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Cosmic Evolution of Black Holes and Spheroids. V. The Relation Between Black Hole Mass and Host Galaxy Luminosity for a Sample of 79 Active Galaxies

We investigate the cosmic evolution of the black hole (BH) mass -- bulge luminosity relation using a sample of 52 active galaxies at $z \sim 0.36$ and $z \sim 0.57$ in the BH mass range of $10^{7.4-9.1} M_{\odot}$. By consistently applying multi-component spectral and structural decomposition to high-quality Keck spectra and high-resolution HST images, BH masses ($M_{\rm BH}$) are estimated using the H$β$ broad emission line combined with the 5100 Å nuclear luminosity, and bulge luminosities ($L_{\rm bul}$) are derived from surface photometry. Comparing the resulting $M_{\rm BH}-L_{\rm bul}$ relation to local active galaxies and taking into account selection effects, we find evolution of the form $M_{\rm BH} / L_{\rm bul} \propto (1+z)^γ$ with $γ=1.8\pm0.7$, consistent with BH growth preceding that of the host galaxies. Including an additional sample of 27 active galaxies with $0.5<z<1.9$ taken from the literature and measured in a consistent way, we obtain $γ=0.9\pm0.7$ for the $M_{\rm BH}-L_{\rm bul}$ relation and $γ=0.4\pm0.5$ for the $M_{\rm BH}$--total host galaxy luminosity ($L_{\rm host}$) relation. The results strengthen the findings from our previous studies and provide additional evidence for host-galaxy bulge growth being dominated by disk-to-bulge transformation via minor mergers and/or disk instabilities.