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

Context. 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 this dust hidden from observation. Aims. 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. Methods. We calculated the dust temperature within standard spherically symmetric prestellar cores for a grid of density power laws in the outer core regions, core masses, and variations in the external multicomponent radiation field. We assume the dust is composed of amorphous silicate and carbon and we discuss variations of its optical properties. As a measure for the distribution of cores and clumps, we used 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. Results. 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 far-infrared to mm modeling of very cold dust emission is smaller than the mass uncertainty owing to the unknown dust opacities. Conclusions. Under typical star formation conditions, dust with temperatures <8 K covers a small mass fraction in molecular cloud cores, but may play a more important role for special cases. The major unknown in determining the total core mass from thermal dust emission is the uncertainty in the dust opacity, not in the underestimated very cold dust mass.