We present a compilation of PRONAOS-based results concerning the temperature dependence of the dust submillimeter spectral index, including data from Galactic cirrus, star-forming regions, dust associated to a young stellar object, and a spiral galaxy. We observe large variations of the spectral index (from 0.8 to 2.4) in a wide range of temperatures (11 to 80 K). These spectral index variations follow a hyperbolic-shaped function of the temperature, high spectral indices (1.6-2.4) being observed in cold regions (11-20 K) while low indices (0.8-1.6) are observed in warm regions (35-80 K). Three distinct effects may play a role in this temperature dependence: one is that the grain sizes change in dense environments, another is that the chemical composition of the grains is not the same in different environments, a third one is that there is an intrinsic dependence of the dust spectral index on the temperature due to quantum processes. This last effect is backed up by laboratory measurements and could be the dominant one.
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