We analyzed Multi Unit Spectroscopic Explorer observations of 42 local z ≲ 0.1 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 (σe) for type 1 active galaxies. The sample spans black hole masses of 106.0 − 109.2 M⊙, bolometric luminosities of 1042.9 − 1046.0 erg s−1, 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 σ* = 60 − 230 km s−1 for the host galaxies. We find stellar velocity dispersion values in agreement with previous measurements for local (z ≲ 0.1) 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 σe from σ* that considers the bulge morphology and observation beam-smearing, we estimate flux-weighted σe = 60 − 250 km s−1. 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•–σe plane for M• ≲ 108 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 the M•–σe relation and Eddington ratio for M• ≲ 108 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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