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 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 Fanaroff-Riley Type 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/10³⁶ W = 1.5+1.8-0.8(L₁₅₁/10²⁷ W Hz^-1)^0.8(1 + ɀ)^1.0(D/kpc)^0.58±0.17, where D is source size and L₁₅₁ 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.