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CO isotopologue transitions are routinely observed in molecular clouds toprobe the column density of the gas, the elemental ratios of carbon and oxygen,and to trace the kinematics of the environment. We aim at estimating theabundances, excitation temperatures, velocity field and velocity dispersions ofthe three main CO isotopologues towards a subset of the Orion B molecularcloud. We use the Cramer Rao Bound (CRB) technique to analyze and estimate theprecision of the physical parameters in the framework oflocal-thermodynamic-equilibrium excitation and radiative transfer with anadditive white Gaussian noise. We propose a maximum likelihood estimator toinfer the physical conditions from the 1-0 and 2-1 transitions of COisotopologues. Simulations show that this estimator is unbiased and efficientfor a common range of excitation temperatures and column densities (Tex > 6 K,N > 1e14 - 1e15 cm-2). Contrary to the general assumptions, the different COisotopologues have distinct excitation temperatures, and the line intensityratios between different isotopologues do not accurately reflect the columndensity ratios. We find mean fractional abundances that are consistent withprevious determinations towards other molecular clouds. However, significantlocal deviations are inferred, not only in regions exposed to UV radiationfield but also in shielded regions. These deviations result from thecompetition between selective photodissociation, chemical fractionation, anddepletion on grain surfaces. We observe that the velocity dispersion of theC18O emission is 10% smaller than that of 13CO. The substantial gain resultingfrom the simultaneous analysis of two different rotational transitions of thesame species is rigorously quantified. The CRB technique is a promising avenuefor analyzing the estimation of physical parameters from the fit of spectrallines.

astronomy and astrophysics

C18O, 13CO, and 12CO abundances and excitation temperatures in the Orion  B molecular cloud: An analysis of the precision achievable when modeling  spectral line within the Local Thermodynamic Equilibrium approximation