LOC tests with lower volume density. Panel (a): we scaled down the volume density profile used for the results shown in Fig. 1 by a factor of 10 and scaled up the abundance profile of N₂H⁺ by a factor of 45 in the effort of reproducing the observed lines. Panel (b): we reduced the volume density profile used in Fig. 1 by a factor of 5 and scaled up the abundance profile of N₂H⁺ by a factor of 15. In both cases, we show that it is not possible to reproduce both transitions with a lower volume density by only increasing the abundance of N₂H⁺.