Stellar velocity dispersion is a key measurable quantity in galactic astronomy, yet its variation
during galaxy mergers is not well-understood theoretically. Thus, while it is fairly common to
measure velocity dispersion in galaxies that are in the process of merging, it is unclear how
these measurements should be interpreted. In this dissertation, I provide a theoretical analysis
of the evolution of stellar velocity dispersion during galaxy mergers. This is done using a set
of numerical simulations. The temporal and directional evolution of velocity dispersion are
examined in detail for a variety of merger simulations. I also examine the effects that dust
attenuation and star formation have on measurements of velocity dispersion by creating detailed, Doppler broadened galaxy spectra. Velocity dispersions are measured from the synthetic
spectra using the same technique that is employed for observations of real galaxies.
I find that velocity dispersion increases rapidly and significantly as two galaxies pass through
one another. As galaxies recede from a collision, their velocity dispersions rapidly decrease and
nearly return to their pre-collision values. Velocity dispersion increases in all directions during
collisions, however the enhancement is most significant along the collision axis. After the nuclei of the progenitor system coalesce, the velocity dispersion oscillates slightly of the coalesced system oscillated around its final equilibrium value for up to several dynamical timescales. I
also find that the mean velocity dispersion of young stars tends to be lower than the velocity
dispersion of the galaxy as a whole. The young stars become dynamically heated with time.
In most cases, the youngest stars are found in dusty environments. Thus, dust preferen-
tially obscures young stars, partially removing them from the flux-weighted velocity dispersion
measurement. This causes flux-weighted velocity dispersion measurements to be elevated with
respect to mass-weighted measurements because the young stars are dynamically cooler. On
the other hand, since young stellar populations are brighter, per unit mass, than older stellar
populations, the low dispersion of young stars tends to weight measurements of velocity dis-
persion downward when the young stars are not more significantly obscured by dust than the
older populations.