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, Ω_gw(ν )=Ω_ανα, with α=-1 and 7 above and below the decoherence frequency respectively, and its normalization scales as Ω_αâ̂(ΔΩ). 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, τ_d=ΔΩ/Ω̇, where Ω̇ is the observed electromagnetic spin-down rate, with τ_dâ‰107 yr for accreting millisecond pulsars and τ_dâ‰105 yr for radio-loud pulsars. Target limits on τ_d are also estimated for future detectors, namely Advanced LIGO and the Einstein Telescope, and are found to be astrophysically interesting.