tokens: field, while higher density regions become dominated by an interplay between the action of gravity and magnetic fields. Similarly to the left-hand panel of Fig. 11 , the right-hand panel shows the HRO curves for two self-gravitating models, and . This was evaluated over the last output of these models, when t = 0.3 t ff (see the right-hand side of Fig. 1 which shows the filamentary 3D distributions for these models). Compared to the models that do not include self-gravity, there is an enhancement in the number of regions perpendicular to the magnetic field at higher densities. With the action of gravity, even the super-Alfvénic model shows a change in the number of counts of cos φ = ±1.0. The critical density (vertical green dashed line in Fig. 12 ) seems to be related to the densest bins, for models with sonic Mach numbers and 7.0. There is a jump in the values of density between the penultimate and last points in the diagrams that comes from the density range considered in the bins (as can be seen in Fig. 11 , the 20th bin has a wider range of densities compared to the 19th). In the super-Alfvénic case, the penultimate point is very close to ρ c for all times considered, while in the sub-Alfvénic case the penultimate point approaches ρ c as the system evolves. Tracing the critical density of a system using the PRS is an interesting possibility, and the exact relation between the two can be further explored following the evolution of the alignment between structures and the magnetic field at smaller scales and at latter times of the collapse. However due to the lack of an adaptive mesh with increasing resolution in the densest regions in our models, this is out of the scope of this work. Still, the results discussed up to this point are very similar to what was shown in the previous section for models without self-gravity. We note that self-gravity does increase the number of denser regions where is parallel to the gradient of density in the sub-Alfvénic models, but it has little or no effect when it comes to the simulations with . At smaller scales this is probably not true, since we expect that magnetic fields should be brought along with the fluid during collapse, at some point these cores must become sub-Alfvénic and once again would influence how the gas collapses. However, the simulations do not have enough resolution to follow the process up to this point. In order to compare the simulations with observations we need once again to integrate along a defined LOS. We will follow same directions used in Section 3.1.1 . Figs 13 and 14 show the PRS analysis ( Z 2D ) for the integrated density (column density) distribution along the three different LOSs. As in Figs 8 (for initial ) and 9 (for initial ), the left-hand column represents the LOS perpendicular to the initial magnetic field, the middle column shows Z 2D for a LOS making an angle of 45° with respect to the initial field, and the right-hand column is for a LOS parallel to the
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