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Near-infrared emission from sublimating dust in collisionally active debris disks

Hot exozodiacal dust is thought to be responsible for excess near-infrared (NIR) emission emanating from the innermost parts of some debris disks. The origin of this dust, however, is still a matter of debate. We test whether hot exozodiacal dust can be supplied from an exterior parent belt by Poynting-Robertson (P-R) drag, paying special attention to the pile-up of dust that occurs due to the interplay of P-R drag and dust sublimation. Specifically, we investigate whether pile-ups still occur when collisions are taken into account, and if they can explain the observed NIR excess. We compute the steady-state distribution of dust in the inner disk by solving the continuity equation. First, we derive an analytical solution under a number of simplifying assumptions. Second, we develop a numerical debris disk model that for the first time treats the complex interaction of collisions, P-R drag, and sublimation in a self-consistent way. From the resulting dust distributions we generate thermal emission spectra and compare these to observed excess NIR fluxes. We confirm that P-R drag always supplies a small amount of dust to the sublimation zone, but find that a fully consistent treatment yields a maximum amount of dust that is about 7 times lower than that given by analytical estimates. The NIR excess due this material is much smaller (<10^-3 for A-type stars with parent belts at >1 AU) than the values derived from interferometric observations (~10^-2). Pile-up of dust still occurs when collisions are considered, but its effect on the NIR flux is insignificant. Finally, the cross-section in the innermost regions is clearly dominated by barely bound grains.