2019ApJ...877..154Y

We present observations of the C-band 1₁₀-1₁₁ (4.8 GHz) and Ku-band 2₁₁-2₁₂ (14.5 GHz) K-doublet lines of H₂CO and the C-band 1₁₀-1₁₁ (4.6 GHz) line of H₂¹³CO toward a large sample of Galactic molecular clouds, through the Shanghai Tianma 65 m radio telescope (TMRT). Our sample with 112 sources includes strong H₂CO sources from the TMRT molecular line survey at C-band and other known H₂CO sources. All three lines are detected toward 38 objects (43 radial velocity components) yielding a detection rate of 34%. Complementary observations of their continuum emission at both C- and Ku-bands were performed. Combining spectral line parameters and continuum data, we calculate the column densities, the optical depths and the isotope ratio H₂¹²CO/H₂¹³CO for each source. To evaluate photon trapping caused by sometimes significant opacities in the main isotopologue's rotational mm-wave lines connecting our measured K-doublets, and to obtain ¹²C/¹³C abundance ratios, we used the RADEX non-LTE model accounting for radiative transfer effects. This implied the use of the new collision rates from Wiesenfeld & Faure. Also implementing distance values from trigonometric parallax measurements for our sources, we obtain a linear fit of ¹²C/¹³C = (5.08 ± 1.10)D_GC + (11.86 ± 6.60), with a correlation coefficient of 0.58. D_GC refers to Galactocentric distances. Our ¹²C/¹³C ratios agree very well with the ones deduced from CN and C¹⁸O but are lower than those previously reported on the basis of H₂CO, tending to suggest that the bulk of the H₂CO in our sources was formed on dust grain mantles and not in the gas phase.