Two channels of supermassive black hole growth as seen on the galaxies mass-size plane

We investigate the variation of black hole masses (M_BH) as a function of their host galaxy stellar mass (M_*) and half-light radius (R_e). We confirm that the scatter in M_BH within this plane is essentially the same as that in the M_BH-σ relation, as expected from the negligible scatter reported in the virial mass estimator σ _v ² = G × M_*/(5 × R_e). All variation in M_BH happens along lines of constant σ_v on the (M_*, R_e) plane, or M_* ∝ R_e for M_* ≲ 2 × 10¹¹ M_⊙. This trend is qualitatively the same as those previously reported for galaxy properties related to stellar populations, like age, metallicity, alpha enhancement, mass-to-light ratio and gas content. We find evidence for a change in the M_BH variation above the critical mass of M_crit ≈ 2 × 10¹¹ M_⊙. This behaviour can be explained assuming that M_BH in galaxies less massive than M_crit can be predicted by the M_BH-σ relation, while M_BH in more massive galaxies follows a modified relation, which is also dependent on M_* once M_* > M_crit. This is consistent with the scenario where the majority of galaxies grow through star formation, while the most massive galaxies undergo a sequence of dissipation-less mergers. In both channels, black holes and galaxies grow synchronously, giving rise to the black hole-host galaxy scaling relations, but there is no underlying single relation that is universal across the full range of galaxy masses.