Leading models for the power source of quasars (QSOs) and active galactic nuclei (AGN) involve gravitational energy release of gas. We propose that a comparison of theoretical models for the gas supply mechanism to the observed luminosity and luminosity evolution of QSOs and AGN may rule out or constrain some such models. In particular, we calculate the gas liberation rate A (t) resulting from (i) physical stellar collisions and (ii) tidal disruptions in a dense star system surrounding a massive black hole, taking into account the dynamical evolution of the stellar system. We obtain a number of analytic, asymptotic results. Our main conclusions are that both mechanisms (i) and (ii) lead to an eventual decreasing function Mdot(t); that for a total mass of 108 Msun or more, a peak value of Mdot(t) exceeding ∼0.1 Msun yr-1 requires a stellar system whose dynamical evolution is dominated by physical collisions; and that Mdot(t) in a collision-dominated system increases until the mass in gas liberated is comparable to the remaining mass in stars, after which Mdot(t) decreases and attains an asymptotic form Mdot(t) ∝ t-2. In all of our models Mdot(t) has an asymptotic power law form Mdot(t) ∝ t-P.
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McMillan et al. (1981) studied this question.