Plasma (solid black) and neutral (dashed) densities with height for ξ_n0 = 0.9 (red), 0.99 (blue), and 0.999 (green). The MHD density is given by the black line and the plasma component of the two-fluid simulation is identical to the MHD density profile. The vertical line indicate the β_v point (where c_s = v_A) for the plasma species (and MHD) only. The coloured vertical lines show the β_vt points using the total densities (ρ_n + ρ_p), that is, c_st = v_At.