Limitations of the modified blackbody fit method for determining molecular cloud properties

Abstract

Achieving a comprehensive understanding of the star and planet formation process is one of the fundamental tasks of astrophysics, requiring detailed knowledge of the physical conditions during the different phases of this process. During the earliest stages, that is, concerning physical processes in molecular clouds and filaments, the column density N(H₂), dust temperature $T$ and dust emissivity index $\beta$ of these objects can be derived by adopting a modified blackbody fit of the far-infrared (FIR) to (sub-)millimeter spectral energy distributions (SEDs). However, this often applied method is based on various assumptions. In addition, the observational basis and required, but only assumed cloud properties, such as a limited wavelength-coverage of the SED and dust properties, respectively, may differ between different studies. We review the basic limitations of this method and evaluate their impact on the derived physical properties of the objects of interest, that is, molecular clouds and filaments. We find that the highest uncertainty when applying this method is introduced by the often poorly constrained dust properties. Therefore, we propose to first derive the optical depth and subsequently the column density with the help of a suitable dust model as the optical depth can be obtained with high accuracy, especially at longer wavelengths. The method provides reliable results up to the high densities and corresponding optical depths observed in molecular clouds. Considering typically used observational data, that is, measurements obtained with FIR instruments like Herschel/PACS, JCMT/SCUBA-2 and SOFIA/HAWC+, data at four wavelengths are sufficient to obtain accurate results. Furthermore, we find that the dust emissivity index $\beta$ derived from this method is not suitable as an indicator of dust grain size.