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.