2020A&A...638A..99S

Context. Isotopologue line intensity ratios of circumstellar molecules have been widely used to trace the photospheric elemental isotopic ratios of evolved stars. However, depending on the molecular species and the physical conditions of the environment, the isotopologue ratio in the circumstellar envelope (CSE) may deviate considerably from the stellar atmospheric value.
Aims. In this paper, we aim to examine how the ¹²CO/¹³CO and H¹²CN/H¹³CN abundance ratios vary radially due to chemical reactions in the outflows of asymptotic giant branch (AGB) stars and the effect of excitation and optical depth on the resulting line intensity ratios. We study both carbon-rich (C-type) and oxygen-rich (O-type) CSEs.
Methods. We performed chemical modeling to derive radial abundance distributions of our selected species in the CSEs over a wide range of mass-loss rates (10^–8<M<10^–4M_☉/yr). We used these as input in a non-local thermodynamic equilibrium radiative transfer code to derive the line intensities of several ground-state rotational transitions. We also test the influence of stellar parameters, physical conditions in the outflows, the intensity of the interstellar radiation field, and the importance of considering the chemical networks in our model results.
Results. We quantified deviations from the atmospheric value for typical outflows. We find that the circumstellar value of ¹²CO/¹³CO can deviate from its atmospheric value by up to 25-94% and 6-60% for C- and O-type CSEs, respectively, in radial ranges that depend on the mass-loss rate. We show that variations of the intensity of the interstellar radiation field and the gas kinetic temperature can significantly influence the CO isotopologue abundance ratio in the outer CSEs of both C-type and O-type. On the contrary, the H¹²CN/H¹³CN abundance ratio is stable throughout the CSEs for all tested mass-loss rates. The radiative transfer modeling shows that the integrated line intensity ratio I12^CO/I13^CO_ of different rotational transitions varies significantly for stars with mass-loss rates in the range from 10^–7 to 10^–6M_☉/yr due to combined chemical and excitation effects. In contrast, the excitation conditions for the HCN isotopologues are the same for both isotopologues.
Conclusions. We demonstrate the importance of using the isotopologue abundance profiles from detailed chemical models as inputs to radiative transfer models in the interpretation of isotopologue observations. Previous studies of circumstellar CO isotopologue ratios are based on multi-transition data for individual sources and it is difficult to estimate the errors in the reported values due to assumptions that are not entirely correct according to this study. If anything, previous studies may have overestimated the circumstellar ¹²CO/¹³CO abundance ratio. The use of the HCN molecule as a tracer of C isotope ratios is affected by fewer complicating problems, but we note that the corrections for high optical depths are very large in the case of high-mass-loss-rate C-type CSEs; and in O-type CSEs the H¹³CN lines may be too weak to detect.