We analyzed Multi Unit Spectroscopic Explorer observations of 42 local $z type 1 active galactic nucleus (AGN) host galaxies taken from the Palomar-Green quasar sample and the close AGN reference survey. Our goal was to study the relation between the black hole mass ($M_ and bulge stellar velocity dispersion (for type 1 active galaxies. The sample spans black hole masses of \,M_ bolometric luminosities of, and Eddington ratios of $0.006-1.2$. We avoided AGN emission by extracting the spectra over annular apertures. We modeled the calcium triplet stellar features and measured stellar velocity dispersions of $ $ for the host galaxies. We find stellar velocity dispersion values in agreement with previous measurements for local ($z AGN host galaxies, but slightly lower compared with those reported for nearby X-ray-selected type 2 quasars. Using a novel annular aperture correction recipe to estimate $ from $ that considers the bulge morphology and observation beam-smearing, we estimate flux-weighted $ $. If we consider the bulge type when estimating $M_ we find no statistical difference between the distributions of AGN hosts and the inactive galaxies on the M_ plane forM_ 10^8\,M_ Conversely, if we do not consider the bulge type when computing M_ we find that both distributions disagree. We find no correlation between the degree of offset from theM_ relation and Eddington ratio for $M_ 10^8\,M_ The current statistics preclude firm conclusions from being drawn for the high-mass range. We argue these observations support notions that a significant fraction of the local type 1 AGNs and quasars have undermassive black holes compared with their host galaxy bulge properties.
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