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 generalising previous calculations for individual sources .
The spectrum resembles a piecewise power law , \Omega _ { gw } ( \nu ) = \Omega _ { \alpha } \nu ^ { \alpha } , with \alpha = -1 and 7 above and below the decoherence frequency respectively , and its normalisation scales as \Omega _ { \alpha } \propto \left ( \Delta \Omega \right ) ^ { 7 } .
Non-detection 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 co-rotation , \tau _ { d } = \Delta \Omega / \dot { \Omega } , where \dot { \Omega } is the observed electromagnetic spin-down rate , with \tau _ { d } \lesssim 10 ^ { 7 } { yr } for accreting millisecond pulsars and \tau _ { d } \lesssim 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 .