Quasars Are Not Light-Bulbs: Testing Models of Quasar Lifetimes with the Observed Eddington Ratio Distribution

Abstract

We use the observed distribution of Eddington ratios as a function of supermassive black hole (BH) mass to constrain models of AGN lifetimes and lightcurves. Given the observed AGN luminosity function, a model for AGN lifetimes (time above a given luminosity) translates directly to a predicted Eddington ratio distribution. Models for self-regulated BH growth, in which feedback produces a 'blowout' decay phase after some peak luminosity (shutting down accretion) make specific predictions for the lifetimes distinct from those expected if AGN are simply gas starved (without feedback) and very different from simple phenomenological 'light bulb' models. Present observations of the Eddington ratio distribution, spanning 5 decades in Eddington ratio, 3 in BH mass, and redshifts z=0-1, agree with the predictions of self-regulated models, and rule out 'light-bulb', pure exponential, and gas starvation models at high significance. We compare the Eddington ratio distributions at fixed BH mass and fixed luminosity (both are consistent, but the latter are much less constraining). We present empirical fits to the lifetime distribution and show how the Eddington ratio distributions place tight limits on AGN lifetimes at various luminosities. We use this to constrain the shape of the typical AGN lightcurve, and provide simple analytic fits. Given independent constraints on episodic lifetimes, most local BHs must have gained their mass in no more than a couple of bright episodes, in agreement with merger-driven fueling models.