The relation between accretion rate and jet power in X-ray luminous elliptical galaxies

Using Chandra X-ray observations of nine nearby, X-ray luminous elliptical galaxies with good optical velocity dispersion measurements, we show that a tight correlation exists between the Bondi accretion rates calculated from the observed gas temperature and density profiles and estimated black hole masses, and the power emerging from these systems in relativistic jets. The jet powers, which are inferred from the energies and time-scales required to inflate cavities observed in the surrounding X-ray emitting gas, can be related to the accretion rates using a power-law model of the form log (P-Bondi/10(43) erg s(-1)) = A + B log (P-jet/10(43) erg s(-1)), with A = 0.65 +/- 0.16 and B = 0.77 +/- 0.20. Our results show that a significant fraction of the energy associated with the rest mass of material entering the Bondi accretion radius (2.2(-0.7)(+1.0) per cent, for P-jet = 10(43) erg s(-1)) eventually emerges in the relativistic jets. The data also hint that this fraction may rise slightly with increasing jet power. Our results have significant implications for studies of accretion, jet formation and galaxy formation. The observed tight correlation suggests that the Bondi formulae provide a reasonable description of the accretion process in these systems, despite the likely presence of magnetic pressure and angular momentum in the accreting gas. The similarity of the P-Bondi and P-jet values argues that a significant fraction of the matter entering the accretion radius flows down to regions close to the black holes, where the jets are presumably formed. The tight correlation between P-Bondi and P-jet also suggests that the accretion flows are approximately stable over time-scales of a few million years. Our results show that the black hole 'engines' at the hearts of large elliptical galaxies and groups can feed back sufficient energy to stem cooling and star formation, leading naturally to the observed exponential cut off at the bright end of the galaxy luminosity function.