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tokens: In agreement with this trend, shows a slow first core outflow; Fig. 9 shows the radial velocity in a slice through the first core at ρ max ≈ 10 −7 g cm −3 . Although a similar ‘X’-shaped pattern is visible for all the non-ideal MHD models, the pattern in has only a narrow band of gas that is slowly outflowing ( r ≲ 0.3 km s −1 ), while the surrounding material is falling at a slightly faster rate; the gas is accreting faster along both the equatorial and polar directions than along the diagonals. Given the high angular momentum in the disc of , outflows are not required to carry angular momentum away. Figure 9. Radial velocity in a slice through the first core for each of the calculations. The white contour is r = 0. There are no first core outflows in the purely hydrodynamics model, and there are narrow, slow outflows embedded in the centre of the diagonal infall of . By contrast, as the ionization rate is decreased for the models with , the speed of the first core outflows increases and broadens. In all cases, the lower ionization rate reduces the magnetic field strength that accounts for the broadening of the outflows. Thus, at any given ζ cr , the difference in outflow speed is necessarily a result of the Hall effect. 1 In the models with , the Hall effect spins down the gas above and below the first core, which reduces the toroidal component of the magnetic field. As previously shown (e.g. Bate et al. 2014 , WBP2018 ), lower ratios of toroidal-to-poloidal magnetic field strengths result in faster outflows. Shortly after the formation of the first core, the trend of decreasing ratios of toroidal-to-poloidal magnetic field strengths corresponds to increasing outflow speeds. Vaytet et al. ( 2018 ) modelled the collapse through the first and stellar core phases using ζ cr = 10 −17 s −1 , however, their model included only ambipolar diffusion and Ohmic resistivity. They found no first core outflows, akin to our but contrary to . Their model had an initial m = 2 perturbation and an initial faster rotation. Thus, their initial conditions promoted disc formation and hence they found results similar to our , in which the Hall effect is responsible for promoting disc formation. 4.5 Counter-rotating envelopes During the first core phase, a counter-rotating envelope forms in , and at its most massive contains ∼10 −3 M ⊙ and extends to r ∼ 30 au. The counter-rotating envelope dissipates with time and disappears completely by ρ max ≈ 2 × 10 −9 g cm −3 , just before the disc forms. This envelope is smaller and less vertically extended than those found by Tsukamoto et al. ( 2015b , 2017 ). Their initially stronger magnetic field strength and faster rotation likely required the larger envelope at larger radii to conserve angular momentum. Thus, counter-rotating envelopes are likely a transient feature, with their properties dependent on the Hall effect, ionization rates (e.g. Wurster, Bate Price 2018b ), and initial conditions. 5 SUMMARY AND CONCLUSION