The Correlation Between Spectral Index And Accretion Rate For AGN
  In this paper, we present a correlation between the spectral index distribution (SED) and the dimensionless accretion rate defined as $\dot{m}={L_{bol}/L_{Edd}}$ for AGN. This quantity is used as a substitute of the physical accretion rate. We select 193 AGN with both broad H$\alpha$ and broad H$\beta$, and with absorption lines near MgI$\lambda5175\AA$ from SDSS DR4. We determine the spectral index and dimensionless accretion rate after correcting for both host galaxy contribution and internal reddening effects. A correlation is found between the optical spectral index and the dimensionless accretion rate for AGN, including low luminosity AGN ($L_{H\alpha}<10^{41}{\rm erg\cdot s^{-1}}$ sometimes called "dwarf AGN" (Ho et al. 1997)). The existence of this correlation provides an independent method to estimate the central BH masses for all types of AGN. We also find that there is a different correlation between the spectral index and the BH masses for normal AGN and low luminosity AGN, which is perhaps due to the different accretion modes in these two types of nuclei. This in turn may lead to the different correlations between BH masses and optical continuum luminosity reported previously (Zhang et al. 2007a), which invalidates the application of the empirical relationship found by Kaspi et al. (2000, 2005) to low luminosity AGN in order to determine their BLR sizes. 
Xue-Guang Zhang, Deborah Dultzin, Ting-Gui Wang