Comparison of the column density and physical conditions obtained towards the Horsehead nebula using different sets of molecular lines. The red contour delineates the pixels associated with dense cores and where H¹³CO⁺ (1 − 0) is detected at the 3σ level. When abundances or abundance ratios are fixed, the values are given in Eq. (16). Only estimations with a good reference precision (CRB) have been kept (see Eq. (21)).