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The mass of prestellar cores is an essential ingredient to understand theonset of star formation in the core. The low level of emission from cold dustmay keep parts of it hidden from observation. We aim to determine the fractionof core mass in the temperature range < 8 K that can be expected for typicallow- and high-mass star formation regions. We calculate the dust temperaturewithin standard spherically symmetric prestellar cores for a grid of densitypowerlaws in the outer core regions, core masses, and variation in the externalmulti-component radiation field. The dust is assumed to be composed ofamorphous silicate and carbon, and variations of its optical properties arediscussed. As measure for the distribution of cores and clumps, we use coremass functions derived for various environments. In view of the high densitiesin very cold central regions, dust and gas temperatures are assumed to beequal. We find that the fraction of mass with temperatures < 8 K in typicallow- and high-mass cores is < 20\%. It is possible to obtain higher fractionsof very cold gas by placing intermediate- or high-mass cores in a typicallow-mass star formation environment. We show that the mass uncertainty arisingfrom FIR to mm modeling of very cold dust emission is smaller than the massuncertainty due to the unknown dust opacities.

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