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 quasar/active galactic nucleus (AGN) lifetimes and light curves. Given the observed (well constrained) AGN luminosity function, a particular model for AGN light curves L(t) or, equivalently, the distribution of AGN lifetimes (time above a given luminosity t (> L)) translates directly and uniquely (without further assumptions) to a predicted distribution of Eddington ratios at each BH mass. Models for self-regulated BH growth, in which feedback produces a self-regulating "decay" or "blowout" phase after the AGN reaches some peak luminosity/BH mass and begins to expel gas and shut down accretion, make specific predictions for the light curves/lifetimes, distinct from, e. g., the expected distribution if AGN simply shut down by gas starvation (without feedback) and very different from the prediction of simple phenomenological "light bulb" scenarios. We show that the present observations of the Eddington ratio distribution, spanning nearly 5 orders of magnitude in Eddington ratio, 3 orders of magnitude in BH mass, and redshifts z = 0-1, agree well with the predictions of self-regulated models, and rule out phenomenological "light bulb" or pure exponential models, as well as gas starvation models, at high significance (similar to 5 sigma). We also compare with observations of the distribution of Eddington ratios at a given AGN luminosity, and find similar good agreement (but show that these observations are much less constraining). We fit the functional form of the quasar lifetime distribution and provide these fits for use, and show how the Eddington ratio distributions place precise, tight limits on the AGN lifetimes at various luminosities, in agreement with model predictions. We compare with independent estimates of episodic lifetimes and use this to constrain the shape of the typical AGN light curve, and provide simple analytic fits to these for use in other analyses. Given these constraints, the average local BH must have gained its mass in no more than a couple of bright, near peak-luminosity episodes, in agreement with models of accretion triggering in interactions and mergers.