We propose a model of quasar lifetimes in which longer periods of rapid black hole accretion are distinguished from observationally inferred lifetimes of quasars owing to gas and dust obscuration. In our picture, quasars are powered by gas funneled to galaxy centers, fueling starbursts and feeding black hole growth, but are "buried" until feedback from the accretion disperses the obscuring material, creating a window in which the black hole is observable as an optical quasar. Eventually, the activity ceases when the accretion rate drops below that required to maintain quasar luminosities. We study this process by simulating galaxy mergers, using the gas density to infer the bolometric luminosity of the black hole and the gas metallicity and column density to determine the B-band attenuation along arbitrary lines of sight. Defining the visible quasar lifetime as the total time with an observed B-band luminosity greater than some lower limit L_(B,min), we find lifetimes ～10-20 Myr for L_(B,min) = 10~(11) solar luminosity (M_B ≈ -23), in good agreement with observations, but significantly shorter than the "intrinsic" lifetime ～100 Myr obtained if attenuation is neglected. The ratio of observed to intrinsic lifetimes is also a strong function of both the limiting luminosity and observed frequency range.
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