This paper by Kauffmann & Heckman discusses the accretion onto central black holes in SDSS. The authors use the OIII line luminosity as a proxy AGN accretion rate, and they infer the black hole mass from the stellar velocity dispersion; thus L[OIII]/M_bh becomes a measure of the Eddington ratio. The upper panel in this figure shows the distribution of Eddington ratios for SDSS galaxies. In the lower panels, the galaxies are split up by the strength of their 4000AA break, which is a measure of galaxy age. It appears that young galaxies have a broad log-normal distribution which is independent of age (it is also independent of M_bh, but that isn't visible in this figure). But older galaxies have an approximate power-law distribution which does depend on age (and also on M_bh).
The authors interpret the log-normal distribution as a reflecting black hole self-regulation, with a negative feedback effect that kicks in at the peak of the distribution (~1% Eddington). But since the distribution doesn't depend on black hole mass or on the star formation in the rest of the galaxy, the feedback must operate only in the immediate vicinity of the black hole. On the other hand, the power-law distribution for the older galaxies does not suggest self-regulation. The authors show that the accretion rate onto the the black hole is roughly proportional to the bulge stellar mass, which is consistent with a scenario in which the black hole is fed by stellar mass loss... however this is a rather speculative conclusion.
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