Defining the (Black Hole)-Spheroid Connection with the Discovery of Morphology-dependent Substructure in the MBH-nsph and MBH-Re,sph Diagrams: New Tests for Advanced Theories and Realistic Simulations

For 123 local galaxies with directly measured black hole masses (M_BH), we provide the host spheroid's Sérsic index (n_sph), effective half-light radius (R_e,sph), and effective surface brightness ( ${\mu }_{{\rm{e}}}$ ), obtained from careful multicomponent decompositions, and we use these to derive the morphology-dependent M_BH-n_sph and M_BH-R_e,sph relations. We additionally present the morphology-dependent M_*,sph-n_sph and M_*,sph-R_e,sph relations. We explored differences due to early-type galaxies (ETGs) versus late-type galaxies (LTGs), Sérsic versus core-Sérsic galaxies, barred versus non-barred galaxies, and galaxies with and without a stellar disk. We detect two different M_BH-n_sph relations due to ETGs and LTGs with power-law slopes 3.95 ± 0.34 and 2.85 ± 0.31. We additionally quantified the correlation between M_BH and the spheroid's central concentration index, which varies monotonically with the Sérsic index. Furthermore, we observe a single, near-linear M_*,sph- ${R}_{{\rm{e}},\mathrm{sph}}^{1.08\pm 0.04}$ relation for ETGs and LTGs, which encompasses both classical and alleged pseudobulges. In contrast, ETGs and LTGs define two distinct M_BH-R_e,sph relations with ${{\rm{\Delta }}}_{\mathrm{rms}| \mathrm{BH}}\sim 0.60\,\mathrm{dex}$ (cf. ∼0.51 dex for the M_BH-σ relation and ∼0.58 dex for the M_BH-M_*,sph relation), and the ETGs alone define two steeper M_BH-R_e,sph relations, offset by ∼1 dex in the $\mathrm{log}{M}_{\mathrm{BH}}$ direction, depending on whether they have a disk or not and explaining their similar offset in the M_BH-M_*,sph diagram. This trend holds using 10%, 50%, or 90% radii. These relations offer pivotal checks for simulations trying to reproduce realistic galaxies, and for theoretical studies investigating the dependence of black hole mass on basic spheroid properties.