The degeneracy between dust colour temperature and spectral index

Abstract

Context. Submillimetre dust emission provides information on the physics of interstellar clouds and dust. However, noise can produce a spurious anticorrelation between the colour temperature T C and the spectral index . These artefacts must be separated from the intrinsic (T ) relation of dust emission. Aims. We compare methods that can be used to analyse the (T ) relation. We wish to quantify their accuracy and bias, especially for observations similar to those made with Planck and Herschel. Methods. We examine submillimetre observations that are simulated either as simple, modified black body emission or using 3D radiative transfer modelling. We used different methods to recover the (T , ) values of individual objects and the parameters of the (T ) relation. In addition to 2 fitting, we examined the results of the SIMEX method, basic Bayesian model, hierarchical models, and a method that explicitly assumes a functional form for (T ). The methods were also applied to one field observed by Herschel.