HN¹²C/HN¹³C ratio as a function of n_H, for different temperatures, at t₁ (top right panel), t₂ (bottom left panel), and t₃ (bottom right panel). The large pink circles in the bottom panels represent the result of the model that simulates the physical conditions in the centre of the pre-stellar core B1b observed by Daniel et al. (2013). The HN¹²C/HN¹³C ratio observed by Daniel et al. (2013) is represented by the dark green star. We note that the error bar is within the symbol. In all the panels, the two vertical purple dashed lines represent the range of densities of the sample of high-mass star-forming region described in Sect. 3.2.2, and the black horizontal dashed lines represent the initial ¹²C/¹³C ratio of 68.