Size dependence of the radio luminosity - mechanical power correlation
  in radio galaxies
  We examine the relationship between source radio luminosity and kinetic power
in Active Galactic Nucleus (AGN) jets. We show that neglecting various loss
processes can introduce a systematic bias in the jet powers inferred from radio
luminosities for a sample of radio galaxies. This bias can be corrected for by
considering source size as well as radio luminosity; effectively the source
size acts as a proxy for source age. Based on a sample of FR-II radio sources
with jet powers derived from the measured hotspot parameters, we empirically
determine a new expression for jet power that accounts for the source size,
Q_jet / 10^{36} W = 1.5 (L_151 / 10^{27} W/Hz)^{0.8} (1+z)^{1.0} (D /
kpc)^{0.58 \pm 0.17}, where D is source size and L_151 the 151 MHz radio
luminosity. By comparing a flux-limited and volume-limited sample, we show that
any derived radio luminosity - jet power relation depends sensitively on sample
properties, in particular the source size distribution and the size-luminosity
correlation inherent in the sample. Such bias will affect the accuracy of the
kinetic luminosity function derived from lobe radio luminosities and should be
treated with caution.
