On the HI column density-radio source size anticorrelation in compact radio sources

Existing studies of the atomic hydrogen gas content in distant galaxies, through the absorption of the 21-cm line, often infer that the total column density, N-HI, is anticorrelated with the linear extent of the background radio source, d(em). We investigate this interpretation, by dissecting the various parameters from which N-HI is derived, and find that the relationship is driven primarily by the observed optical depth, tau(obs), which, for a given absorber size, is anticorrelated with d(em). Therefore, the inferred N-HI-d(em) anticorrelation is merely the consequence of geometry, in conjunction with the assumption of a common spin temperature/covering factor ratio for each member of the sample, an assumption for which there is scant observational justification. While geometry can explain the observed correlation, many radio sources comprise two radio lobes and so we model the projected area of a two-component emitter intercepted by a foreground absorber. From this, the observed tau(obs)-d(em) relationship is best reproduced through models which approximate either of the two Fanaroff & Riley classifications, although the observed scatter in the sample cannot be duplicated using a single deprojected radio source size. Furthermore, the trend is best reproduced using an absorber of diameter similar to 100-1000 pc, which is also the range of values of d(em) at which the 21-cm detection rate peaks. This may indicate that this is the characteristic linear size of the absorbing gas structure.