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 rest-frame frequencies 0.4GHz and
5GHz, possibly combined with the total linear size of the radio structure.
