Recent infrared observations have revealed the presence of compact (radii R ☉) debris disks around more than a dozen metal-rich white dwarfs (WDs), likely produced by a tidal disruption of asteroids. Accretion of high-Z material from these disks may account for the metal contamination of these WDs. It was previously shown using local calculations that the Poynting-Robertson (PR) drag acting on the dense, optically thick disk naturally drives metal accretion onto the WD at the typical rate ?g?s–1. Here we extend this local analysis by exploring the global evolution of the debris disk under the action of the PR drag for a variety of assumptions about the disk properties. We find that massive disks (mass 1020 g), which are optically thick to incident stellar radiation, inevitably give rise to metal accretion at rates . The magnitude of and its time evolution are determined predominantly by the initial pattern of the radial distribution of the debris (i.e., ring-like versus disk-like) but not by the total mass of the disk. The latter determines only the disk lifetime, which can be several Myr or longer. The evolution of an optically thick disk generically results in the development of a sharp outer edge of the disk. We also find that the low-mass ( 1020 g), optically thin disks exhibit and evolve on a characteristic timescale ~105-106 yr, independent of their total mass.
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