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 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 micron 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.
