Gravitational Radiation from Nonaxisymmetric Spherical Couette Flow in a Neutron Star

The gravitational wave signal generated by global, nonaxisymmetric shearflows in a neutron star is calculated numerically by integrating theincompressible Navier--Stokes equation in a spherical, differentially rotatingshell. At Reynolds numbers $\Rey \gsim 3 \times 10^{3}$, the laminar Stokesflow is unstable and helical, oscillating Taylor--G\"ortler vortices develop.The gravitational wave strain generated by the resulting kinetic-energyfluctuations is computed in both $+$ and $\times$ polarizations as a functionof 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} {\rmrad} {\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 pressurefluctuations, herringbone flows, Stuart vortices, and fully developedturbulence (for $\Rey \gsim 10^{6}$).Comment: (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 Letter