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, ΔΩ, 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, Ωgw(ν)=Ω_αν^α, with α=-1 and 7 above and below the decoherence frequency respectively, and its normalization scales as Ω_α∝(ΔΩ)⁷. Nondetection of a stochastic signal by Initial LIGO implies an upper limit on ΔΩ and hence by implication on the internal relaxation time scale for the crust and core to come into corotation, τd=ΔΩ/ ̇ Ω, where ̇ Ω is the observed electromagnetic spin-down rate, with τd10⁷ yr for accreting millisecond pulsars and τd10⁵ yr for radio-loud pulsars. Target limits on τd are also estimated for future detectors, namely Advanced LIGO and the Einstein Telescope, and are found to be astrophysically interesting.