A New Method for Determining the Dust Temperature Distribution in Star-forming Regions

We describe a new dust temperature inversion technique, the Fourier method, and apply it to determine the dust temperature distribution in the molecular regions Sgr B2(M), M17, and six Bok globules. The results of the Fourier method generally agree with those from the previous dust inversion methods, i.e., the analytical method and the MEM method, except that the double-peaked form in the distribution obtained with the latter technique is not seen. In order to evaluate the uncertainty in the derived dust mass, tests are carried out using power-law dust temperature distributions and different dust emissivities. Assuming that the dust emissivity k_ν is accurately known and the dust emission is optically thin, the calculation indicates that the derived mass is close to the correct value if the dust in the region is heated to about 5 K or above. The derived mass is, however, significantly affected by k_ν. The Fourier method requires a well-sampled dust emission spectrum, but has the advantage of not depending on any temperature assumption in deriving the dust mass, compared with single-temperature calculations and gray-body fitting. It is straightforward to implement compared to other inversion techniques.