  There is a large observational scatter toward low velocities in the stellar
mass Tully-Fisher relation if disturbed and compact objects are included.
However, this scatter can be eliminated if one replaces rotation velocity with
$\rm S_{\rm 0.5}$, a quantity that includes a velocity dispersion term added in
quadrature with the rotation velocity. In this work we use a large suite of
hydrodynamic N-body galaxy merger simulations to explore a possible mechanism
for creating the observed relations. Using mock observations of the
simulations, we test for the presence of observational effects and explore the
relationship between $\rm S_{\rm 0.5}$ and intrinsic properties of the
galaxies. We find that galaxy mergers can explain the scatter in the TF as well
as the tight $\rm S_{\rm 0.5}$-stellar mass relation. Furthermore, $\rm S_{\rm
0.5}$ is correlated with the total central mass of a galaxy, including
contributions due to dark matter.
