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Under the hypothesis of gravitational redshift induced by the centralsupermassive black hole, and based on line widths and shifts of redward shiftedH$\beta$ and Fe ii broad emission lines for a sample of 1973 $z<0.8$ SDSS DR5quasars, we measured the virial factor in determining supermassive black holemasses, usually estimated by the reverberation mapping (RM) method or therelevant secondary methods. The virial factor had been believed to be from thegeometric effect of broad-line region. The measured virial factor of Fe ii islarger than that of H$\beta$ for 98% of these quasars. The virial factor isvery different from object to object and for different emission lines. For mostof these quasars, the virial factor of H$\beta$ is larger than these averagesthat were usually used in determining the masses of black holes. There arethree positive correlations among the measured virial factor of H$\beta$,dimensionless accretion rate and Fe ii/H$\beta$ line ratio. A positivethree-dimensional correlation is found among these three quantities, and thiscorrelation indicates that the virial factor is likely dominated by thedimensionless accretion rate and metallicity. A negative correlation is foundbetween the redward shift of H$\beta$ and the scaled size of broad-line regionradius in units of the gravitational radius of black hole. This negativecorrelation will be expected naturally if the redward shift of H$\beta$ ismainly from the gravity of black hole. Radiation pressure from accretion diskmay be a significant contributor to the virial factor.

Measuring the Virial Factor in SDSS DR5 Quasars with Redshifted H$\beta$ and Fe ii Broad Emission Lines