Calculating the Excitation Temperature for H2CO Absorption Lines in Molecular Clouds

The excitation temperature Tex 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 Tex, 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 Tex 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 Tex 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 Tex 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.