A Possible Correlation Between the Luminosities and Lifetimes of Active Galactic Nuclei

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Abstract
We use the clustering of galaxies around distant AGN to show with ~90% confidence that fainter AGN are longer lived. Our argument is simple: since the measured galaxy-AGN cross-correlation length r_0 ~ 5h^-1 Mpc does not vary significantly over a 10 magnitude range in AGN optical luminosity, faint and bright AGN must reside in dark matter halos with similar masses. The halos that host bright and faint AGN therefore have similar intrinsic abundances, and the large observed variation in AGN number density with luminosity reflects a change in duty cycle.

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