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  1. Abstract We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback and magnetic fields, to investigate the effectiveness of different fitting methods for volume and column density probability distribution functions (PDFs). The first method fits a piecewise lognormal and power-law (PL) function to recover PDF parameters such as the PL slope and transition density. The second method fits a polynomial spline function and examines the first and second derivatives of the spline to determine the PL slope and the functional transition density. The first PL (set by the transition between lognormal and PL function) can also be visualized in the derivatives directly. In general, the two methods produce fits that agree reasonably well for volume density but vary for column density, likely due to the increased statistical noise in the column density PDFs as compared to the volume density PDFs. We test a well-known conversion for estimating volume density PL slopes from column density slopes and find that the spline method produces a better match (χ2of 3.34 versusχ2of 5.92), albeit with a significant scatter. Ultimately, we recommend the use of both fitting methods on column density data to mitigate the effects of noise. 
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  2. Abstract We study the evolution of populations of binary stars within massive cluster-forming regions. We simulate the formation of young massive star clusters within giant molecular clouds with masses ranging from 2 × 104to 3.2 × 105M. We use Torch, which couples stellar dynamics, magnetohydrodynamics, star and binary formation, stellar evolution, and stellar feedback through the Amuseframework. We find that the binary fraction decreases during cluster formation at all molecular cloud masses. The binaries’ orbital properties also change, with stronger and quicker changes in denser, more massive clouds. Most of the changes we see can be attributed to the disruption of binaries wider than 100 au, although the close binary fraction also decreases in the densest cluster-forming region. The binary fraction for O stars remains above 90%, but exchanges and dynamical hardening are ubiquitous, indicating that O stars undergo frequent few-body interactions early during the cluster formation process. Changes to the populations of binaries are a by-product of hierarchical cluster assembly: most changes to the binary population take place when the star formation rate is high, and there are frequent mergers between subclusters in the cluster-forming region. A universal primordial binary distribution based on observed inner companions in the Galactic field is consistent with the binary populations of young clusters with resolved stellar populations, and the scatter between clusters of similar masses could be explained by differences in their formation history. 
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  3. Mass segregation is seen in many star clusters, but whether massive stars form in the center of a cluster or migrate there dynamically is still debated.N-body simulations show that early dynamical mass segregation is possible when sub-clusters merge to form a dense core with a small crossing time. However, the effect of gas dynamics on both the formation and dynamics of the stars could inhibit the formation of the dense core. We aim to study the dynamical mass segregation of star cluster models that include gas dynamics and selfconsistently form stars from the dense substructure in the gas. Our models use the TORCH framework, which is based on AMUSE and includes stellar and magnetized gas dynamics, as well as stellar evolution and feedback from radiation, stellar winds, and supernovae. Our models consist of three star clusters forming from initial turbulent spherical clouds of mass 104, 105, 106Mand radius 11.7 pc that have final stellar masses of 3.6 × 103M, 6.5 × 104M, and 8.9 × 105M, respectively. There is no primordial mass segregation in the model by construction. All three clusters become dynamically mass segregated at early times via collapse confirming that this mechanism occurs within sub-clusters forming directly out of the dense substructure in the gas. The dynamics of the embedded gas and stellar feedback do not inhibit the collapse of the cluster. We find that each model cluster becomes mass segregated within 2 Myr of the onset of star formation, reaching the levels observed in young clusters in the Milky Way. However, we note that the exact values are highly time-variable during these early phases of evolution. Massive stars that segregate to the center during core collapse are likely to be dynamically ejected, a process that can decrease the overall level of mass segregation again. 
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    Free, publicly-accessible full text available March 1, 2026