c-C3H2 deuteration towards prestellar and starless cores in the Perseus Molecular Cloud

Deuterium fractionation becomes highly efficient in cold, dense cores where CO is frozen out. Cyclopropenylidene (c-C3H2), an early-formed carbon ring, and its deuterated isotopologues trace gas-phase deuteration in these environments. We present a statistical study of c-C3H2 deuteration in starless and prestellar cores of the Perseus Molecular Cloud using observations of c-C3H2, c-C3HD and c-C3D2 obtained with the Yebes 40 m, ARO 12 m and IRAM 30 m telescopes towards 16 cores. Gaussian fits and RADEX modeling yield column densities for the detected species. c-C3H2 is detected in 14/15 covered cores, c-C3HD in 15/16, and c-C3D2 in 9/16. Derived column densities range from 0.5-8.1 x 10^{13} cm^{-2} for c-C3H2, 0.2-2.1 x 10^{12} cm^{-2} for c-C3HD, and 0.6-1.6 x 10^{11} cm^{-2} for c-C3D2. The ortho-to-para ratio of c-C3H2 is obtained for all but one core, with a median value of 3.5\pm0.4. Statistically corrected D/H ratios span 0.5-9.2% (median 1.5\pm0.2%), and D2/D ratios 9-55% (median 25.9\pm4.3%). No trend is found between the c-C3H2 ortho-to-para ratio and core evolutionary stage traced by n(H2). The median D/H ratio in Perseus appears lower than values reported for Taurus and Chamaeleon, while the D2/D ratio agrees with Taurus within uncertainties. A positive correlation between D/H and n(H2) supports the use of D/H as an evolutionary tracer. D2/D does not correlate with n(H2), but shows a positive correlation with T_{kin}, suggesting that its formation is influenced by a mildly endothermic pathway.