On the origin of the fundamental metallicity relation and the scatter in galaxy scaling relations

We present a simple toy model to understand what sets the scatter in star formation and metallicity of galaxies at fixed mass. According to this model, the scatter ultimately arises from the intrinsic scatter in the accretion rate, but may be substantially reduced depending on the time-scale on which the accretion varies compared to the time-scale on which the galaxy loses gas mass. This model naturally produces an anticorrelation between star formation and metallicity at a fixed mass, the basis of the fundamental metallicity relation. We show that observational constraints on the scatter in galaxy scaling relations can be translated into constraints on the galaxy-to-galaxy variation in the mass loading factor at fixed mass, and the time-scales and magnitude of a stochastic component of accretion on to star-forming galaxies. We find a remarkably small scatter in the mass loading factor, ≲0.1 dex, and that the scatter in accretion rates is smaller than that expected from N-body simulations.