Effect of the total disk gas mass on the equilibrium solution when varying the parameter M_disk from 0.005 M_⋆ (gas-poor disk) to 0.10 M_⋆ (gas-rich disk close to the GI limit): The case M_disk = 0.005 M_⋆ is shown in blue, M_disk = 0.01 M_⋆ in dark orange, M_disk = 0.05 M_⋆ in green (fiducial model), and M_disk = 0.10 M_⋆ in red. The panels show the various steady-state profiles of some key quantities, for the model parameters M_⋆ = 1 M_⊙, L_⋆ = 2 L_⊙, a_dust =1 μm, f_dg = 10⁻², and α_hydro = 10⁻⁴. Panel a: pressure-weighted vertically integrated turbulent parameter, (Eq. (6)). Panel b: gas surface density, Σ_gas (Eq. (42)). Panel c: mid-plane total ionization rate, ζ (Eq. (10)). Panel d: mid-plane optimal r.m.s. magnetic field strength, B, that is required for the MRI activity to be at the maximal efficiency as permitted by Ohmic resistivity and ambipolar diffusion. Panel e: accretion rate, Ṁ_acc (Eq. (43)). Panel f: mid-plane radial dead zone outer edge location, R_DZ, defined as the mid-plane radial location where both the Ohmic and ambipolar condition are met for the first time (Sect. 3.1). The dashed black lines in panels e and f correspond to a power-law fit of Ṁ_acc and R_DZ as a functionof M_disk, respectively.