We investigate the relationship between the mass of the central supermassive black hole, M_bh, and the host galaxy luminosity, L_gal, in a sample of quasars from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We use composite quasar spectra binned by black hole mass and redshift to assess galaxy features that would otherwise be overwhelmed by noise in individual spectra. The black hole mass is calculated using the photoionization method, and the host galaxy luminosity is inferred from the depth of the Ca II H + K features in the composite spectra. We evaluate the evolution in the M_bh - L_gal relationship by examining the redshift dependence of Delta log M_bh, the offset in black hole mass from the local black hole - bulge relationship. There is little systematic trend in Delta log M_bh out to z = 0.8. Using the width of the [O III] emission line as a proxy for the stellar velocity dispersion, sigma_*, we find agreement of our derived host luminosities with the locally-observed Faber-Jackson relation. This supports the utility of the width of the [O III] line as a proxy for sigma_* in statistical studies.
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