Ultramassive Black Holes in the Most Massive Galaxies: M_BH–σ versus M_BH–R_b

We investigate the nature of the relations between black hole (BH) mass (M _BH) and the central velocity dispersion (σ) and, for core-Sérsic galaxies, the size of the depleted core (R _b). Our sample of 144 galaxies with dynamically determined M _BH encompasses 24 core-Sérsic galaxies, thought to be products of gas-poor mergers, and reliably identified based on high-resolution Hubble Space Telescope imaging. For core-Sérsic galaxies, i.e., combining normal-core (R _b < 0.5 kpc) and large-core galaxies (R _b ≳ 0.5 kpc), we find that M _BH correlates remarkably well with R _b such that $M_{BH}\propto R_b^{1.20\pm 0.14}$ (rms scatter in log M _BH of Δ_rms ∼ 0.29 dex), confirming previous works on the same galaxies apart from three new ones. Separating the sample into Sérsic, normal-core and large-core galaxies, we find that Sérsic and normal-core galaxies jointly define a single log-linear M _BH–σ relation M _BH ∝ σ ^4.88±0.29 with Δ_rms ∼ 0.47 dex; however, at the high-mass end, large-core galaxies (four with measured M _BH) are offset upward from this relation by (2.5–4) × σ _s, explaining the previously reported steepening of the M _BH–σ relation for massive galaxies. Large-core spheroids have magnitudes M _V ≲ −23.50 mag, half-light radii R _e ≳ 10 kpc, and are extremely massive, M _* ≳ 10¹² M _☉. Furthermore, these spheroids tend to host ultramassive BHs (M _BH ≳ 10¹⁰ M _☉) tightly connected with their R _b rather than σ. The less popular M _BH–R _b relation exhibits ∼62% less scatter in log M _BH than the M _BH–σ relations. Our findings suggest that large-core spheroids form via multiple major "dry" merger events involving super/ultramassive BHs, consistent with the flattening of the σ–L _V relation observed at M _V ≲ −23.5 mag.