Testing galaxy quenching theories with scatter in the stellar-to-halo mass relation

We use the scatter in the stellar-to-halo mass relation to constrain galaxy evolution models. If the efficiency of converting accreted baryons into stars varies with time, haloes of the same present-day mass but different formation histories will have different z = 0 galaxy stellar mass. This is one of the sources of scatter in stellar mass at fixed halo mass, σ_{log M*}. For massive haloes that undergo rapid quenching of star formation at z ∼ 2, different mechanisms that trigger this quenching yield different values of σ_{log M*}. We use this framework to test various models in which quenching begins after a galaxy crosses a threshold in one of the following physical quantities: redshift, halo mass, stellar mass and stellar-to-halo mass ratio. Our model is highly idealized, with other sources of scatter likely to arise as more physics is included. Thus, our test is whether a model can produce scatter lower than observational bounds, leaving room for other sources. Recent measurements find σ_{log M*} = 0.16 dex for 10¹¹ M_⊙ galaxies. Under the assumption that the threshold is constant with time, such a low value of σ_{log M*} rules out all of these models with the exception of quenching by a stellar mass threshold. Most physical quantities, such as metallicity, will increase scatter if they are uncorrelated with halo formation history. Thus, to decrease the scatter of a given model, galaxy properties would correlate tightly with formation history, creating testable predictions for their clustering. Understanding why σ_{log M*} is so small may be key to understanding the physics of galaxy formation.