The bulge masses of TDE host galaxies and their scaling with black hole mass

Tidal disruption events (TDEs) provide a means to probe the low end of the supermassive black hole (SMBH) mass distribution, as they are only observable below the Hills mass ($\lesssim 10^8$ M$_\odot$). Here we attempt to calibrate the scaling of SMBH mass with host galaxy bulge mass, enabling SMBH masses to be estimated for large TDE samples without the need for follow-up observations or extrapolations of relations based on high-mass samples. We derive host galaxy masses using Prospector fits to the UV-MIR spectral energy distributions for the hosts of 29 well-observed TDEs with BH mass estimates from MOSFiT. We then conduct detailed bulge/disk decomposition using SDSS and PanSTARRS imaging, and provide a catalog of bulge masses. We measure a positive correlation between SMBH and bulge mass for the TDE sample, with a power-law slope of 0.28 and significance $p=0.06$ (Spearmans) and $p=0.05$ (Pearsons), and an intrinsic scatter of 0.2 dex. Applying MC resampling and bootstrapping, we find a more conservative estimate of the slope is $0.18\pm0.11$, dominated by the systematic errors from Prospector and MOSFiT. This is shallower than the slope at high SMBH mass, which may be due to a bias in the TDE sample towards lower mass BHs that can more easily disrupt low-mass stars outside of the event horizon. When combining the TDE sample with that of the high mass regime, we find that TDEs are successful in extending the SMBH - stellar mass relationship further down the mass spectrum and provide a relationship across the full range of SMBH masses.