Abstract We investigate the MBH-σ* relation for radio-loud quasars with redshift z<0.83 in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The sample consists of 3772 quasars with better models of the Hβ and [O III] lines and available radio luminosity, including 306 radio-loud quasars, 3466 radio-quiet quasars with measured radio luminosity or upper-limit of radio luminosity (181 radio-quiet quasars with measured radio luminosity). The virial supermassive black hole mass (MBH) is calculated from the broad Hβ line, and the host stellar velocity dispersion (σ*) is traced by the core [O III] gaseous velocity dispersion. The radio luminosity and radio loudness are derived from the FIRST catalog. Our results are as follows: (1) For radio-quiet quasars, we confirm that there is no obvious deviation from the MBH-σ* relation defined for inactive galaxies when the uncertainties in MBH and the luminosity bias are concerned. (2) We find that the radio-loud quasars deviate more from the MBH-σ* relation than do the radio-quiet quasars. This deviation is only partly due to a possible cosmological evolution of the MBH-σ* relation and the luminosity bias. (3) The radio luminosity is proportional to MBH1.28+0.23−0.16(LBol/LEdd)1.29+0.31−0.24 for radio-quiet quasars and to MBH3.10+0.60−0.70(LBol/LEdd)4.18+1.40−1.10 for radio-loud quasars. The weaker dependence of the radio luminosity on the mass and the Eddington ratio for radio-loud quasars shows that other physical effects would account for their radio luminosities, such as the spin of the black hole.
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