The dust temperature distribution in prestellar cores
We have computed the dust temperature distribution to be expected in a pre-protostellar core in the phase prior to the onset of gravitational instability. We have done this in the approximation that the heating of the dust grains is solely due to the attenuated external radiation field and that the core is optically thin to its own radiation. This permits us to consider non spherically symmetric geometries. We predict the intensity distributions of our model cores at millimeter and sub-millimeter wavelengths and compare with observations of the well studied object L1544. We have also developed an analytical approximation for the temperature at the center of spherically symmetric cores and we compare this with the numerical calculations. Our results show (in agreement with Evans et al. 2001) that the temperatures in the nuclei of cores of high visual extinction (> 30 magnitudes) are reduced to values of below ~8 K or roughly half of the surface temperature. This has the consequence that maps at wavelengths shortward of 1.3 mm see predominantly the low density exterior of pre-protostellar cores. It is extremely difficult to deduce the true density distribution from such maps alone. We have computed the intensity distribution expected on the basis of the models of Ciolek & Basu (2000) and compared with the observations of L1544. The agreement is good with a preference for higher inclinations (37 degrees instead of 16) than that adopted by Ciolek & Basu (2000). We find that a simple extension of the analytic approximation allows a reasonably accurate calculation of the dust temperature as a function of radius in cores with density distributions approximating those expected for Bonnor-Ebert spheres and suggest that this may be a useful tool for future calculations of the gas temperature in such cores.