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-$\sigma$ 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.
