Stochastic gravitational wave background from hydrodynamic turbulence in differentially rotating neutron stars

TL;DR

This paper models the stochastic gravitational wave background generated by turbulence in differentially rotating neutron stars, providing constraints on internal relaxation timescales based on current and future detector sensitivities.

Contribution

It generalizes previous models to a cosmological population, deriving the spectrum shape and linking non-detections to internal neutron star dynamics.

Findings

Spectrum peaks near sensitive frequency band of ground-based detectors.

Upper limits on crust-core differential rotation imply specific relaxation timescales.

Future detectors could probe neutron star internal relaxation processes.

Abstract

Hydrodynamic turbulence driven by crust-core differential rotation imposes a fundamental noise floor on gravitational wave observations of neutron stars. The gravitational wave emission peaks at the Kolmogorov decoherence frequency which, for reasonable values of the crust-core shear, \Delta\Omega, occurs near the most sensitive part of the frequency band for ground-based, long-baseline interferometers. We calculate the energy density spectrum of the stochastic gravitational wave background from a cosmological population of turbulent neutron stars generalising previous calculations for individual sources. The spectrum resembles a piecewise power law, \Omega_{gw}(\nu)=\Omega_{\alpha}\nu^{\alpha}, with \alpha=-1 and 7 above and below the decoherence frequency respectively, and its normalisation scales as \Omega_{\alpha}\propto(\Delta\Omega)^{7}. Non-detection of a stochastic signal by Initial LIGO implies an upper limit on \Delta\Omega and hence by implication on the internal relaxation time-scale for the crust and core to come into co-rotation, \tau_{d}=\Delta\Omega/\dot{\Omega}, where \dot{\Omega} is the observed electromagnetic spin-down rate, with \tau_{d}\lesssim 10^{7} yr for accreting millisecond pulsars and \tau_{d}\lesssim 10^{5} yr for radio-loud pulsars. Target limits on \tau_{d} are also estimated for future detectors, namely Advanced LIGO and the Einstein Telescope, and are found to be astrophysically interesting.