Comparison of Radio Observations and Numerical Simulations of the Radio Lobes of Cygnus A

We present a comparison of radio observations of the powerful archetypal radio galaxy Cyg A and two-dimensional numerical hydrodynamic simulations. We characterize some global trends in the observed radio properties and compare them with the properties of a simulated radio source. The observational results are the following. The width of the observed surface brightness distribution perpendicular to the source axis can be well characterized by a Gaussian over most of the length of the source. The ratio of the Gaussian FWHM to the second moment is fairly constant along the source, with an average value of about 2.5, indicating that they give roughly consistent measurements of the source width. The average observed surface brightness, estimated pressure, and estimated minimum-energy B-field decrease with distance from the hot spots. We find evidence for significant structure in the estimated cross-sectional slices of the emissivity. The numerical results are the following. Jets propagating in a constant-density atmosphere decelerate with time. Thus, the estimated dynamical age of the source is greater than the actual age of the source. For a source similar to Cyg A, the difference is about a factor of 2. The second moment gives an accurate representation of the "true" width of the simulated source. The Gaussian FWHM tends to be about 40% larger than the true width and can be systematically in error if the surface brightness exhibits multiple peaks. We suggest that the ratio of the Gaussian FWHM to the second moment may be a diagnostic of the emissivity profile in the lobes. The simulations can qualitatively reproduce the overall observed morphology, the behavior of the cross sections in surface brightness, the decline in surface brightness with distance from the hot spots, and the width of the lobes. This suggests that the two-dimensional simulations give a reasonable representation of the properties of Cyg A.