Effects of inclination on measuring velocity dispersion and implications for black holes

The relation of central black hole mass and stellar spheroid velocity dispersion (the M-σ 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 disc galaxies from cosmological SPH simulations and find that line-of-sight effects due to galaxy orientation can affect the measured σ_los by 30 per cent, 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 disc stars when measuring line-of-sight quantities. We caution observers that the uncertainty of velocity dispersion measurements is at least 20 km s^-1, and can be much larger for moderate inclinations. This effect may account for some of the scatter in the locally measured M-σ relation, particularly at the low-mass end. We provide a method for correcting observed σ_los values for inclination effects based on observable quantities.