2D cross sections of the y = 0 plane time-averaged over ∼5 ms for our most strongly magnetized models with B_P = 3 × 10¹⁵ G, for three different spin periods (left to right) P = 18 ms, P = 1.8 ms, and P = 1 ms. Top: Rest-mass density ρ (z > 0) and net neutrino-heating rate ﹩{\dot{q}}_{{\rm{net}}}\equiv {\dot{q}}_{+}-{\dot{q}}_{-}﹩ (z < 0). White shading represents regions of net cooling, and red contours denote the electron antineutrino sphere (﹩{\tau }_{{\bar{\nu }}_{e}}\,\simeq \,2/3﹩). Bottom: Radial three-velocity v^r (z > 0) and magnetization σ = b²/4πρ (z < 0). The blue (outer) contour denotes the Alfvén surface (where the radial Alfvén velocity ﹩{v}_{{\rm{A}}}^{r}={v}^{r}﹩), whereas the brown (inner) contour denotes the slow magnetosonic surface.