# Black Hole Mass Scaling Relations for Early-Type Galaxies: $M_{BH}$-$M_{*,sph}$ and $M_{BH}$-$M_{*,gal}$

## TL;DR

This study refines black hole mass scaling relations in early-type galaxies, revealing significant differences between galaxy types and providing new insights into galaxy formation and black hole growth.

## Contribution

It presents an expanded sample analysis, discovering offset relations for disk galaxies and providing updated scaling relations with implications for galaxy evolution theories.

## Key findings

- Early-type galaxies follow a $M_{BH} ext{-}M_{*,sph}$ relation with a slope of 1.27.
- Disk galaxies are offset from ellipticals by over a factor of ten in $M_{BH}/M_{*,sph}$.
- Late-type galaxies follow steeper relations with slopes around 2.16 and 3.05.

## Abstract

Analyzing a sample of 84 early-type galaxies with directly-measured super-massive black hole masses---nearly doubling the sample size of such galaxies with multi-component decompositions---a symmetric linear regression on the reduced (merger-free) sample of 76 galaxies reveals $M_{BH}\propto M_{*,sph}^{1.27\pm 0.07}$ with a total scatter of $\Delta_{rms}=$ 0.52 dex in the $\log(M_{BH})$ direction. However, and importantly, we discover that the ES/S0-type galaxies with disks are offset from the E-type galaxies by more than a factor of ten in their $M_{BH}/M_{*,sph}$ ratio, with ramifications for formation theories, simulations, and some virial factor measurements used to convert AGN virial masses into $M_{BH}$. Separately, each population follows a steeper relation with slopes of $1.86\pm0.20$ and $1.90\pm0.20$, respectively. The offset mass ratio is mainly due to the exclusion of the disk mass, with the two populations offset by only a factor of two in their $M_{BH}/M_{*,gal}$ ratio in the $M_{BH}$-$M_{*,gal}$ diagram where $M_{BH}\propto M_{*,gal}^{1.8\pm 0.2}$ and $\Delta_{rms}=0.6\pm 0.1$ dex depending on the sample. For $M_{BH} \gtrsim 10^7 M_{\odot}$, we detect no significant bend nor offset in either the $M_{BH}$-$M_{*,sph}$ or $M_{BH}$-$M_{*,gal}$ relations due to barred versus non-barred, or core-S\'ersic versus S\'ersic, early-type galaxies. For reference, the ensemble of late-type galaxies (which invariably are S\'ersic galaxies) follow $M_{BH}$-$M_{*,sph}$ and $M_{BH}$-$M_{*,gal}$ relations with slopes equal to $2.16\pm 0.32$ and $3.05\pm 0.70$, respectively. Finally, we provide some useful conversion coefficients, $\upsilon$, accounting for the different stellar mass-to-light ratios used in the literature, and we report the discovery of a local, compact massive spheroid in NGC 5252.