We assess evolution in the black hole mass - stellar velocity dispersion relationship (M-sigma relationship) for quasars in the Sloan Digital Sky Survey Data Release 7 for the redshift range 0.1 < z < 1.2. We estimate the black hole mass using the photoionization method, with the broad Hbeta or Mg II emission line and the quasar continuum luminosity. For the stellar velocity dispersion, we use the narrow [O III] or [O II] emission line as a surrogate. This study is a follow-up to an earlier study in which we investigated evolution in the M-sigma relationship in quasars from Data Release 3. The greatly increased number of quasars in our new sample has allowed us to break our lower-redshift subsample into black hole mass bins and probe the M-sigma relationship for constant black hole mass. The M-sigma relationship for the highest-mass (log M > 9 solar masses) and lowest-mass (log M < 7.5 solar masses) black holes appears to evolve significantly, however most or all of this apparent evolution can be accounted for by various observational biases due to intrinsic scatter in the relationship and to uncertainties in observed quantities. The M-sigma relationship for black holes in the middle mass range (7.5 < log M < 9 solar masses) shows minimal change with redshift. The overall results suggest a limit of +/- 0.2 dex on any evolution in the M-sigma relationship for quasars out to z ~ 1 compared with the relationship observed in the local universe. Intrinsic scatter may also provide a plausible way to reconcile the wide range of results of several different studies of the black hole - galaxy relationships.
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