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 bare and icy grains
co- exist 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).Comment: accepted in A&