AGN jet power and feedback characterised by Bondi accretion in brightest
  cluster galaxies
  (Abridged) We propose a new method to estimate the Bondi (hot gas) accretion
rates, \dot M_B, onto the supermassive black holes (SMBHs) at the centres of
elliptical galaxies. It can be applied even if the Bondi radius is not
well-resolved in X-ray observations. This method is based on two simple
assumptions: (1) hot gas outside the Bondi radius is in nearly a hydrostatic
equilibrium, and (2) the gas temperature near the galaxy centre is close to the
virial temperature. We apply this method to 28 bright elliptical galaxies in
nearby galaxy clusters (27 of them are the brightest cluster galaxies; BCGs).
We find a correlation between the Bondi accretion rates and the power of jets
associated with the SMBHs over four orders of magnitude in \dot M_B. For most
galaxies, the accretion rates are large enough to account for the jet powers.
Our results indicate that the feedback from the active galactic nuclei (AGN)
correlates with the properties of the hot gas surrounding the SMBHs. We also
find that more massive SMBHs in BCGs tend to have larger specific growth rates.
This may explain the hyper masses (~ 10^10 M_sun) of some of the SMBHs.
Comparison between the accretion rates and the X-ray luminosities of the AGN
suggests that the AGN in the BCGs are extremely radiatively inefficient
compared with X-ray binaries in the Milky Way, even when their Eddington
accretion ratio, \dot M_B/\dot M_Edd, exceeds 0.01. Lastly, we find a tight
correlation between the Bondi accretion rates and the X-ray luminosities of
cool cores. Their relation is linear and the power generated by the Bondi
accretion is large enough to compensate the radiative cooling of the cool
cores. Although the `classical' Bondi accretion model is a greatly
oversimplified one, the correlations we find here demonstrate that the
accretion onto the SMBHs reflects broadly the properties of the Bondi
accretion.
