The supermassive black hole mass-Sersic index relations for bulges and elliptical galaxies

Scaling relations between supermassive black hole mass, M-BH, and host galaxy properties are a powerful instrument for studying their co-evolution. A complete picture involving all of the black hole scaling relations, in which each relation is consistent with the others, is necessary to fully understand the black hole-galaxy connection. The relation between M-BH and the central light concentration of the surrounding bulge, quantified by the Sersic index n, may be one of the simplest and strongest such relations, requiring only uncalibrated galaxy images. We have conducted a census of literature Sersic index measurements for a sample of 54 local galaxies with directly measured M-BH values. We find a clear M-BH-n relation, despite an appreciable level of scatter due to the heterogeneity of the data. Given the current M-BH-L-sph and the L-sph-n relations, we have additionally derived the expected M-BH-n relations, which are marginally consistent at the 2 Sigma level with the observed relations. Elliptical galaxies and the bulges of disc galaxies are each expected to follow two distinct bent M-BH-n relations due to the Sersic/core-Sersic divide. For the same central light concentration, we predict that M-BH in the Sersic bulges of disc galaxies are an order magnitude higher than in Sersic elliptical galaxies if they follow the same M-BH-L-sph relation.