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. Our aim is to derive the proportion of bare grains around the theoretical snow line position for a typical low-mass protostellar disk and a massive protostar, and estimate the size of this mixing zone compared to the dust envelope size. 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. Numerical applications use standard numbers obtained by previous observations or modelling of the astrophysical objects studied. 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 estimated from 10² to 10⁵ yr. Conclusions. The presence of a zone, a so-called snow border, in which bare and icy grains coexist can have a major impact on our knowledge of protostellar environments. From a theoretical point of view, the progression of icy grains to bare grains as the temperature increases, could be a realistic way to model hot cores and hot corinos. Also, in this zone, the formation of planetesimals will require the coagulation of bare and icy grains. Observationally, this zone allows high abundances of gas phase species at large scales, for massive protostars particularly, even at low temperatures (down to 50 K). This could be a critical point for the analysis of upcoming water observations by the Herschel Space Observatory.