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 FRII 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 broad-band 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 an extensive modeling of the largest currently available sample of FRII radio sources, for which good-quality multi-wavelength radio flux measurements could be collected. In the analyzed dataset, we notice a significant and non-obvious correlation between the spectral index of the non-thermal 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 emitted frequencies 0.4 GHz and 5 GHz, possibly combined with the total linear size of the radio structure.