UV dose rates in Parsamian cometary nebulae: cosmic-ray-induced energetic processing of C2H2, H2CO, and CH3OH

We quantify absorbed UV dose rates for acetylene (C₂H₂), formaldehyde (H₂CO), and methanol (CH₃OH) in Parsamian cometary nebulae (Pa 13 and Pa 21) under two physical scenarios: a static molecular cloud (\(n(\mathrm{H}_{2}) = 10^{3}\text{ cm}^{-3}\)) and a gravitationally collapsing core (\(n(r) \propto r^{-1.5}\), from \(10^{18}\) to \(10^{14}\text{ cm}\)). The energy source is the internal UV field from cosmic-ray (CR) excitation of H₂ via the Prasad–Tarafdar mechanism (parametrized following Padovani et al. 2024, validated with cloudy C25), with secondary electrons (\({\sim }30\text{--}50\text{ eV}\)) dominating at \(r \leq 10^{14}\text{ cm}\) (\(n \geq 10^{9}\text{ cm}^{-3}\)). Integrated over \(10^{6}\) years, doses reach \({\sim }10^{3}\text{ eV}\,\text{molecule}^{-1}\) (static) and exceed \(10^{4}\text{ eV}\,\text{molecule}^{-1}\) (collapsing), several orders of magnitude above the single-electron reaction threshold for glycine formation and within the energetically permissive regime identified in laboratory ice-irradiation studies, enabling isoprene (C₅H₈) precursor formation via acetylene polymerization. The C₂H₂/CH₃OH abundance ratio is the key diagnostic separating the prebiotic (isoprene) from the carbonaceous (PAH) pathway, placing Pa 13 and Pa 21 within the regime for complex prebiotic chemistry.