Authors:Roberto Soria, Alister Graham, Giuseppina Fabbiano, Alessandro Baldi, Martin Elvis, Helmut Jerjen, Silvia Pellegrini, Aneta Siemiginowska
Abstract: Our X-ray study of the nuclear activity in a new sample of six quiescent early-type galaxies, and in a larger sample from the literature, confirmed (Soria et al., Paper I) that the Bondi accretion rate of diffuse hot gas is not a good indicator of the supermassive black hole (SMBH) X-ray luminosity. Here we suggest that a more reliable estimate of the accretion rate must include the gas released by the stellar population inside the sphere of influence of the SMBH, in addition to the Bondi inflow of hot gas across that surface. We use optical surface-brightness profiles to estimate the mass-loss rate from stars in the nuclear region: we show that for our sample of galaxies it is an order of magnitude higher (≈ 10-4 - 10-3 Msun yr-1) than the Bondi inflow rate of hot gas, as estimated from Chandra (Paper I). Only by taking into account both sources of fuel can we constrain the true accretion rate, the accretion efficiency, and the power budget. Radiatively efficient accretion is ruled out, for quiescent SMBHs. For typical radiatively inefficient flows, the observed X-ray luminosities of the SMBHs imply accretion fractions ≈ 1 - 10% (i.e. ≈ 90 - 99% of the available gas does not reach the SMBH) for at least five of our six target galaxies, and most of the other galaxies with known SMBH masses. We discuss the conditions for mass conservation inside the sphere of influence, so that the total gas injection is balanced by accretion plus outflows. We show that a fraction of the total accretion power (mechanical plus radiative) would be sufficient to sustain a self-regulating, slow outflow which removes from the nuclear region all the gas that does not sink into the BH (``BH feedback''). The rest of the accretion power may be carried out in a jet, or advected. We also discuss scenarios that would lead to an intermittent nuclear activity.