Calculating the Excitation Temperature for H_2CO 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 H_(2)CO 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 H_(2)CO,two equations with two unknowns may be used to determine the excitation temperature T_(ex)and the optical depthτ,if other parameters can be determined from measurements.Published observational data of the4.83 GHz(λ=6 cm)H_(2)CO(1_(10)-1_(11))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 H110αemission of the H II regions in M17 and DR17 and with the H_(2)CO(1_(10)-1_(11))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.