  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.

Astrophysics