Variation of column density with excitation temperature, T_ex. The y-axis shows the T_ex-dependent parameters in Eq. (1) normalized to T_ex = 10 K. For ¹³CO(2 − 1), we can see that the difference between the assumption of T_ex = 10 K and 40 K (which is the temperature estimated by the detailed work of Torii et al. (2010a) is ~ 10%. Most of the species in the 3-mm molecular transitions show a factor of less than two if we increase the T_ex at 40 K, with the exception of CH₃ OH which is highly dependent of the T_ex; and OCS and HC₃N.