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Metal accretion onto white dwarfs caused by Poynting-Robertson drag on their debris disks

Recent discoveries of compact (sizes $<R_\odot$) debris disks around more than a dozen of metal-rich white dwarfs (WDs) suggest that pollution of these stars with metals may be caused by accretion of high-Z material from the disk. But the mechanism responsible for efficient transfer of mass from a particulate disk to the WD atmosphere has not yet been identified. Here we demonstrate that radiation of the WD can effectively drive accretion of matter through the disk towards the sublimation radius (located at several tens of WD radii), where particles evaporate, feeding a disk of metal gas accreting onto the WD. We show that, contrary to some previous claims, Poynting-Robertson (PR) drag on the debris disk is effective at providing metal accretion rate $\dot M_{PR}\sim 10^8$ g/s and higher, scaling quadratically with WD effective temperature. We compare our results with observations and show that, as expected, no WD hosting a particulate debris disk shows evidence of metal accretion rate below that produced by the PR drag. Existence of WDs accreting metals at rates significantly higher than $\dot M_{PR}$ suggests that another mechanism in addition to PR drag drives accretion of high-Z elements in these systems.