On the Maximum Luminosity of Galaxies and Their Central Black Holes: Feedback from Momentum‐driven Winds

We investigate large-scale galactic winds driven by momentum deposition. Momentum injection is provided by (1) radiation pressure produced by the continuum absorption and scattering of photons on dust grains and (2) supernovae (momentum injection by supernovae is important even if the supernova energy is radiated away). Radiation can be produced by a starburst or active galactic nucleus (AGN) activity. We argue that momentum-driven winds are an efficient mechanism for feedback during the formation of galaxies. We show that above a limiting luminosity, momentum deposition from star formation can expel a significant fraction of the gas in a galaxy. The limiting, Eddington-like luminosity is L M ≃ (4 f g c / G )σ 4 , where σ is the galaxy velocity dispersion and f g is the gas fraction; the subscript M refers to momentum driving. A starburst that attains L M moderates its star formation rate and its luminosity does not increase significantly further. We argue that elliptical galaxies attain this limit during their growth at z ≳ 1 and that this is the origin of the Faber-Jackson relation. We show that Lyman break galaxies and ultraluminous infrared galaxies have luminosities near L M . Since these starbursting galaxies account for a significant fraction of the star formation at z ≳ 1, this supports our hypothesis that much of the observed stellar mass in early-type galaxies was formed during Eddington-limited star formation. Star formation is unlikely to efficiently remove gas from very small scales in galactic nuclei, i.e., scales much smaller than that of a nuclear starburst. This gas is available to fuel a central black hole (BH). We argue that a BH clears gas out of its galactic nucleus when the luminosity of the BH itself reaches ≈ L M . This shuts off the fuel supply to the BH and may also terminate star formation in the surrounding galaxy. As a result, the BH mass is fixed to be M BH ≃ ( f g κ es /π G 2 )σ 4 , where κ es is the electron scattering opacity. This limit is in accord with the observed M BH -σ relation.