We study the abundance of CCH in prestellar cores both because of its role in the chemistry and because it is a potential probe of the magnetic field. We also consider the non-LTE behaviour of the N=1-0 and N=2-1 transitions of CCH and improve current estimates of the spectroscopic constants of CCH. We used the IRAM 30m radiotelescope to map the N=1-0 and N=2-1 transitions of CCH towards the prestellar cores L1498 and CB246. Towards CB246, we also mapped the 1.3 mm dust emission, the J=1-0 transition of N2H+ and the J=2-1 transition of C18O. We used a Monte Carlo radiative transfer program to analyse the CCH observations of L1498. We derived the distribution of CCH column densities and compared with the H2 column densities inferred from dust emission. We find that while non-LTE intensity ratios of different components of the N=1-0 and N=2-1 lines are present, they are of minor importance and do not impede CCH column density determinations based upon LTE analysis. Moreover, the comparison of our Monte-Carlo calculations with observations suggest that the non-LTE deviations can be qualitatively understood. For L1498, our observations in conjunction with the Monte Carlo code imply a CCH depletion hole of radius 9 x 10^{16} cm similar to that found for other C-containing species. We briefly discuss the significance of the observed CCH abundance distribution. Finally, we used our observations to provide improved estimates for the rest frequencies of all six components of the CCH(1-0) line and seven components of CCH(2-1). Based on these results, we compute improved spectroscopic constants for CCH. We also give a brief discussion of the prospects for measuring magnetic field strengths using CCH.
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