Empirical correlation between the observed single-dish N₂ H⁺ intensities (Hacar et al. 2017a), normalized by the local gas kinetic temperature T_K (Friesen et al. 2017), and the total (gas + dust) column densities N(H₂ ) derived in previous Herschel-Planck measurements (Lombardi et al. 2014). This plot includes all the positions detected at R(Trapezium) ≥ 0.3 pc in both OMC-1 and OMC-2 clouds (red dots). Those points belonging to the OMC-1 region are highlighted in blue. The thick black line indicates the results of the linear fit defining Eq. (2). The green dashed line indicates the expected correlation for the observed N₂ H⁺ intensities in the NGC1333 proto-cluster assuming a constant temperature of 10 K (Hacar et al. 2017b).