2020MNRAS.497.1851S

Analysing the Galactic plane CO survey with the Nobeyama 45-m telescope, we compared the spectral column density (SCD) of N_ H₂ calculated for the ¹²CO (J = 1-0) line using the current conversion factor X_ ^12CO to that for the ¹³CO (J = 1-0) line under the LTE (local thermal equilibrium) assumption in the M16 and W43 regions. Here, SCD is defined by dN_ H₂/dv with N_ H₂ and v being the column density and radial velocity, respectively. It is found that the X_ ^12CO method significantly underestimates the H₂ density in a cloud or region, where SCD exceeds a critical value (∼3 x 10²¹ [H₂ cm^–2 (km s^–1)^–1]), but overestimates in lower SCD regions. We point out that the actual CO-to-H₂ conversion factor varies with the H₂ column density or with the CO line intensity: it increases in the inner and opaque parts of molecular clouds, whereas it decreases in the low-density envelopes. However, in so far as the current X_^12 CO^ is used combined with the integrated ¹²CO intensity averaged over an entire cloud, it yields a consistent value with that calculated using the ¹³CO intensity by LTE. Based on the analysis, we propose a new CO-to-H₂ conversion relation, N_ H₂^*=∫X_* CO_ (T_ B_) T_ B_ dv, where X_* CO_ (T_ B_)=(T B_/T B*^)β_X ^12CO is the modified spectral conversion factor as a function of the brightness temperature, T_B, of the ¹²CO (J = 1-0) line, and β ∼ 1-2 and T_ B_^*=12-16 K are empirical constants obtained by fitting to the observed data. The formula corrects for the over/underestimation of the column density at low/high CO line intensities, and is applicable to molecular clouds with T_B >= 1 K (¹²CO (J = 1-0) line rms noise in the data) from envelope to cores at sub-parsec scales (spatial resolution).