We revisit the possibility of redshift evolution in the MBH-σ relation with a sample of 22 Seyfert 1 galaxies with black holes (BHs) in the mass range 6.3-8.3 (log10 MBH) and redshift range 0.03 < z < 0.57 with spectra obtained from spatially resolved Keck Low-Resolution Imaging Spectrometer observations. Stellar velocity dispersions were measured directly from the MgIb region, taking into consideration the effect of FeII contamination, active galactic nucleus (AGN) dilution, and host-galaxy morphology on our measurements. BH masses are estimated using the H-beta line width, and the luminosity at 5100 Å is estimated from surface brightness decomposition of the AGN from the host galaxy using high-resolution imaging from the Hubble Space Telescope. Our selection criteria allowed us to probe lower-luminosity AGNs and lower-mass BHs in the non-local universe than those measured in previous single-epoch studies. We find that any offset in the MBH-σ relation up to z~0.6 is consistent with the scatter of local BH masses, and address the sources of biases and uncertainties that contribute to this scatter.

We also present Bayesian AGN Decomposition Analysis for SDSS Spectra (BADASS), an open source spectral analysis code designed for automatic detailed deconvolution of AGN and host galaxy spectra, implemented in Python, and designed for the next generation of large scale surveys. BADASS simultaneously fits all spectral components, including power-law continuum, stellar line-of-sight velocity distribution, FeII emission, as well as narrow, broad, and outflow emission line features, all performed using Markov Chain Monte Carlo to obtain robust parameter uncertainties and autocorrelation analysis to assess parameter convergence.

We use BADASS to perform correlation analysis of 63 SDSS Seyfert 1 galaxies with evidence of strong non-gravitational outflow kinematics in the [OIII]λ5007 emission line. We confirm findings from previous studies that show the core of the [OIII] profile is a suitable surrogate for $\sigma_*$, however there is evidence that the core experiences broadening that scales with outflow velocity. We find sufficient evidence that σ, [OIII] core dispersion, and the non-gravitational outflow dispersion of the [OIII] profile form a plane whose fit results in a scatter of ~0.1 dex. Finally, we discuss the implications, caveats, and recommendations when using the [OIII] dispersion as a surrogate for sigma* for the MBH-σ relation.