3.2. Density Contrast
An argument originally due to Scheuer (1974) can be used to set limits on the density contrast, that is the ratio between the internal and external densities, = n / next. In order to inflate the lobes of FRII sources, the advance speed of the hot-spots, vh, must be much less than the flow velocity of the jet, vj.
implying that << 1. Williams (1991) showed that the ratio of lobe width to jet width ~ M1/j / 1/4, where Mj is the Mach number of the jet and is the ratio of specific heats. This implies that ~ 10-3 - 10-4 for Cygnus A. It should be possible to refine this scaling relation by numerical modeling (cf. Norman, these proceedings). The basic implication, however, is that strong-flavor jets are significantly lighter than their surroundings.
The same qualitative argument can be made for the FRI sources which show bridges rather than tails (the majority in complete samples such as that of Parma et al. 1987) and it seems likely that the jets in these sources are also light, albeit subsonic where they terminate (Bicknell 1984, 1986a, b).