Effects of Inclination on Measuring Velocity Dispersion and Implications for Black Holes

TL;DR

This paper shows that galaxy orientation significantly impacts velocity dispersion measurements, which affects black hole mass estimates, and provides a correction method to account for inclination effects.

Contribution

It reveals the extent of inclination effects on velocity dispersion measurements and offers a correction method to improve black hole mass estimates.

Findings

Line-of-sight effects can alter velocity dispersion by up to 30%.

Black hole mass predictions can vary by up to 1.0 dex due to inclination.

A correction method for inclination effects is proposed.

Abstract

The relation of central black hole mass and stellar spheroid velocity dispersion (the M-$\sigma$ relation) is one of the best-known and tightest correlations linking black holes and their host galaxies. There has been much scrutiny concerning the difficulty of obtaining accurate black hole measurements, and rightly so; however, it has been taken for granted that measurements of velocity dispersion are essentially straightforward. We examine five disk galaxies from cosmological SPH simulations and find that line-of-sight effects due to galaxy orientation can affect the measured $\sigma$ by 30%, and consequently black hole mass predictions by up to 1.0 dex. Face-on orientations correspond to systematically lower velocity dispersion measurements, while more edge-on orientations give higher velocity dispersions, due to contamination by disk stars when measuring line of sight quantities. We caution observers that the uncertainty of velocity dispersion measurements is at least 20 km/s, and can be much larger for moderate inclinations. This effect may account for some of the scatter in the locally measured M-$\sigma$ relation, particularly at the low-mass end. We provide a method for correcting observed $\sigma_{\rm los}$ values for inclination effects based on observable quantities.