Ratio of the mass estimated with our numerical model to that computed by URQ18 for the compact sources identified in the ATLASGAL survey (black dots). The input parameters are taken from URQ18. For our estimates, we assumed two template cases: q = −0.4, p = −1.5 (top panel) and q = −0.54, p = −2.6 (bottom panel). The red and blue dots indicate, respectively, the contribution of opacity and RJ approximation to the mass ratio, with the horizontal lines denoting the corresponding mean values for the black dots (0.64 top panel; 0.25 bottom panel), red dots (1.01 top panel; 1.07 bottom panel), and blue dots (0.87 top panel; 0.72 bottom panel). The green line is the factor (0.74 top panel; 0.33 bottom panel) taking into account temperature and density gradients (see text for a detailed explanation).