  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 circumstellar isotopologue ratio may deviate
considerably from the stellar atmospheric value. In this paper, we aim to
examine how the CO and HCN abundance ratios vary radially due to chemical
reactions in the outflows of AGB stars and the effect of excitation and optical
depth on the resulting line intensity ratios. We find that the circumstellar
12CO/13CO can deviate from its atmospheric value by up to 25-94% and 6-60% for
C- and O-type CSEs, respectively. We show that variations of the intensity of
the ISRF and the gas kinetic temperature can significantly influence the CO
isotopologue ratio in the outer CSEs. On the contrary, the H12CN/H13CN ratio is
stable for all tested mass-loss rates. The RT modeling shows that the
integrated line intensity ratio of CO of different rotational transitions
varies significantly for stars with intermediate mass-loss rates due to
combined chemical and excitation effects. In contrast, the excitation
conditions for the both HCN isotopologues are the same. We demonstrate the
importance of using the isotopologue abundance profiles from chemical models as
inputs to RT models in the interpretation of isotopologue observations.
Previous studies of 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 as a tracer of C
isotope ratios is affected by fewer complicating problems, provided one
accounts corrections for high optical depths.
