Prescriptions for v_in, v_out, and v_DBz normalized by the sound speed as a function of β. The solid blue line is supposed to represent a disk where the magnetic flux’s advection by turbulent accretion is more efficient than diffusion at large β. The dashed blue line gives v_in(β) in the case where the magnetic flux’s advection by turbulent accretion is less efficient than diffusion at large β as studied in Sect. 3.2. The dotted black line gives the value of β_eq.