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We investigate the $\mbh- \sigma_*$ relation for radio-loud quasars withredshift $z<0.83$ in Data Release 3 of the Sloan Digital Sky Survey (SDSS). Thesample consists of 3772 quasars with better model of H$\beta$ and \oiii linesand available radio luminosity, including 306 radio-loud quasars, 3466radio-quiet quasars with measured radio luminosity or upper-limit of radioluminosity (181 radio-quiet quasars with measured radio luminosity). The virialsupermassive black hole mass (\mbh) is calculated from the broad \hb line, thehost stellar velocity dispersion ($\sigma_*$) is traced by the core \oiiigaseous velocity dispersion, and the radio luminosity and the radio loudnessare derived from the FIRST catalog. Our results are follows: (1) Forradio-quiet quasars, we confirm that there is no obvious deviation from the$\mbh- \sigma_*$ relation defined in inactive galaxies when \mbh uncertaintiesand luminosity bias are concerned. (2) We find that radio-loud quasars deviatemuch from the $\mbh- \sigma_*$ relation respect to that for radio-quietquasars. This deviation is only partly due to the possible cosmology evolutionof the $\mbh- \sigma_*$ relation and the luminosity bias. (3) The radioluminosity is proportional to$\mbh^{1.28^{+0.23}_{-0.16}}(\lb/\ledd)^{1.29^{+0.31}_{-0.24}}$ for radio-quietquasars and $\mbh^{3.10^{+0.60}_{-0.70}}(\lb/\ledd)^{4.18^{+1.40}_{-1.10}}$ forradio-loud quasars. The weaker correlation of the radio luminosity dependenceupon the mass and the Eddington ratio for radio-loud quasars shows that otherphysical effects would account for their radio luminosities, such as the blackhole spin.

The radio luminosity, black hole mass and Eddington ratio for quasars from the Sloan Digital Sky Survey