Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star

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--Görtler 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 $6.5({\Omega }_{\ast }/10^4\mathrm{rad}{\mathrm{s}}^{-1}{)}^{7/2}$ for a star at 1 {\rm kpc} with angular velocity ${\Omega }_{\ast }$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for $\Rey \gsim 10^{6}$).

(1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal Letters