The $M_\bullet$-$\sigma_e$ relation for local type 1 AGNs and quasars

We analyzed MUSE 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 ($M_\bullet$) and bulge stellar velocity dispersion ($\sigma_e$) for type 1 active galaxies. The sample spans black hole masses of $10^{6.0}-10^{9.2}\,M_\odot$, bolometric luminosities of $10^{42.9}-10^{46.0}\,$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 $\sigma_* = 60-230\,$km$\,$s$^{-1}$ for the host galaxies. We find $\sigma_*$ values in agreement with previous measurements for local 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 $\sigma_e$ from $\sigma_*$ that considers the bulge morphology and observation beam-smearing, we estimate flux-weighted $\sigma_e = 60-250\,$km$\,$s$^{-1}$. If we consider the bulge type when estimating $M_\bullet$, we find no statistical difference between the distributions of AGN hosts and the inactive galaxies on the $M_\bullet - \sigma_e$ plane for $M_\bullet \lesssim 10^8\,M_\odot$. Conversely, if we do not consider the bulge type when computing $M_\bullet$, we find that both distributions disagree. We find no correlation between the degree of offset from the $M_\bullet - \sigma_e$ relation and Eddington ratio for $M_\bullet \lesssim 10^8\,M_\odot$. 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.