The effect of noise in dust emission maps on the derivation of column density, temperature, and emissivity spectral index

We have mapped the central 10' x 10' of the dense core TMC-1C at 450, 850, and 1200 mu m using SCUBA on the James Clerk Maxwell Telescope and MAMBO on the IRAM 30 m telescope. We show that although one can, in principle, use images at these wavelengths to map the emissivity spectral index, temperature, and column density independently, noise and calibration errors would have to be less than similar to 2% to accurately derive these three quantities from a set of three emission maps. Because our data are not this free of errors, we use our emission maps to fit the dust temperature and column density assuming a constant value of the emissivity spectral index and explore the effects of noise on the derived physical parameters. We find that the derived extinction values for TMC-1C are large for a starless core (similar to 80 mag A(V)) and the derived temperatures are low (similar to 6 K) in the densest regions of the core, using our derived value of beta = 1.8.