Size dependence of the radio-luminosity-mechanical-power correlation in radio galaxies
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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, (Qjet/1036 W) = 1.5+1.8 −0.8(L151/1027WHz−1)0.8(1 + z)1.0(D/kpc)0.58±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.
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