Scattering of gravitational radiation Intensity fluctuations

Aims. The effect of gravitational microlensing on the intensity of gravitational radiation as it propagates through an inhomogeneous medium is considered. Lensing by both stars and a power law spectrum of density perturbations is examined. Methods. The long wavelengths characteristic of gravitational radiation mandate a statistical, physical-optics approach to treat the effect of the lensing. Results. A model for the mass power spectrum of a starfield, including the effects of clustering and allowing for a distribution of stellar masses, is constructed and used to determine both the amplitude of fluctuations in the gravitational wave strain and its associated temporal fluctuation spectrum. For a uniformly distributed starfield the intensity variance scales linearly with stellar density, σ, but is enhanced by a factor >∼σr F when clustering is important, where rF is the Fresnel scale. The effect of lensing by a power law mass spectrum, applicable to lensing by small scale fluctuations in gas and dark matter, is also considered. For power law mass density spectra with indices steeper than −2 the wave amplitude exhibits rms fluctuations 1.3〈∆Σ2〉1/4(Deff/1 Gpc)%, where 〈∆Σ2〉 is the variance in the mass surface density measured in M pc −4 and Deff is the effective distance to the lensing medium. For shallower spectra the amplitude of the fluctuations depends additionally on the inner length scale and power law index of the density fluctuations. The intensity fluctuations are dominated by temporal fluctuations on long timescales. For lensing material moving at a speed v across the line of sight the fluctuation timescale exceeds v−1(Deffλ)1/2. Lensing by small scale structure induces at most ≈15% rms variations if the line of sight to a gravitational wave source intersects a region with densities ∼100 M pc−2, which are typically encountered in the vicinity of galaxy clusters.