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The Snow Border

Context. The study of the snow line is an important topic in several domains of astrophysics, and particularly for the evolution of proto-stellar environments and the formation of planets. Aims. The formation of the first layer of ice on carbon grains requires low temperatures compared to the temperature of evaporation (T > 100 K). This asymmetry generates a zone in which bare and icy dust grains coexist. Methods. We use Monte-Carlo simulations to describe the formation time scales of ice mantles on bare grains in protostellar disks and massive protostars environments. Then we analytically describe these two systems in terms of grain populations subject to infall and turbulence, and assume steady-state. Results. Our results show that there is an extended region beyond the snow line where icy and bare grains can coexist, in both proto-planetary disks and massive protostars. This zone is not negligible compared to the total size of the objects: on the order of 0.4 AU for proto-planetary disks and 5400 AU for high-mass protostars. Times to reach the steady-state are respectively es- timated from 10^2 to 10^5 yr. Conclusions. The presence of a zone, a so-called snow border, in which ba