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Fig. 7

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Cumulative mass m(r) vs. the three-dimensional radius r for the gas initially (plain symbols) and the stars at t = 2 Myr (open symbols) with density indices p0 quoted in the key. For a power-law density profile of index p0 (Eq. (1)), the slope of the mass distribution in the r − m(r) space is 3 − p0 (Eq. (21)). The steeper density profiles of the stellar component thus lead to r − m(r) relations shallower than their initial gas analogs (i.e. 3 − q vs. 3 − p0). Note that the slope of the stellar tracks get steeper towards the clump centre due to the shallower stellar density profiles there. The dash-dotted symbol-free line has a slope of 0.5, as expected for the r − m(r) relation of the stellar component in the low-density regime when p0 = 1.7, i.e. 3 − q ≃ 3−3p0/2 = 0.5. While it indeed fits the model with p0 = 1.7 well in the clump ’s outer regions (green open symbols; r ≳ 1 pc), the deviation increases towards the clump centre as the stellar density profile gets shallower than q = 3p0/2 (see middle panel of Fig. 1).

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