The black hole mass - spheroid luminosity relation

The differing M_bh -L relations presented in McLure & Dunlop, Marconi & Hunt and Erwin et al. have been investigated. A number of issues have been identified and addressed in each of these studies, including but not limited to the removal of a dependency on the Hubble constant, a correction for dust attenuation in the bulges of disc galaxies, the identification of lenticular galaxies previously treated as elliptical galaxies and the application of the same (Y | X) regression analysis. These adjustments result in relations which now predict similar black hole masses. The optimal K-band relation is log(M_bh/M_solar) = -0.37(+/-0.04)(M_K + 24) + 8.29(+/-0.08), with a total (not intrinsic) scatter in logM_bh equal to 0.33dex. This level of scatter is similar to the value of 0.34dex from the relation of Tremaine et al. and compares favourably with the value of 0.31dex from the M_bh -n relation of Graham & Driver. Using different photometric data, consistent relations in the B and R band are also provided, although we do note that the small (N = 13) R-band sample used by Erwin et al. is found here to have a slope of -0.30 +/- 0.06. Performing a symmetrical regression on the larger K-band sample gives a slope of ~ -0.40, implying M_bh ~ L^1.00. Implications for galaxy-black hole co-evolution, in terms of dry mergers, are briefly discussed, as are the predictions for intermediate mass black holes. Finally, as noted by others, a potential bias in the galaxy sample used to define the M_bh -L relations is shown and a corrective formula provided.