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Fig. B.1

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RADEX non-LTE modeling of the relation between the kinetic temperature and the average ratio of H2CO 322−221/303−202 and 321−220/303−202 with an assumed density of n(H2)=105 cm−3 and column densities N(para-H2CO)=1.0× 1013, 6.6 ×1013, and 1.0×1014cm−2 (red, green, and blue), the LTE (cyan), and an averaged line width of 3.8 km s−1. The LTE kinetic temperature (TLTE) was determined using the methodology described in Mangum & Wootten (1993) and Tang et al. (2017b). TLTE is calculated as TLTE=47.1ln(0.556/ Ratio )  K${T_{{\rm{LTE}}}} = {{47.1} \over {\ln (0.556/{\rm{ Ratio }})}}\,\,{\rm{K}}$, where Ratio represents the average ratio of H2CO 322−221/303−202 and 321−220/303−202. The black points are derived from our observed H2CO line ratios from the DR21 filament for a column density N(para-H2CO) = 6.6 × 1013 cm−2. The temperature uncertainties are obtained from observed H2CO line ratio errors.

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