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Context. In cores deuterium fractionation becomes highly efficient due to low temperatures and CO freeze-out. Cyclopropenylidene (c-C₃H₂), a small cyclic molecule formed early in chemical evolution, and its deuterated forms serve as valuable tracers of gas-phase deuteration in these environments.
Aims. In order to statistically explore the c-C₃H₂ deuteration ratios towards starless and prestellar cores, we present observations of c-C₃H₂ and its deuterated isotopologues on a sample of cores in the Perseus molecular cloud.
Methods. Transitions of c-C₃H₂, c-C₃HD, and c-C₃D₂ were observed with the Yebes 40m, the Arizona Radio Observatory (ARO) 12m and the Institut de Radioastronomie Millimétrique (IRAM) 30 metre telescopes towards a total of 16 starless and prestellar cores in the Perseus molecular cloud. The lines were fitted with Gaussian profiles and their column densities were computed using the non-local thermodynamic equilibrium (non-LTE) software RADEX.
Results. The main isotopologue c-C₃H₂ is detected in 93% (14/15) of the targeted cores (for one of the 16 cores, none of its transitions were covered), its singly deuterated form c-C₃HD is detected in 94% (15/16) of the targeted cores, and its doubly deuterated form c-C₃D₂ is detected towards 56% (9/16) of the cores detected. A range of column densities towards the different cores was derived: for c-C₃H₂, (0.5-8.1)×10¹³ cm^–2; for c-C₃HD, (0.2-2.1)×10¹² cm^–2; and for c-C₃D₂, (0.6-1.6)×10¹¹ cm^–2. The ortho-to-para ratio of c-C₃H₂ was obtained for all except one core with a median value of 3.5 ± 0.4. The D/H and D₂/D ratios were obtained for the cores with detections, yielding a statistically corrected D/H range of 0.5-9.2% with a median value of 1.5 ± 0.2% and a statistically corrected D₂/D range 9.0-55.2% with a median value of 25.9 ± 4.3%.
Conclusions. No apparent trend is seen with the ortho-to-para ratio of c-C₃H₂ and the evolutionary stage of the core, as traced by volume density n_H2. The median c-C₃H₂ D/H ratio in Perseus' starless cores appears lower than the value for the Taurus molecular cloud and the Chamaeleon molecular cloud. The D₂/D ratio is equivalent between the Perseus and Taurus molecular clouds within the uncertainties. There is a correlation with the D/H ratio and the n_H2 of the cores in Perseus, strengthening the idea of D/H being a tracer of core evolution. The D₂/D ratio does not correlate with n_H2, but positively correlates with T_kin, suggesting that its formation is favoured by a slightly endothermic reaction.