Gravitational waves from r-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 idealised as a slowly-rotating, unmagnetised, 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 ${\nu }_{\mathrm{s}}$. The gravitational wave strain implicitly depends on the equation of state through the damping timescale. The root-mean-square strain is $h_{\mathrm{rms}}\approx 10^{-35}({\nu }_{\mathrm{s}}/10\mathrm{Hz}{)}^2(R_{\ast }/10\mathrm{km}{)}^2(\Delta t_{\mathrm{acc}}/1\mathrm{yr}{)}^{1/2}(f_{\mathrm{acc}}/1\mathrm{kHz}{)}^{-1/2}(\dot{M}/10^{-8}{\text{M}}_{\odot }{\text{yr}}^{-1})(v/0.4c)(d/1\mathrm{kpc}{)}^{-1}$, which is comparable to the strain from $g$-, $p$- and $f$-modes excited by stochastic accretion, where $R_{\ast }$ is the radius of the star, $\Delta t_{\mathrm{acc}}$ is the uninterrupted duration of an accretion episode, $f_{\mathrm{acc}}$ 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.

11 pages, 1 figure, 1 table. Accepted for publication in MNRAS

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