3.4. Average Hot-Spot Advance Speeds from Spectral Measurements
Estimates of h can be made by measuring the effects of synchrotron losses in the lobes of FRII sources. If the synchrotron electrons are accelerated at the hot-spot and stream away to form the lobe, then the curvature of the spectrum at a given point in the lobe is determined by the subsequent energy losses. The assumptions most usually made are that the losses are due entirely to synchrotron radiation and Inverse-Compton scattering off the microwave background radiation, that the input energy distribution is a power law consistent with the low-frequency spectral index of the hot-spot and that the electrons radiate in a uniform magnetic field whose strength is given by the equipartition condition. Any of these assumptions may be incorrect.
The most extensive sets of multifrequency measurements are those of Alexander & Leahy (1987) and Liu, Pooley & Riley (1992). Figure 3 (taken from the latter reference) shows a plot of mean advance speed against radio luminosity for the combined samples. The trend is for the velocities to increase from h ~ 0.01c at luminosities around the FRI/FRII division to h ~ 0.15c at very high luminosities. The velocities are sensitive to the assumptions used to derive the magnetic field strength, but even if the electrons lose energy purely by Inverse Compton scattering off the microwave background radiation, the velocities can be as high as 0.07c.
Figure 3. A plot of mean hot-spot advance speed, h / c against radio luminosity for a sample of FRII sources (Liu, Pooley & Riley 1992 and references therein). The derived speeds and luminosities have been adjusted to H0 = 100 kms-1 Mpc-1.