The sizes of BLRs and BH masses of double-peaked broad low-ionization emission line objects

In this paper, the sizes of the BLRs and BH masses of DouBle-Peaked broad low-ionization emission line emitters (dbp emitters) are compared using different methods: virial BH masses vs BH masses from stellar velocity dispersions, the size of BLRs from the continuum luminosity vs the size of BLRs from the accretion disk model. First, the virial BH masses of dbp emitters estimated by the continumm luminosity and line width of broad H$\beta$ are about six times (a much larger value, if including another dbp emitters, of which the stellar velocity dispersions are traced by the line widths of narrow emission lines) larger than the BH masses estimated from the relation $M_{BH} - \sigma$ which is a more accurate relation to estimate BH masses. Second, the sizes of the BLRs of dbp emitters estimated by the empirical relation of $R_{BLR} - L_{5100\AA}$ are about three times (a much larger value, if including another dbp emitters, of which the stellar velocity dispersions are traced by the line widths of narrow emission lines) larger than the mean flux-weighted sizes of BLRs of dbp emitters estimated by the accretion disk model. The higher electron density of BLRs of dbp emitters would be the main reason which leads to smaller size of BLRs than the predicted value from the continuum luminosity.Comment: 7 pages, two figures and one table. Accepted by MNRA

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.Comment: 10 pages, 7 figures, accepted for publication in MNRA

A Note on State Decomposition Independent Local Invariants

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations