2016MNRAS.460.2322M

We examine a model for the variable free-free and neutral hydrogen absorption inferred towards the cores of some compact radio galaxies in which a spatially fluctuating medium drifts in front of the source. We relate the absorption-induced intensity fluctuations to the statistics of the underlying opacity fluctuations. We investigate models in which the absorbing medium consists of either discrete clouds or a power-law spectrum of opacity fluctuations. We examine the variability characteristics of a medium comprised of Gaussian-shaped clouds in which the neutral and ionized matter are co-located, and in which the clouds comprise spherical constant-density neutral cores enveloped by ionized sheaths. The cross-power spectrum indicates the spatial relationship between neutral and ionized matter, and distinguishes the two models, with power in the Gaussian model declining as a featureless power-law, but that in the ionized sheath model oscillating between positive and negative values. We show how comparison of the H i and free-free power spectra reveals information on the ionization and neutral fractions of the medium. The background source acts as a low-pass filter of the underlying opacity power spectrum, which limits temporal fluctuations to frequencies ω\lesssim {dot}θ_v/θ_src, where {dot}θ_v is the angular drift speed of the matter in front of the source, and it quenches the observability of opacity structures on scales smaller than the source size θ_src. For drift speeds of ∼10^3 km s^-1 and source brightness temperatures ∼10^12 K, this limitation confines temporal opacity fluctuations to time-scales of order several months to decades.