ATLASGAL-selected massive clumps in the inner Galaxy: VI. Kinetic temperature and spatial density measured with formaldehyde

Context. Formaldehyde (H2CO) is a reliable tracer to accurately measure the physical parameters of dense gas in star-forming regions. Aim. We aim to determine directly the kinetic temperature and spatial density with formaldehyde for the ~100 brightest ATLASGAL-selected clumps (the TOP100 sample) at 870 ?m representing various evolutionary stages of high-mass star formation. Methods. Ten transitions (J = 3–2 and 4–3) of ortho- and para-H2CO near 211, 218, 225, and 291 GHz were observed with the Atacama Pathfinder EXperiment (APEX) 12 m telescope. Results. Using non-LTE models with RADEX, we derived the gas kinetic temperature and spatial density with the measured para-H2CO 321–220/303–202, 422–321/404–303, and 404–303/303–202 ratios. The gas kinetic temperatures derived from the para-H2CO 321–220/303–202 and 422–321/404–303 line ratios are high, ranging from 43 to >300 K with an unweighted average of 91 ± 4 K. Deduced Tkin values from the J = 3–2 and 4–3 transitions are similar. Spatial densities of the gas derived from the para-H2CO 404–303/303–202 line ratios yield 0.6–8.3 × 106 cm?3 with an unweighted average of 1.5 (±0.1) × 106 cm?3. A comparison of kinetic temperatures derived from para-H2CO, NH3, and dust emission indicates that para-H2CO traces a distinctly higher temperature than the NH3 (2, 2)/(1, 1) transitions and the dust, tracing heated gas more directly associated with the star formation process. The H2CO line widths are found to be correlated with bolometric luminosity and increase with the evolutionary stage of the clumps, which suggests that higher luminosities tend to be associated with a more turbulent molecular medium. It seems that the spatial densities measured with H2CO do not vary significantly with the evolutionary stage of the clumps. However, averaged gas kinetic temperatures derived from H2CO increase with time through the evolution of the clumps. The high temperature of the gas traced by H2CO may be mainly caused by radiation from embedded young massive stars and the interaction of outflows with the ambient medium. For Lbol/Mclump ? 10 L?/M?, we find a rough correlation between gas kinetic temperature and this ratio, which is indicative of the evolutionary stage of the individual clumps. The strong relationship between H2CO line luminosities and clump masses is apparently linear during the late evolutionary stages of the clumps, indicating that LH_2CO does reliably trace the mass of warm dense molecular gas. In our massive clumps H2CO line luminosities are approximately linearly correlated with bolometric luminosities over about four orders of magnitude in Lbol, which suggests that the mass of dense molecular gas traced by the H2CO line luminosity is well correlated with star formation.