Measuring the Virial Factor in SDSS DR5 Quasars with Redshifted H$\beta$
  and Fe ii Broad Emission Lines
  Under the hypothesis of gravitational redshift induced by the central
supermassive black hole, and based on line widths and shifts of redward shifted
H$\beta$ and Fe ii broad emission lines for a sample of 1973 $z<0.8$ SDSS DR5
quasars, we measured the virial factor in determining supermassive black hole
masses, usually estimated by the reverberation mapping (RM) method or the
relevant secondary methods. The virial factor had been believed to be from the
geometric effect of broad-line region. The measured virial factor of Fe ii is
larger than that of H$\beta$ for 98% of these quasars. The virial factor is
very different from object to object and for different emission lines. For most
of these quasars, the virial factor of H$\beta$ is larger than these averages
that were usually used in determining the masses of black holes. There are
three positive correlations among the measured virial factor of H$\beta$,
dimensionless accretion rate and Fe ii/H$\beta$ line ratio. A positive
three-dimensional correlation is found among these three quantities, and this
correlation indicates that the virial factor is likely dominated by the
dimensionless accretion rate and metallicity. A negative correlation is found
between the redward shift of H$\beta$ and the scaled size of broad-line region
radius in units of the gravitational radius of black hole. This negative
correlation will be expected naturally if the redward shift of H$\beta$ is
mainly from the gravity of black hole. Radiation pressure from accretion disk
may be a significant contributor to the virial factor.
