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Individual Estimates of the Virial Factor in 10 Quasars: Implications on the Kinematics of the Broad Line Region

Assuming a gravitational origin for the Fe III$λλ$2039-2113 redshift and using microlensing based estimates of the size of the region emitting this feature, we obtain individual measurements of the virial factor, $f$, in 10 quasars. The average values for the Balmer lines, $\langle f_{Hβ}\rangle={\bf 0.43\pm 0.20}$ and $\langle f_{Hα}\rangle={\bf 0.50\pm 0.24}$, are in good agreement with the results of previous studies for objects with lines of comparable widths. In the case of Mg II, consistent results, $f_{Mg II} \sim {\bf 0.44}$, can be also obtained accepting a reasonable scaling for the size of the emitting region. The modeling of the cumulative histograms of individual measurements, $CDF(f)$, indicates a {relatively} high value for the ratio between isotropic and cylindrical motions, $a\sim {\bf 0.4}-0.7$. On the contrary, we find very large values of the virial factor associated to the Fe III$λλ$2039-2113 blend, $f_{FeIII}=14.3\pm2.4$, which can be explained if this feature arises from a flattened nearly face-on structure, similar to the accretion disk.