Does the lockstep growth between black holes and bulges create their mass relation?

Abstract Recent studies have revealed a strong relation between the sample-averaged black hole (BH) accretion rate (BHAR) and star formation rate (SFR) among bulge-dominated galaxies—i.e., “lockstep” BH–bulge growth—in the distant universe. This relation might be closely connected to the BH–bulge mass correlation observed in the local universe. To further understand BH–bulge coevolution, we present Atacama Large Millimeter/submillimeter Array (ALMA) CO(2–1) or CO(3–2) observations of seven star-forming bulge-dominated galaxies at z = 0.5–2.5. Using the ALMA data, we detect significant (>3 σ ) CO emission from four objects. For our sample of seven galaxies, we measure (or constrain with upper limits) their CO line fluxes and estimate their molecular gas masses ( M gas ). We also estimate their stellar masses ( M star ) and SFRs, by modeling their spectral energy distributions. Using these physical properties, we derive the gas depletion timescales ( τ dep ≡ M gas /SFR) and compare them with the bulge/BH growth timescales ( τ grow ≡ M star /SFR ∼ M BH /BHAR). Our sample generally has τ dep shorter than τ grow by a median factor of ≳4, indicating that the cold gas will be depleted before significant bulge/BH growth takes place. This result suggests that BH–bulge lockstep growth is mainly responsible for maintaining the mass relation, not creating it. We note that our sample is small and limited to z < 2.5; JWST and ALMA will be able to probe to higher redshifts in the near future.