The shape of a scatter-broadened image - II. Interferometric visibilities

We consider the angular broadening of a point source due to the effect of strong scattering and analytically estimate the rms image visibilities that would be measured by a two-element interferometer. The analysis, which is based on thin-screen scalar diffraction theory, confirms our earlier result that the measured visibilities depend both on the integration time of the observations and on the bandwidth employed. Three regimes of these parameters are identified. For the intermediate regime, corresponding to so-called 'average' visibilities, we obtain formulae which relate the rms visibility | V_a(b)|_rms on a baseline b to the power spectrum of phase fluctuations in the scattering screen. We show that |V_a(b)|_rms depends on the strength of the scattering, the power-law index of the power spectrum, and the magnitudes of the inner and outer scales of the spectrum. VLBI observations of compact radio sources which are scattered by the interstellar medium (ISM) correspond to the intermediate regime and therefore measure 'average' visibilities. Our results may help in interpretating such measurements and may provide valuable information on electron density fluctuations in the ISM on length-scales ~ 10⁸-10¹⁵ cm.