How Much Mass Hides in a Temperature Assumption? Submillimetre Dust Masses for a Fiducial Cloud

Dust masses from submillimetre fluxes are only as good as the temperature and emissivity adopted, and this paper prices that dependence for a fiducial cloud. For an integrated 850 micron flux of 10 janskys at 400 parsecs with the widely used opacity of 0.077 square metres per kilogram, the inferred dust mass is 0.682 solar masses at 10 K, 0.205 at 20 K, and 0.117 at 30 K, a factor of 5.83 between the cold and warm assumptions; the predicted 450-to-850 micron colour at 15 K moves from 4.92 at emissivity index 1.5 to 7.69 at index 2.2, showing how colour data can in principle break the degeneracy that a single band cannot. A single-band mass quoted without its temperature is not a measurement but the visible part of a two-parameter family, and this paper states the family explicitly. All values are computed, not measured.