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.
