The Effect of Line-of-Sight Temperature Variation and Noise on Dust Continuum Observations

We investigate the effect of line-of-sight temperature variations and noise on two commonly used methods to determine dust properties from dust-continuum observations of dense cores. One method employs a direct fit to a modified blackbody spectral energy distribution (SED); the other involves a comparison of flux ratios to an analytical prediction. Fitting fluxes near the SED peak produces inaccurate temperature and dust spectral index estimates due to the line-of-sight temperature (and density) variations. Longer wavelength fluxes in the Rayleigh-Jeans part of the spectrum ( 600 mm for typical cores) may more accurately recover the spectral index, but both methods are very sensitive to noise. The temperature estimate approaches the density-weighted temperature, or 'column temperature,' of the source as short wavelength fluxes are excluded. An inverse temperature-spectral index correlation naturally results from SED fitting, due to the inaccurate isothermal assumption, as well as noise uncertainties. We show that above some 'threshold' temperature, the temperatures estimated through the flux ratio method can be highly inaccurate. In general, observations with widely separated wavelengths, and including shorter wavelengths, result in higher threshold temperatures; such observations thus allow for more accurate temperature estimates of sources with temperatures less than the threshold temperature. When only three fluxes are available, a constrained fit, where the spectral index is fixed, produces less scatter in the temperature estimate when compared to the estimate from the flux ratio method.