Stochastic gravitational wave background from hydrodynamic turbulence in differentially rotating neutron stars

Hydrodynamic turbulence driven by crust-core differential rotation imposes a fundamental noise floor on gravitational wave observations of neutron stars. The gravitational wave emission peaks at the Kolmogorov decoherence frequency which, for reasonable values of the crust-core shear, Delta Omega, occurs near the most sensitive part of the frequency band for ground-based, long-baseline interferometers. We calculate the energy density spectrum of the stochastic gravitational wave background from a cosmological population of turbulent neutron stars generalizing previous calculations for individual sources. The spectrum resembles a piecewise power law, Omega(gw)(v) = Omega(alpha)v(alpha), with alpha = -1 and 7 above and below the decoherence frequency respectively, and its normalization scales as Omega(alpha) proportional to (Delta Omega)(7). Nondetection of a stochastic signal by Initial LIGO implies an upper limit on Delta Omega and hence by implication on the internal relaxation time scale for the crust and core to come into corotation, tau(d) = Delta Omega/(Omega) over dot, where (Omega) over dot is the observed electromagnetic spin-down rate, with tau(d) less than or similar to 10(7) yr for accreting millisecond pulsars and tau(d) less than or similar to 10(5) yr for radio-loud pulsars. Target limits on tau(d) are also estimated for future detectors, namely Advanced LIGO and the Einstein Telescope, and are found to be astrophysically interesting. DOI: 10.1103/PhysRevD.87.063004