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Mass estimates for very cold (< 8 K) gas in molecular cloud cores

The mass of prestellar cores is an essential ingredient to understand the onset of star formation in the core. The low level of emission from cold dust may keep parts of it hidden from observation. We aim to determine the fraction of core mass in the temperature range < 8 K that can be expected for typical low- and high-mass star formation regions. We calculate the dust temperature within standard spherically symmetric prestellar cores for a grid of density powerlaws in the outer core regions, core masses, and variation in the external multi-component radiation field. The dust is assumed to be composed of amorphous silicate and carbon, and variations of its optical properties are discussed. As measure for the distribution of cores and clumps, we use core mass functions derived for various environments. In view of the high densities in very cold central regions, dust and gas temperatures are assumed to be equal. We find that the fraction of mass with temperatures < 8 K in typical low- and high-mass cores is < 20\%. It is possible to obtain higher fractions of very cold gas by placing intermediate- or high-mass cores in a typical low-mass star formation environment. We show that the mass uncertainty arising from FIR to mm modeling of very cold dust emission is smaller than the mass uncertainty due to the unknown dust opacities.