The degeneracy between dust colour temperature and spectral index. Comparison of methods for estimating the β(T) relation
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 β. These artefacts must be separated from the intrinsic β(T) relation of dust emission.
Aims: We compare methods that can be used to analyse the β(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, β) values of individual objects and the parameters of the β(T) relation. In addition to χ^{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 β(T). The methods were also applied to one field observed by Herschel.
Results: All methods exhibit some bias, even in the idealised case of white noise. The results of the Bayesian method show significantly lower bias than direct χ^{2} fits. The same is true for hierarchical models that also result in a smaller scatter in the temperature and spectral index values. However, significant bias was observed in cases with high noise levels. When the signaltonoise ratios are different for different sources, all β and T estimates of the hierarchical model are biased towards the relation determined by the data with the highest signaltonoise ratio. This can significantly alter the recovered β(T) function. With the method where we explicitly assume a functional form for the β(T) relation, the bias is similar to the Bayesian method. In the case of the actual Herschel field, all methods agree on some degree of anticorrelation between T and β.
Conclusions: The Bayesian method and the hierarchical models can both reduce the noiseinduced parameter correlations. However, all methods can exhibit nonnegligible bias. This is particularly true for hierarchical models and observations of varying signaltonoise ratios and this must be taken into account when interpreting the results.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 2013
 DOI:
 10.1051/00046361/201220910
 arXiv:
 arXiv:1305.2130
 Bibcode:
 2013A&A...556A..63J
 Keywords:

 ISM: clouds;
 infrared: ISM;
 radiative transfer;
 submillimeter: ISM;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Submitted to A&