The Symmetry Landscape of Cosmic Molecules: From TMC-1 to Orion KL and IRC+10216

Molecular inventories of astronomical sources are usually compared through composition, abundance, excitation, and reaction chemistry. Here we introduce a complementary group-theoretical approach in which molecular symmetry is treated as a statistical descriptor of astronomical molecular populations. Three chemically and physically distinct molecular corpora are analysed: 75 main-isotopic species from the GOTHAM inventory of the cold dark cloud TMC-1, 39 molecular species detected in the Herschel/HIFI survey of Orion KL, and 23 distinct main species obtained by collapsing isotopologues in a recent 3-mm survey of the carbon-rich circumstellar envelope IRC+10216. Each molecular carrier is assigned a point group using an equilibrium-structure, species-level convention. The resulting symmetry distributions are strongly uneven: a small number of symmetry classes and, in particular, reflection and proper axial symmetry dominate all three molecular corpora. Under the adopted classification, every species in all three corpora possesses at least one mirror plane, making reflection symmetry the most universal structural feature identified in the present census. Proper axial symmetry is likewise exceptionally prevalent: the fractions of species possessing a nontrivial proper rotational axis increase from 65.3% in TMC-1 to 79.5% in Orion KL and 95.7% in IRC+10216. Linear molecules alone constitute 44.0%, 51.3%, and 78.3% of the three corpora, respectively. Thus, the observed molecular symmetry landscape is far from uniform: mirror and axial symmetries occupy an exceptional position, whereas other symmetry types are comparatively weakly represented or absent. The persistence of reflection symmetry across a cold dark cloud, a hot high-mass star-forming region, and a radially stratified carbon-rich circumstellar envelope demonstrates that its prevalence cannot be attributed to low temperature alone. In contrast, the strong source-to-source variation of linear symmetry points to environmental chemistry and reaction-network topology as major controlling factors, with IRC+10216 providing a particularly clear example of carbon-chain growth that constructs and preserves linear molecular skeletons. We therefore propose that the strongly nonuniform symmetry distribution of an astronomical molecular inventory, and especially the exceptional prevalence of mirror and axial symmetry, can serve as a compact structural descriptor of its chemical formation history. Rotational-spectroscopic selection and conformer populations remain important limitations, and the reported distributions characterize detected molecular corpora rather than complete, bias-free molecular populations.