The rotational spectral lines of c-C3H2 and two kinds of the 13C isotopic species, c-13CCCH2 (C2v symmetry) and c-CC13CH2 (Cs symmetry), have been observed in the 1-3 mm band toward the low-mass star-forming region L1527. We have detected 7, 3, and 6 lines of c-C3H2, c-13CCCH2, and c-CC13CH2, respectively, with the Nobeyama 45 m telescope and 34, 6, and 13 lines, respectively, with the IRAM 30 m telescope, where seven, two, and two transitions, respectively, are observed with both telescopes. With these data, we have evaluated the column densities of the normal and 13C isotopic species. The [c-C3H2]/[c-13CCCH2] ratio is determined to be 310 ± 80, while the [c-C3H2]/[c-CC13CH2] ratio is determined to be 61 ± 11. The [c-C3H2]/[c-13CCCH2] and [c-C3H2]/[c-CC13CH2] ratios expected from the elemental 12C/13C ratio are 60-70 and 30-35, respectively, where the latter takes into account the statistical factor of 2 for the two equivalent carbon atoms in c-C3H2. Hence, this observation further confirms the dilution of the 13C species in carbon-chain molecules and their related molecules, which are thought to originate from the dilution of 13C+ in the gas-phase C+ due to the isotope exchange reaction: 13C+ + CO → 13CO + C+. Moreover, the abundances of the two 13C isotopic species are different from each other. The ratio of c-13CCCH2 species relative to c-CC13CH2 is determined to be 0.20 ± 0.05. If 13C were randomly substituted for the three carbon atoms, the [c-13CCCH2]/[c-CC13CH2] ratio would be 0.5. Hence, the observed ratio indicates that c-CC13CH2 exists more favorably. Possible origins of the different abundances are discussed.
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