Dust spectral energy distributions in the era of Herschel and Planck: a hierarchical bayesian-fitting technique - Kelly, Brandon C.; Shetty, Rahul; Stutz, Amelia M. (The astrophysical journal, 2012)
We present a hierarchical Bayesian method for fitting infrared spectral energy distributions (SEDs) of dust emission to observed fluxes. Under the standard assumption of optically thin single temperature ( T ) sources, the dust SED as represented by a power-law-modified blackbody is subject to a strong degeneracy between T and the spectral index β. The traditional non-hierarchical approaches, typically based on χ 2 minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and β even with modest levels of observational noise. The hierarchical Bayesian method rigorously and self-consistently treats measurement uncertainties, including calibration and noise, resulting in more precise SED fits. As a result, the Bayesian fits do not produce any spurious anti-correlations between the SED parameters due to measurement uncertainty. We demonstrate that the Bayesian method is substantially more accurate than the χ 2 fit in recovering the SED parameters, as well as the correlations between them. As an illustration, we apply our method to Herschel and submillimeter ground-based observations of the star-forming Bok globule CB244. This source is a small, nearby molecular cloud containing a single low-mass protostar and a starless core. We find that T and β are weakly positively correlated—in contradiction with the χ 2 fits, which indicate a T -β anti-correlation from the same data set. Additionally, in comparison to the χ 2 fits the Bayesian SED parameter estimates exhibit a reduced range in values.