Populating the low-mass end of the $M_{\rm BH}-\sigma_{\ast}$ relation
  We present high resolution spectroscopy taken with the Keck Echellete
Spectrograph and Imager to measure stellar velocity dispersions for eight
active dwarf galaxies ($M_{\ast}<3\times10^{9}~M_{\odot}$) with virial black
hole masses. We double the number of systems in this stellar mass regime with
measurements of both black hole mass ($M_{\rm BH}$) and stellar velocity
dispersion ($\sigma_{\ast}$), and place them on the $M_{\rm BH}-\sigma_{\ast}$
relation. The tight relation between $M_{\rm BH}$ and $\sigma_{\ast}$ for
higher mass galaxies is a strong piece of evidence for the co-evolution of BHs
and their host galaxies, but it has been unclear whether this relation holds in
the dwarf galaxy regime. Our sample is in good agreement with the extrapolation
of the $M_{\rm BH}-\sigma_{\ast}$ relation to low BH/galaxy masses, suggesting
that the processes which produce $M_{\rm BH}-\sigma_{\ast}$ can also operate in
dwarf galaxies. These results provide important constraints for massive black
hole seed formation models and models exploring the impact of AGN feedback in
dwarf galaxies.
