A relationship between AGN jet power and radio power

Using Chandra X-ray and VLA radio data, we investigate the scaling relationship between jet power, P_jet, and synchrotron luminosity, P_rad. We expand the sample presented in Birzan et al. (2008) to lower radio power by incorporating measurements for 21 gEs to determine if the Birzan et al. (2008) P_jet-P_rad scaling relations are continuous in form and scatter from giant elliptical galaxies (gEs) up to brightest cluster galaxies (BCGs). We find a mean scaling relation of P_jet approximately 5.8x10^43 (P_rad/10^40)^(0.70) erg/s which is continuous over ~6-8 decades in P_jet and P_rad with a scatter of approximately 0.7 dex. Our mean scaling relationship is consistent with the model presented in Willott et al. (1999) if the typical fraction of lobe energy in non-radiating particles to that in relativistic electrons is > 100. We identify several gEs whose radio luminosities are unusually large for their jet powers and have radio sources which extend well beyond the densest parts of their X-ray halos. We suggest that these radio sources are unusually luminous because they were unable to entrain appreciable amounts of gas.