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Fig. 2.

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(Left) Predictions for ϵff from turbulence-regulated SF models with a hybrid LN plus PL smooth-PDF proposed by Burkhart (2018) in the SFF (blue) or multi-free-fall (red) scenarios. In these hybrid PDFs, the transition from LN to PL behavior is set to the critical density, st = scrit, as argued by Burkhart & Mocz (2019). A range of PL slopes 1.6 < α < 2.1 set to the range observed by Kainulainen et al. (2014) and Schneider et al. (2022) are indicated by the width of each band. In this example, ϵcore = 0.5, αvir = 5, b = 0.87, and the sound speed cs = 0.3 km s−1. Following Burkhart (2018), we set ϕt = 1. Light gray points show the PHANGS measurements from Leroy et al. (2025), and the dark gray bar and point depict the Dessauges-Zavadsky et al. (2023)z ∼ 1 clumps, repeated from Figure 1. (Right) Illustration of the typical hybrid density PDFs associated with the ϵff predictions in the SFF (blue) and multi-free-fall (red) scenarios at the average cloud-scale velocity dispersion ⟨σc⟩ = 5 km s−1, corresponding to ℳ = 16.7. The blue PDF adopts a PL with slope α = 1.8, which is associated with st = 6.9 (see Eq. (11); marked by the vertical dotted blue line) given the average σc, and yields SFF ϵff predictions such as those shown in blue in the left panel. The red PDF adopts a PL with slope α = 2.7 from the range required to match MFF predictions to the observed ϵff. In this case, the PL starts at st = 11.4 (marked by the vertical dotted red line). Also shown are PDFs with properties matching those measured in local clouds by Schneider et al. (2022). Out of two LNs and two PL components identified by Schneider et al. (2022), only the primary LN and PL components are indicated. These have st = 1 − 2, marked by the narrow vertical gray band, resulting in a kinked appearance. The lighter, wider vertical gray band shows the range in st predicted using Eq. (13) given the observed properties of the plotted regions.

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