A Fully Bayesian Approach For Inferring Physical Properties With Credibility Intervals From Noisy Astronomical Data

The atoms and molecules of interstellar clouds emit photons when passing from an excited state to a lower energy state. The resulting emission lines can be detected by telescopes in the different wavelength domains (radio, infrared, visible, UV...). Through the excitation and chemical conditions they reveal, these lines provide key constraints on the local physical conditions reigning in giant molecular clouds (GMCs), which constitute the birthplace of stars in galaxies. Inferring these physical conditions from observed maps of GMCs using complex astrophysical models of these regions remains a complicated challenge due to potentially degenerate solutions and widely varying signal-to-noise ratios over the map. We propose a Bayesian framework to infer the probability distributions associated to each of these physical parameters, taking a spatial smoothness prior into account to tackle the challenge of low signal-to-noise ratio regions of the observed maps. A numerical astrophysical model of the cloud is involved in the likelihood within an approximate Bayesian computation (ABC) method. This enables to both infer pointwise estimators (e.g., minimum mean square or maximum a posteriori) and quantify the uncertainty associated to the estimation process. The benefits of the proposed approach are illustrated based on noisy synthetic observation maps.