Calculating the Excitation Temperature for H2CO Absorption Lines in Molecular Clouds

The excitation temperature T _ex for molecular emission and absorption lines is an essential parameter for interpreting the molecular environment. This temperature can be obtained by observing multiple molecular transitions or hyperfine structures of a single transition, but it remains unknown for a single transition without hyperfine structure lines. Earlier H₂CO absorption experiments for a single transition without hyperfine structures adopted a constant value of T _ex, which is not correct for molecular regions with active star formation and H II regions. For H₂CO, two equations with two unknowns may be used to determine the excitation temperature T _ex and the optical depth τ, if other parameters can be determined from measurements. Published observational data of the 4.83 GHz (λ = 6 cm) H₂CO (1₁₀‑1₁₁) absorption line for three star formation regions, W40, M17 and DR17, have been used to verify this method. The distributions of T _ex in these sources are in good agreement with the contours of the H110α emission of the H II regions in M17 and DR17 and with the H₂CO (1₁₀‑1₁₁) absorption in W40. The distributions of T _ex in the three sources indicate that there can be significant variation in the excitation temperature across star formation and H II regions and that the use of a fixed (low) value results in misinterpretation.