Optical depth of p–H₂CO (3_0,3–2_0,2) as a function of n(H₂)-N(p–H₂CO) for a fix value of T_kin. The color hexagonally binned distributions display the PyRADEX+MCMC constrained n(H₂) and N(p–H₂CO) of our sources. The black solid curves show the optical depth of τ = 1 and 5 for p–H₂CO (3_0,3–2_0,2) transition on top of n(H₂) and N(p–H₂CO) space, assuming fixed kinetic temperature of 66 K (the median temperature of our sample; left panel) and 200 K (higher temperature; right panel). The blue dashed curves indicate the contour corresponding to the brightest, average, and faintest observed intensities for p–H₂CO (3_0,3–2_0,2) transition (see the text).