Investigating AGN Black Hole Masses and the M-$\sigma_e$ relation for
  Low Surface Brightness Galaxies
  We present an analysis of the optical nuclear spectra from the active
galactic nuclei (AGN) in a sample of low surface brightness (LSB) galaxies.
Using data from the Sloan Digital Sky Survey (SDSS), we derived the virial
black hole (BH) masses of 24 galaxies from their broad H$\alpha$ parameters. We
find that our estimates of nuclear BH masses lie in the range
$10^{5}-10^{7}~M_{\odot}$, with a median mass of 5.62 x 10$^{6}~M_{\odot}$. The
bulge stellar velocity dispersion $\sigma_{e}$ was determined from the
underlying stellar spectra. We compared our results with the existing BH mass -
velocity dispersion ($M_{BH}-\sigma_{e}$) correlations and found that the
majority of our sample lie in the low BH mass regime and below the
$M_{BH}-\sigma_{e}$ correlation. We analysed the effects of any systematic bias
in the M$_{BH}$ estimates, the effects of galaxy orientation in the measurement
of $\sigma_e$ and the increase of $\sigma_e$ due to the presence of bars and
found that these effects are insufficient to explain the observed offset in
M$_{BH}$ - $\sigma_e$ correlation. Thus the LSB galaxies tend to have low mass
BHs which probably are not in co-evolution with the host galaxy bulges. A
detailed study of the nature of the bulges and the role of dark matter in the
growth of the BHs is needed to further understand the BH-bulge co-evolution in
these poorly evolved and dark matter dominated systems.
