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 HI 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 \omega \la \dot { \theta } _ { v } / \theta _ { src } , where \dot { \theta } _ { 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 \theta _ { src } .
For drift speeds of \sim 10 ^ { 3 } km s ^ { -1 } and source brightness temperatures \sim 10 ^ { 12 } K , this limitation confines temporal opacity fluctuations to timescales of order several months to decades .