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tokens: 3000 au × 3000 au region of the densest collapsed core in each simulation (projections for the entire simulation domain are shown in Figure 2 ). The mean field points in the horizontal ( x ) direction. The strong-field case () shows highly elongated structure (perpendicular to the mean-field direction) and a classical hourglass magnetic field morphology aligned with the mean-field direction. The weak-field simulations () show more chaotic magnetic field morphology dictated by turbulence, with pinches and clumps. Figure 3 shows the deviation in the mean magnetic field () from its large (parsec) scale direction as a function of scale: alignment becomes poorer with weaker mean-field strengths. The degree of alignment can remain tight to the smallest scales in the strong mean-field regime. Figure 3 also shows a related quantity: the (volume) fraction of gas within a sphere of radius r (the length scale) that has a magnetic field aligned within 30° of the large-scale mean-field value (). Figure 1. Density-averaged line-of-sight magnetic field and projected gas densities zoomed in on a core in each of the simulations. The arrow in the top left represents the initial magnetic field. Figure 2. Density-averaged line-of-sight magnetic field and projected gas densities of the entire simulation domain (5.2 pc) for the four simulations. Each box is centered on the corresponding prestellar cores shown in Figure 1 . Figure 3. Top: deviation of the mean magnetic field averaged over some length scale around the core from the large (parsec) scale field. Bottom: fraction of gas inside a sphere of radius the length scale with the magnetic field aligned within 30° of the large-scale mean-field value. 4. Density Scaling of the Magnetic Field The relationship between density and magnetic field is important for theoretical models and observations. B ∝ ρ 2/3 is predicted for collapsing clouds with weak magnetic fields (i.e., gravitational energy dominating magnetic energy). The same scaling is also predicted for flux-frozen, isotropic collapse in general. Lazarian et al. ( 2012 ) interpreted the observed B ∝ ρ 2/3 from Zeeman measurements as a signature of reconnection diffusion being most efficient at lower densities (i.e., before collapse proceeds) in the weak-field limit. In contrast, theoretical predictions for anisotropic contraction models, often expected in the strong-field limit, predict a weaker scaling: B ∝ ρ 1/2 (Tritsis et al. 2015 ). We test the density magnetic field scaling relationship using our high dynamic range Arepo simulations. We plot the occupation of the gas in the density/magnetic field phase diagram for our simulations in Figure 4 . The collapse occurs where the gas is compressed by turbulence above the critical density , which is defined as the density at which the background level of turbulent pressure is subdominant to the gas pressure (Krumholz McKee 2005 ; Li et al. 2015b ). That is, the critical pressure is obtained by equating with .