From flux to dust mass: Does the grain-temperature distribution matter for estimates of cold dust masses in supernova remnants?

The amount of dust estimated from infrared to sub-millimetre (submm) observations strongly depends on assumptions of different grain sizes, compositions and optical properties. Here we use a simple model of thermal emission from cold silicate/carbon dust at a range of dust grain temperatures and fit the spectral energy distribution (SED) of the Crab Nebula as a test. This can lower the derived dust mass for the Crab by ~50% and 30-40% for astronomical silicates and amorphous carbon grains compared to recently published values (0.25M_sun -> 0.12M_sun and 0.12M_sun -> 0.072M_sun, respectively), but the implied dust mass can also increase by as much as almost a factor of six (0.25M_sun -> 1.14M_sun and 0.12M_sun -> 0.71M_sun) depending on assumptions regarding the sizes/temperatures of the coldest grains. The latter values are clearly unrealistic due to the expected metal budget, though. Furthermore, we show by a simple numerical experiment that if a cold-dust component does have a grain-temperature distribution, it is almost unavoidable that a two-temperature fit will yield an incorrect dust mass estimate. But we conclude that grain temperatures is not a greater uncertainty than the often poorly constrained emissivities (i.e., material properties) of cosmic dust, although there is clearly a need for improved dust emission models. The greatest complication associated with deriving dust masses still arises in the uncertainty in the dust composition.