A Novel Method for Estimating the Ambient Medium Density around Distant Radio Sources from Their Observed Radio Spectra

The dynamical evolution and radiative properties of luminous radio galaxies and quasars of the FR II type, are well understood. As a result, through the use of detailed modeling of the observed radio emission of such sources, one can estimate various physical parameters of the systems, including the density of the ambient medium into which the radio structure evolves. This, however, requires rather comprehensive observational information, i.e., sampling the broadband radio continua of the targets at several frequencies, and imaging their radio structures with high resolution. Such observations are, on the other hand, not always available, especially for high-redshift objects. Here, we analyze the best-fit values of the source physical parameters, derived from extensive modeling of the largest currently available sample of FR II radio sources, for which good-quality multiwavelength radio flux measurements could be collected. In the analyzed data set, we notice a significant and nonobvious correlation between the spectral index of the nonthermal radio emission continuum, and density of the ambient medium. We derive the corresponding correlation parameters, and quantify the intrinsic scatter by means of Bayesian analysis. We propose that the discovered correlation could be used as a cosmological tool to estimate the density of ambient medium for large samples of distant radio galaxies. Our method does not require any detailed modeling of individual sources, and relies on limited observational information, namely, the slope of the radio continuum between the rest-frame frequencies 0.4 and 5 GHz, possibly combined with the total linear size of the radio structure.