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

Scaling relations between supermassive black hole mass, MBH, 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 MBH and the central light concentration of the surrounding bulge, quantified by the Sérsic index n, may be one of the simplest and strongest such relations, requiring only uncalibrated galaxy images. We have conducted a census of literature Sérsic index measurements for a sample of 54 local galaxies with directly measured MBH values. We find a clear MBH-n relation, despite an appreciable level of scatter due to the heterogeneity of the data. Given the current MBH-Lsph and the Lsph-n relations, we have additionally derived the expected MBH-n relations, which are marginally consistent at the 2σ level with the observed relations. Elliptical galaxies and the bulges of disc galaxies are each expected to follow two distinct bent MBH-n relations due to the Sérsic/core-Sérsic divide. For the same central light concentration, we predict that MBH in the Sérsic bulges of disc galaxies are an order magnitude higher than in Sérsic elliptical galaxies if they follow the same MBH-Lsph relation.