The Black Hole -- Bulge Mass Relation including Dwarf Galaxies Hosting Active Galactic Nuclei

We present a new relationship between central black hole (BH) mass and host galaxy stellar bulge mass extending to the lowest BH masses known in dwarf galaxies ($M_{\rm BH} \lesssim 10^{5} M_{\odot}$; $M_{\star} \sim 10^{9} M_{\odot}$). We have obtained visible and near-infrared $Hubble \ Space \ Telescope \ (HST)$ imaging of seven dwarf galaxies with optically-selected broad-line active galactic nuclei (AGN) and BH mass estimates from single epoch spectroscopy. We perform 2D photometric modeling with GALFIT to decompose the structure of these galaxies and find that the majority have an inner bulge/pseudobulge component with an exponential disk that dominates the total stellar mass. Using the modeling results and color-dependent mass-to-light ratios, we determine the stellar mass of each photometric component in each galaxy. We determine the $M_{\rm BH} - M_{\rm bulge}$ relation using a total of 12 dwarf galaxies hosting broad-line AGNs, along with a comparison sample of 88 galaxies with dynamical BH masses and 37 reverberation-mapped AGNs. We find a strong correlation between BH mass and bulge mass with ${\rm log}(M_{\rm BH}/M_\odot) = (1.24\pm 0.08)~{\rm log}(M_{\rm bulge}/10^{11} M_\odot) + (8.80\pm 0.09)$. The near-linear slope and normalization are in good agreement with correlations found previously when only considering higher mass systems. This work has quadrupled the number of dwarf galaxies on the BH-bulge mass relation, with implications for BH seeding and predictions for gravitational wave detections of merging BHs at higher redshifts with $LISA$.