Exploring the Limits of Spectral Line Stacking in Spectral Line Data and Application toward the Detection of Bulk 13 C Enrichment of Aromatics in TMC-1

The formation history of polycyclic aromatic hydrocarbons (PAHs) in the interstellar medium remains a topic of active debate, with proposed mechanisms ranging from high-temperature stellar ejecta processes to low-temperature chemistry within molecular clouds. Recently, the identification of small PAHs in the cold, dark cloud TMC-1 has provided some circumstantial evidence of the latter. If these are formed in situ, their isotopic ratios, particularly 12 C/ 13 C, should reflect the local, bulk material of the molecular cloud; in contrast, PAHs formed in the circumstellar envelopes of evolved stars may show enhanced 13 C abundances. The expected radio signals of these 13 C substituted species will be faint, and thus we conducted a detailed proof-of-concept analysis examining whether spectral line stacking and matched filtering techniques can robustly retrieve signal from multiple singly substituted 13 C isotopologues in aggregate. We find that while retrieved signal decreases in the limit of spectral line confusion, false positive detections are exceedingly improbable at the adopted 5 σ matched filter response detection threshold. We then demonstrate the technique on actual observational data of isotopologues of HC 9 N toward TMC-1. Finally, we show using synthetic data that if laboratory rotational spectra of all singly substituted 13 C isotopologues of cyanonaphthalene and cyanopyrene isomers existed, current observations of TMC-1 would be sensitive enough to discriminate between a local, bulk 12 C/ 13 C ratio and one with an enhanced 13 C abundance suggestive of inheritance.