrotating, unmagnetised, one-component star with uniform polytropic index $n_{\rm poly}$ assuming Newtonian gravity and the Cowling approximation. We find that the excited mode amplitudes grow with increasing $n_{\rm poly}$ and mode order $n$. The gravitational wave signal forms a sequence of amplitude-modulated packets for $n_{\rm poly}=1$, lasting $\sim 10^{-3}$s after each impact. The gravitational wave strain increases with increasing $n_{\rm poly}$, but decreases with increasing $n$ and increasing multipole order $l$ for $n_{\rm poly}=1$. In the observing band of current long-baseline interferometers, $g$-modes emit higher, narrower peaks in the amplitude spectral density than $f$- and $p$-modes, with the highest peaks reaching $\sim 10^{-26}$Hz$^{-1/2}$ for modes with damping time $\tau_{nl} \sim 10^{8}$yr. The root-mean-square strain $h_{\text{rms}}$, calculated by summing over modes with $2\leq l\leq4$ and $\tau_{nl} \leq 10^{8}$yr, spans the range $10^{-33} \leq h_{\text{rms}} \leq 10^{-32}$ for $1\leq n_{\text{poly}}\leq 2$.