The black hole mass – spheroid luminosity relation

The differing Mbh–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(Mbh/M⊙) =−0.37(±0.04)(MK+ 24) + 8.29(±0.08), with a total (not intrinsic) scatter in logMbh equal to 0.33 dex. This level of scatter is similar to the value of 0.34 dex from the $M_{\mathrm bh^{-\sigma}}$ relation of Tremaine et al. and compares favourably with the value of 0.31 dex from the Mbh–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 Mbh∝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 Mbh–L relations is shown and a corrective formula provided.