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

References in corpus (22)

• On the Sound Speed in Neutron Stars
• Accretion to Magnetized Stars through the Rayleigh-Taylor Instability: Global Three-Dimensional Simulations
• A Horizon Study for Cosmic Explorer: Science, Observatories, and Community
• Searches for Continuous-Wave Gravitational Radiation
• How to adapt broad-band gravitational-wave searches for r-modes
• Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
• Oscillations of rapidly rotating stratified neutron stars
• Distances of the bulge globular clusters Terzan 5, Liller 1, UKS 1 and Terzan 4 based on HST NICMOS photometry
• Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective
• R-mode frequencies of slowly rotating relativistic neutron stars with realistic equations of state
• Search for continuous gravitational waves from 20 accreting millisecond X-ray pulsars in O3 LIGO data
• Excitation of a nonradial mode in a millisecond X-ray pulsar XTE J1751-305
• Search of the Early O3 LIGO Data for Continuous Gravitational Waves from the Cassiopeia A and Vela Jr. Supernova Remnants
• Search for gravitational waves from five low mass X-ray binaries in the second Advanced LIGO observing run with an improved hidden Markov model
• X-ray bounds on the r-mode amplitude in millisecond pulsars
• Relativistic ocean $r$-modes during type-I X-ray bursts
• Rotating Love: The dynamical tides of spinning Newtonian stars
• The r-modes of slowly rotating, stratified neutron stars
• Relativistic correction to the r-mode frequency in light of multi-messenger constraints
• Search for continuous gravitational waves from PSR J0437$-$4715 with a hidden Markov model in O3 LIGO data
• Formulating the r-mode problem for slowly rotating neutron stars
• Gravitational waves from nonradial oscillations of stochastically accreting neutron stars