NH₃ inversion line ratios as a function of the H₂ density (n_H2) and kinetic temperature (T_kin). The red and blue lines mark the (2,2)/(1,1) and (6,6)/(4,4) line ratios, respectively, obtained from the large velocity gradient model outlined in Sect. 4. Dashed lines show the line ratios measured with the GBT. [NH₃]/(dv/dr) = 10^-8 pc (km s^-1)^-1 ([NH₃]  = N(NH₃)/N(H₂) is the fractional abundance of ammonia). At high densities the (1,1) and (2,2) lines saturate, which causes the steeply declining T_kin values with rising density for a given (2,2)/(1,1) line ratio.