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

Using Chandra X-ray observations of 9 nearby, X-ray luminous ellipticals with good optical velocity dispersion measurements, we show that a tight correlation exists between the Bondi accretion rates calculated from the X-ray data and estimated black hole masses, and the power emerging from these systems in relativistic jets. The jet powers, inferred from the energies and timescales required to inflate the cavities observed in the surrounding X-ray emitting gas, can be related to the accretion rates by a power law model. A significant fraction (2.2^{+1.0}_{-0.7} per cent, for P_jet=10^{43} erg/s) of the energy associated with the rest mass of material entering the accretion radius eventually emerges in the 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 tight correlation between P_Bondi and P_jet suggests that the Bondi formulae provide a reasonable description of the accretion process, despite the likely presence of magnetic pressure and angular momentum in the accreting gas, and that the accretion flows are approximately stable over timescales 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.