Gravitational Radiation From Hydrodynamic Turbulence in a Differentially Rotating Neutron Star

The mean-square current quadrupole moment associated with vorticity fluctuations in high-Reynolds-number turbulence in a differentially rotating neutron star is calculated analytically, as are the amplitude and decoherence time of the resulting, stochastic gravitational wave signal. The calculation resolves the subtle question of whether the signal is dominated by the smallest or largest turbulent eddies: for the Kolmogorov-like power spectrum observed in superfluid spherical Couette simulations, the wave strain is controlled by the largest eddies, and the decoherence time approximately equals the maximum eddy turnover time. For a neutron star with spin frequency ν s and Rossby number Ro, at a distance d from Earth, the root mean square wave strain reaches h rms ≈ 3 × 10 −24 Ro 3 (ν s /30 Hz) 3 ( d /1 kpc) −1 . Ordinary rotation-powered pulsars (ν s ≲ 30 Hz, Ro ≲ 10 −4 ) are too dim to be detected by the current generation of long-baseline interferometers. Millisecond pulsars are brighter; for example, an object born recently in a Galactic supernova or accreting near the Eddington rate can have ν s ∼ 1 kHz, Ro ≳ 0.2, and hence h rms ∼ 10 −21 . A cross-correlation search can detect such a source in principle, because the signal decoheres over the timescale τ c ≈ 1 × 10 −3 Ro −1 (ν s /30 Hz) −1 s, which is adequately sampled by existing long-baseline interferometers. Hence, hydrodynamic turbulence imposes a fundamental noise floor on gravitational wave observations of neutron stars, although its polluting effect may be muted by partial decoherence in the hectohertz band, where current continuous-wave searches are concentrated, for the highest frequency (and hence most powerful) sources. This outcome is contingent on the exact shape of the turbulent power spectrum, which is modified by buoyancy and anisotropic global structures, such as stratified boundary layers, in a way that is understood incompletely even in laboratory situations.