Authors: Alister W. Graham & Simon P. Driver
Abstract: We reinvestigate the correlation between black hole mass and bulge concentration. With an increased galaxy sample, updated estimates of galaxy distances, black hole masses and Sersic indices n - a measure of concentration - we perform a least-squares regression analysis to obtain a relation suitable for the purpose of predicting black hole masses in other galaxies. In addition to the linear relation log(Mbh) = (7.81±0.08) + (2.69±0.28)log(n/3) with εintrinsic = 0.31 dex, we investigated the possibility of a quadratic Mbh-n relation, finding the second order term in the quadratic is inconsistent with a value of zero at greater than the 99.99% confidence level. The optimal relation is given by log(Mbh) = (7.98±0.09) + (3.70±0.46)[log(n/3)] - (3.10±0.84)[log(n/3)]2, with εintrinsic = 0.18 dex and a total absolute scatter of 0.31 dex. Extrapolating the quadratic relation, it predicts black holes with masses of ~103 Msun in n=0.5 dwarf elliptical galaxies, compared to ~105 Msun from the linear relation, and a finite maximum SMBH mass equal to 1.2+2.6-0.4 X 109 Msun.
In addition, we show that the nuclear star clusters at the centers of low-luminosity elliptical galaxies follow an extrapolation of the same quadratic relation - implying a (previously noted) possible evolutionary link between SMBHs and nuclear star clusters. Moreover, we speculate that the merger of two such nucleated galaxies, accompanied by the merger and runaway collision of their central star clusters, may result in the `late-time' formation of some supermassive black holes.