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(Abridged) We propose a new method to estimate the Bondi (hot gas) accretionrates, \dot M_B, onto the supermassive black holes (SMBHs) at the centres ofelliptical galaxies. It can be applied even if the Bondi radius is notwell-resolved in X-ray observations. This method is based on two simpleassumptions: (1) hot gas outside the Bondi radius is in nearly a hydrostaticequilibrium, and (2) the gas temperature near the galaxy centre is close to thevirial temperature. We apply this method to 28 bright elliptical galaxies innearby galaxy clusters (27 of them are the brightest cluster galaxies; BCGs).We find a correlation between the Bondi accretion rates and the power of jetsassociated with the SMBHs over four orders of magnitude in \dot M_B. For mostgalaxies, 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 alsofind 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 AGNsuggests that the AGN in the BCGs are extremely radiatively inefficientcompared with X-ray binaries in the Milky Way, even when their Eddingtonaccretion ratio, \dot M_B/\dot M_Edd, exceeds 0.01. Lastly, we find a tightcorrelation between the Bondi accretion rates and the X-ray luminosities ofcool cores. Their relation is linear and the power generated by the Bondiaccretion is large enough to compensate the radiative cooling of the coolcores. Although the `classical' Bondi accretion model is a greatlyoversimplified one, the correlations we find here demonstrate that theaccretion onto the SMBHs reflects broadly the properties of the Bondiaccretion.

AGN jet power and feedback characterised by Bondi accretion in brightest cluster galaxies