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 Sersic index (n(sph)), effective half-light radius (R-e,R-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,R-sph relations. We additionally present the morphology-dependent M-*,M-sph-n(sph) and M-*,M-sph-R-e,R-sph relations. We explored differences due to early-type galaxies (ETGs) versus late-type galaxies (LTGs), Sersic versus core-Sersic 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 Sersic index. Furthermore, we observe a single, near-linear M-*,M-sph- R-e,sph(1.08 +/- 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,R-sph relations with Delta(rms vertical bar BH) similar to 0.60 dex cf. similar to 0.51 dex for the M-BH-sigma relation and similar to 0.58 dex for the M-BH-M-*,M-sph relation), and the ETGs alone define two steeper M-BH-R-e,R-sph relations, offset by similar to 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-*,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.