The hyperfine transitions of the ground-rotational state of the hydroxyl radical (OH) have emerged as a versatile tracer of the diffuse molecular interstellar medium. We present a novel automated Gaussian decomposition algorithm designed specifically for the analysis of the paired on-source and off-source optical depth and emission spectra of these transitions. In contrast to existing automated Gaussian decomposition algorithms, AMOEBA (Automated MOlecular Excitation Bayesian line-fitting Algorithm) employs a Bayesian approach to model selection, fitting all 4 optical depth and 4 emission spectra simultaneously. AMOEBA assumes that a given spectral feature can be described by a single centroid velocity and full width at half-maximum, with peak values in the individual optical depth and emission spectra then described uniquely by the column density in each of the four levels of the ground-rotational state, thus naturally including the real physical constraints on these parameters. Additionally, the Bayesian approach includes informed priors on individual parameters which the user can modify to suit different data sets. Here we describe AMOEBA and evaluate its validity and reliability in identifying and fitting synthetic spectra with known parameters.
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