The impact of applying black hole-host galaxy scaling relations to large galaxy populations

Supermassive black holes (SMBHs) with dynamically measured masses have shown empirical correlations with host galaxy properties. These correlations are often the only method available to estimate SMBH masses and gather statistics for large galaxy populations across a range of redshifts, even though the scaling relations themselves are derived from a small subset of nearby galaxies. Depending on the scaling relation used, estimated SMBH masses can vary significantly. The most widely used scaling relations are the M$_{BH}-$M$_{\mathrm{bulge}}$ and M$_{BH}- \sigma$ relations, where M$_{\mathrm{bulge}}$ is galaxy bulge mass and $\sigma$ is the bulge velocity dispersion. In this paper, we determine how severely the choice of scaling relation impacts SMBH mass estimates for different subsets of a large galaxy population. For this analysis we use a sample of $\sim$ 400,000 galaxies, including 1,240 Type 1 AGN from the Sloan Digital Sky Survey. We calculate SMBH masses from M$_{BH}-$M$_{\mathrm{bulge}}$ and M$_{BH}- \sigma$ and compare to single-epoch virial SMBH masses from broad-line H$\beta$, which are derived independently of black hole-host galaxy scaling relations. We find that SMBH masses derived from the single-epoch virial relation for H$\beta$ are better reproduced by M$_{BH}- \sigma$ than M$_{BH}-$M$_{\mathrm{bulge}}$. Finally, in cases where $\sigma$ and M$_{\mathrm{bulge}}$ cannot be measured directly, we show that it is possible to infer $\sigma$ from photometry with more accuracy than we can infer M$_{\mathrm{bulge}}$.