Mass–radius distributions for the ATLASGAL 870 μm cores. The green dots show the six cores in the small filament, while the red dots show the six cores in the large clump. The surface density of 0.024 g cm⁻² shown in green lines gives the average surface density thresholds for efficient star formation, which are derived by Lada et al. (2010) and Heiderman et al. (2010), respectively. A core with a mass surface density of >1 g cm⁻² (shown as a green line) can avoid further fragmentation and form massive stars (Krumholz & McKee 2008). We refer to the discussion about the lines in the Sect. 4.2.