Defining the (Black Hole)–Spheroid Connection with the Discovery of Morphology-dependent Substructure in the M_BH–n_sph and M_BH–R_e,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 (${\mu }_e$), 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–$R_{e,sph}^{1.08\pm 0.04}$ 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 ${\Delta }_{rms|BH}\sim 0.60dex$ (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 $log{M}_{BH}$ 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.