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.