Absorption variability as a probe of the multiphase interstellar media surrounding active galaxies

Abstract

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 ≲ θ˙υ/θsrc, where θ˙υ 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 θsrc. For drift speeds of ~103 km s-1 and source brightness temperatures ~1012 K, this limitation confines temporal opacity fluctuations to time-scales of order several months to decades.