Gravitational Radiation from Hydrodynamic Turbulence in a Differentially Rotating Neutron Star

TL;DR

This paper analytically calculates the gravitational wave signal from turbulence in rotating neutron stars, showing it is dominated by large eddies and could be detectable with current interferometers, setting a fundamental noise limit.

Contribution

It provides the first analytical estimate of the gravitational wave signal from turbulence in neutron stars, clarifying the dominant eddy scale and decoherence time.

Findings

Wave strain is controlled by the largest turbulent eddies.

Decoherence time is approximately the maximum eddy turnover time.

Potential detectability with existing gravitational wave detectors.

Abstract

(Abridged.) 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 $\nu_s$ and Rossby number $Ro$, at a distance $d$ from Earth, the root-mean-square wave strain reaches $h_{RMS} \approx 3\times 10^{-24} Ro^3 (\nu_s / 30 Hz)^3 (d/1 kpc)^{-1}$. A cross-correlation search can detect such a source in principle, because the signal decoheres over the time-scale $\tau_c \approx 10^{-3} Ro^{-1} (\nu_s / 30 Hz)^{-1} s$, 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.