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An empirical relation between the broad line region (BLR) size and opticalcontinuum luminosity is often adopted to estimate the BLR size and then theblack hole mass of AGNs. However, optical luminosity may not be a goodindicator of photoionizing luminosity for extremely radio-loud AGNs because thejets usually contribute significantly to the optical continuum. Therefore, theblack hole masses derived for blazar-type AGNs with this method are probablyoverestimated. Here we first derived a tight empirical relation between the BLRsize and the H$_\beta$ emission line luminosity, $R(\rm{light-days})=24.05(L_{H_\beta}/10^{42} ergs s^{-1})^{0.68}$, from a sample of 34 AGNs withthe BLR size estimated with the reverberation mapping technique. Then weapplied this relation to estimate the black hole masses of some AGNs and foundthat for many extremely radio-loud AGNs the black hole masses obtained with the$R-L_{H_\beta}$ relation are systematically lower than those derived previouslywith the $R-L_{5100\AA}$ relation, while for radio-quiet and slightlyradio-loud AGNs the results obtained with these two methods are almost thesame. The difference of black hole masses estimated with these two relationsincreases with the radio-loudness for extremely radio-loud AGNs, which isconsistent with the fact that their equivalent widths of H$_{\beta}$ emissionline become smaller at higher radio-loudness. If the small H$_{\beta}$equivalent widths of extremely radio-loud AGNs are indeed caused by the beamingeffect, we argue that the optical emission line luminosity may be a bettertracer of ionizing luminosity for blazar-type AGNs and the black hole massderived with the $R-L_{H_\beta}$ relation are probably more accurate.Comment: 7 pages, accepted for publication in Astronomy & Astrophysic

Black hole mass estimation using a relation between the BLR size and emission line luminosity of AGN