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Relation between Black Hole Mass and Bulge Luminosity in Hard X-ray selected Type 1 AGNs

Using $I$-band images of 35 nearby ($z<0.1$) type 1 active galactic nuclei (AGNs) obtained with Hubble Space Telescope, selected from the 70-month Swift-BAT X-ray source catalog, we investigate the photometric properties of the host galaxies. With a careful treatment of the point-spread function (PSF) model and imaging decomposition, we robustly measure the $I$-band brightness and the effective radius of bulges in our sample. Along with black hole (BH) mass estimates from single-epoch spectroscopic data, we present the relation between BH mass and $I$-band bulge luminosity ($M_{\rm BH}-M_{I,\rm bul}$ relation) of our sample AGNs. We find that our sample lies offset from the $M_{\rm BH}-M_{I,\rm bul}$ relation of inactive galaxies by 0.4 dex, i.e., at a given bulge luminosity, the BH mass of our sample is systematically smaller than that of inactive galaxies. We also demonstrate that the zero point offset in the $M_{\rm BH}-M_{I,\rm bul}$ relation with respect to inactive galaxies is correlated with the Eddington ratio. Based on the Kormendy relation, we find that the mean surface brightness of ellipticals and classical bulges in our sample is comparable to that of normal galaxies, revealing that bulge brightness is not enhanced in our sample. As a result, we conclude that the deviation in the $M_{\rm BH}-M_{I,\rm bul}$ relation from inactive galaxies is possibly because the scaling factor in the virial BH mass estimator depends on the Eddington ratio.