Gravitational waves from r-mode oscillations of stochastically accreting neutron stars

TL;DR

This paper models how stochastic accretion impacts excite r-mode oscillations in neutron stars, producing gravitational waves with strain levels comparable to other modes, and proposes an observational test to detect these effects.

Contribution

It introduces a model for impact-excited r-modes in neutron stars and suggests a method to distinguish this excitation from other gravitational wave sources.

Findings

R-mode amplitude weakly depends on the equation of state.

Strain amplitude is sensitive to the star's rotation frequency.

Proposes an autocorrelation-based observational test.

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 $\nu_{\rm s}$. The gravitational wave strain implicitly depends on the equation of state through the damping timescale. 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.