Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star

TL;DR

This study numerically investigates gravitational waves generated by nonaxisymmetric shear flows in neutron stars, revealing potential detectability with LIGO II and highlighting the influence of flow instability and turbulence.

Contribution

It introduces a numerical method to compute gravitational wave signals from shear flows in neutron stars, considering nonaxisymmetric, turbulent flows at high Reynolds numbers.

Findings

Gravitational wave strain scales with star’s angular velocity as $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 6.5 (\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 10^{4} { m rad} { m s}^{-1})^{7/2}$ for a star at 1 kpc.

Signal-to-noise ratio is significant for long integration times ($10^8$ s) with LIGO II.

The analysis provides a lower limit, excluding effects like pressure fluctuations and turbulence at very high Reynolds numbers.

Abstract

The gravitational wave signal generated by global, nonaxisymmetric shear flows in a neutron star is calculated numerically by integrating the incompressible Navier--Stokes equation in a spherical, differentially rotating shell. At Reynolds numbers $\Rey \gsim 3 \times 10^{3}$, the laminar Stokes flow is unstable and helical, oscillating Taylor--G\"ortler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both $+$ and $\times$ polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, $10^{8}$-{\rm s} integration with LIGO II scales as $ 6.5 (\Omega_*/10^{4} {\rm rad} {\rm s}^{-1})^{7/2}$ for a star at 1 {\rm kpc} with angular velocity $\Omega_*$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for $\Rey \gsim 10^{6}$).