The combination of the faint GPS sample and bright GPS and CSS samples from the literature gave a unique opportunity to investigate the relation between the spectral peak and size of young radio sources. Not surprisingly, the inverse correlation between peak frequency, p, and angular size, , was confirmed. However, in addition, a correlation was found between the peak flux density, Sp, and angular size. The strengths and signs of these two correlations are exactly as expected for synchrotron self absorption (SSA), for which 2 Sp B1/2 p-5/2, where B is the magnetic field. This strongly suggests that SSA is indeed the cause of the spectral turnovers in GPS and CSS sources, and not free-free absorption as recently proposed by Bicknell et al. (1997).
The solid angle subtended by the dominant features, the mini-lobes, determines the strength and frequency of the spectral peak (see fig 1). The angular size determined from VLBI observations, corresponds to the overall angular size of the object. The correlations discussed above therefore imply a constant ratio of overall size to lobe size in samples of faint and bright GPS and CSS galaxies. This indicates that young radio sources grow in a self-similar way.
Figure 1. (Left) A schematic view of a young radio source. The overall angular size can be determined from VLBI observations, while the sizes of the lobes can be derived from the synchrotron self-absorption turnover. (Right) The overall size to lobe size ratio in faint and bright samples of GPS and CSS galaxies, assuming a fixed- (top panel) and an equipartition magnetic field (bottom panel).
The sizes derived for the lobes are slightly dependent on the magnetic field strength (see above). The ratios of the overall to lobe sizes were determined for a fixed magnetic field of 10-3 Gauss and for an equipartition magnetic field (Scott & Readhead 1977). The results are shown in the top and bottom panel of fig 1 respectively. The ratios, calculated using an equipartition magnetic field, do not show a trend with linear size, but they show a decline with linear size when a fixed magnetic field is used. This seems to indicate that the self-similar evolution scenario (dashed line) is better fitted (solid line) for an equipartition magnetic field than for a constant magnetic field.