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tokens: is not excluded when taking into account the noise level, but we do see a systematic trend across the velocity: a dip in the estimated α + around the [C II ] peak at position 1 and a gradient at 235–240 km s −1 at position 5. In addition, the estimated α + of 20–30 is lower than the measured 12 C/ 13 C in N159 ( Johansson et al. 1994 ). Therefore, the scenario of optically thick [ 12 C II ] discussed in Sect. 4.1 is more likely. Fig. 3. Estimate of α + = 12 C + / 13 C + when assuming [ 12 C II ] is optically thin. Asterisks indicate the derived α + together with the error bars. Blue lines show the [C II ] emission profiles. 4.3. Fractionation Because the fractionation reaction from 13 C + to 12 C + is an exothermal reaction (the exothermicity is 35 K; Langer et al. 1984 ), 13 C + tends to be underabundant with respect to 12 C + at low temperatures, namely at higher A V in a PDR. Röllig Ossenkopf (2013) calculated the fractionation in the clump integrated intensity of [ 12 C II ] and [ 13 C II ], and showed that only models with low UV fields ( χ ≤ 100) and high densities ( n ≥ 10 5 cm −3 ) trace the chemical fractionation, which would result in α α + , and that the derived [ 12 C II ] optical depth is a lower limit. On the other hand, it is unlikely that the fractionation is significant in the regions in this study because the estimated PDR properties are either low density and low UV field, or high density and high UV field ( Okada et al. 2019 ). 4.4. Metallicity effect Model predictions do not indicate a clear metallicity dependence of the [C II ] optical depth. For a high density PDR clump where the C + layer consists of a thin surface, the surface brightness of the [C II ] emission is almost constant with the metallicity ( Röllig et al. 2006 ) because the surface brightness is proportional to the thickness of the layer and the density of C + ions, with the former being proportional to the inverse of the metallicity due to the dust extinction and the latter being proportional to the metallicity as a first-order approximation. The derived optical depths in the LMC regions are similar to those of some Galactic regions (M 43 and Horsehead measured by Guevara et al. 2019 ); however, this study does not provide enough statistics to conclude that we do not see a metallicity dependence in the [C II ] optical depth. 4.5. Implications for the interpretation of the [C II] intensity The impact of the optical depth effect depends strongly on the actual geometry of the sources. Most PDR models compute the [C II ] intensity emerging from the surface of an externally illuminated clump or a face-on plane-parallel structure. For this geometry the radiative transfer computation takes the optical depth correctly into account. However, when the [C II ] emission stems from a mixture of components including surfaces illuminated from the back (negative temperature gradient toward the observer) or an ensemble of clumps we can no longer simply sum up the intensity