Fig. 4: Schematic of the proposed scenario on how BHs regulate cool gas content in galaxies.

The large arrow indicates the μ_HI–M_BH correlation. The background colour scale indicates the quiescent galaxy fraction as a function of M_BH, which shows a sharp increase at M_BH ≳ 10^7.5M_⊙ (Methods and Extended Data Fig. 5), corresponding to μ_HI < 10%. At fixed M_BH, galaxies could maintain their μ_HI at a certain level determined by the relative strength of the inner halo binding energy and M_BH. Once gas accretion is enhanced onto galaxies (and their BHs), which increases μ_HI, M_BH will also grow and release additional heating energy that prevents further gas cooling or accretion. This will bring down μ_HI together with increasing M_⋆ by star formation and reach a balance at higher M_BH. Although the same process takes place in both SFGs and quiescent galaxies, the growth of M_BH or M_⋆ should be much less significant in quiescent galaxies than in SFGs, and the large range of M_BH among quiescent galaxies (M_BH ~ 10⁷⁻¹⁰M_⊙) is probably inherited from their different star-forming progenitors when they were quenched.