Recalibration of the $M_{BH}-\sigma_{\star}$ Relation for AGN

We present a re-calibration of the $M_{BH}-\sigma_{\star}$ relation, based on a sample of 16 reverberation-mapped galaxies with newly determined bulge stellar velocity dispersions ($\sigma_{\star}$) from integral-field spectroscopy (IFS), and a sample of 32 quiescent galaxies with publicly available IFS. For both samples, $\sigma_{\star}$ is determined via two different methods that are popular in the literature, and we provide fits for each sample based on both sets of $\sigma_{\star}$. We find the fit to the AGN sample is shallower than the fit to the quiescent galaxy sample, and that the slopes for each sample are in agreement with previous investigations. However, the intercepts to the quiescent galaxy relations are notably higher than those found in previous studies, due to the systematically lower $\sigma_{\star}$ measurements that we obtain from IFS. We find that this may be driven, in part, by poorly constrained measurements of bulge effective radius ($r_{e}$) for the quiescent galaxy sample, which may bias the $\sigma_{\star}$ measurements low. We use these quiescent galaxy parameterizations, as well as one from the literature, to recalculate the virial scaling factor $f$. We assess the potential biases in each measurement, and suggest $f=4.82\pm1.67$ as the best currently available estimate. However, we caution that the details of how $\sigma_{\star}$ is measured can significantly affect $f$, and there is still much room for improvement.