# Selection bias in dynamically-measured super-massive black hole samples: dynamical masses and dependence on S\'ersic index

## TL;DR

This study compares local galaxies with measured supermassive black holes to SDSS galaxies, revealing that black hole host galaxies are structurally similar and that velocity dispersion is more fundamental than Sersic index in black hole scaling relations, with biases identified in black hole mass estimates.

## Contribution

The paper demonstrates that black hole host galaxies are structurally similar to SDSS galaxies and highlights the importance of velocity dispersion over Sersic index in scaling relations, also quantifying biases in black hole mass estimates.

## Key findings

- Black hole host galaxies have similar properties to SDSS galaxies.
- Velocity dispersion is more fundamental than Sersic index in scaling relations.
- Significant bias in observed black hole masses at fixed Sersic index for massive galaxies.

## Abstract

We extend the comparison between the set of local galaxies having dynamically measured black holes with galaxies in the Sloan Digital Sky Survey (SDSS). We first show that the most up-to-date local black hole samples of early-type galaxies with measurements of effective radii, luminosities, and S\'ersic indices of the bulges of their host galaxies, have dynamical mass and S\'ersic index distributions consistent with those of SDSS early-type galaxies of similar bulge stellar mass. The host galaxies of local black hole samples thus do not appear structurally different from SDSS galaxies, sharing similar dynamical masses, light profiles and light distributions. Analysis of the residuals reveals that velocity dispersion is more fundamental than S\'ersic index n in the scaling relations between black holes and galaxies. Indeed, residuals with S\'ersic index could be ascribed to the (weak) correlation with bulge mass or even velocity dispersion. Finally, targetted Monte Carlo simulations that include the effects of the sphere of influence of the black hole, and tuned to reproduce the observed residuals and scaling relations in terms of velocity dispersion and stellar mass, show that, at least for galaxies with Mbulge > 1e10 Msun and n>5, the observed mean black hole mass at fixed S\'ersic index is biased significantly higher than the intrinsic value.