  The kinetic power of radio jets is a quantity of fundamental importance to
studies of the AGN feedback process and radio galaxy physics. A widely used
proxy for jet power is the extended radio luminosity. A number of empirical
methods have been used to calibrate a scaling relationship between jet power
(Q) and radio luminosity (L) of the form log(Q) = beta_L * log(L) + C. The
regression slope has typically been found to be beta_L ~ 0.7 - 0.8. Here we
show that the previously reported scaling relations are strongly affected by
the confounding variable, distance. We find that in a sample of FRI X-ray
cavity systems, after accounting for the mutual distance dependence, the jet
power and radio luminosity are only weakly correlated, with slope beta_L ~ 0.3:
significantly flatter than previously reported. We also find that in previously
used samples of high-power sources, no evidence for an intrinsic correlation is
present when the effect of distance is accounted for. Using a simple model we
show that beta_L is expected to be significantly lower in samples of FRI radio
galaxies than it is for FRIIs, due to the differing dynamics for these two
classes of radio source. For FRI X-ray cavity systems the model predicts beta_L
(FRI) ~ 0.5 in contrast to FRII radio galaxies, for which beta_L(FRII) ~ 0.8.
We discuss the implications of our finding for studies of radio mode feedback,
and radio galaxy physics.
