The Evolution of Stellar Velocity Dispersion During Dissipationless
  Galaxy Mergers
  Using N-body simulations, we studied the detailed evolution of central
stellar velocity dispersion, {\sigma}, during dissipationless binary mergers of
galaxies. Stellar velocity dispersion was measured using the common
mass-weighting method as well as a flux-weighting method designed to simulate
the technique used by observers. A toy model for dust attenuation was
introduced in order to study the effect of dust attenuation on measurements of
{\sigma}. We found that there are three principal stages in the evolution of
{\sigma} in such mergers: oscillation, phase mixing, and dynamical equilibrium.
During the oscillation stage, {\sigma} undergoes damped oscillations of
increasing frequency. The oscillation stage is followed by a phase mixing stage
during which the amplitude of the variations in {\sigma} is smaller and more
chaotic than in the oscillation stage. Upon reaching dynamical equilibrium,
{\sigma} assumes a stable value. We used our data regarding the evolution of
{\sigma} during mergers to characterize the scatter inherent in making
measurements of {\sigma} in non-quiescent systems. In particular, we found that
{\sigma} does not fall below 70% nor exceed 200% of its final, quiescent value
during a merger and that a random measurement of {\sigma} in such a system is
much more likely to fall near the equilibrium value than near an extremum. Our
toy model of dust attenuation suggested that dust can systematically reduce
observational measurements of {\sigma} and increase the scatter in {\sigma}
measurements.
