Dynamically defined bulges reveal that early-type galaxies with compact bulges host more massive black holes

Abstract

We revisit the $M_{BH}-M_{bulge}$ relation for early-type galaxies by introducing a uniform bulge defined by dynamical decomposition. From the set of nearby galaxies with accurately measured black hole masses, we select 30 early-type galaxies that have been observed with wide-field integral-field unit instruments (MUSE, ATLAS3D, or PPAK). For each galaxy, we construct an orbit-superposition Schwarzschild model and obtain its stellar orbit distribution. In this framework, we define the bulge uniformly as comprising stellar orbits with circularity $λ_z < 0.7$ (or, in an alternative definition, $λ_z < 0.2$) and lying within $r < 3$ kpc. From these orbits, we reconstruct the spatial density distribution of the bulge and measure its mass ($M_{bulge}$), size ($R_{bulge}$) and surface density slope ($γ_{bulge}$). We find that the dynamical bulge defined by $λ_z < 0.7$ yields masses that are systematically consistent with the photometric bulge masses. Comparing to the bulge from photometric decomposition, using this dynamical bulge definition slightly decreases the scatter around the best-fitting from 0.56 to 0.47. More interestingly, we identify a clear trend: at a given bulge mass, galaxies hosting more compact bulges (i.e. smaller bulge sizes or steeper bulge density slopes) systematically contain more massive black holes; eight outliers show overmassive BHs together with ultra-compact bulges. We interpret this as direct observational evidence that the $M_{BH}-M_{bulge}$ relation evolves over a galaxy&#39;s merger history, with that history imprinted in bulge compactness. Incorporating compactness via an $M_{BH}-M_{bulge}-R_{e, bulge}$ (or $γ_{bulge}$) relation brings the outliers into agreement and reduces the overall scatter of the sample to $\sim 0.3$.