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tokens: abundance of polycyclic aromatic hydrocarbons (PAHs; Geers et al. 2009 ). Because of these drawbacks and the chemical complexity, we restrict our model to EUV and X-ray dominated heating. 3 Numerical model All simulations of this paper are two-dimensional axisymmetric, including the toroidal velocity and magnetic field component (i.e., 2.5 dimensional). They were carried out with the PLUTO code (version 4.3) ( Mignone et al. 2007 , 2012 ), which allows solving the MHD equations on a spherical grid, including ohmic resistivity. Throughout this section, we present the basis of the numerical model, that is, the X-ray and EUV heating approach, disk structure, magnetic field, and dynamic treatment of ohmic diffusion. 3.1 MHD equations Relevant equations are the conservation of mass, the conservation of momentum, the energy equation, and the induction equation, where P is the thermal gas pressure, ρ the gas density, B the magnetic flux density vector, J the electric current density vector, η the ohmic diffusion coefficient, v the gas velocity vector, and the gravitational potential. To update the cells, the HLLD Riemann solver ( Miyoshi Kusano 2005 ) was used. To ensure the condition ∇ ⋅ B = 0, the divergence cleaning method ( Dedner et al. 2002 ) was applied. All simulations were evolved with an adiabatic equation of state, using an isentropic exponent of κ = 5∕3. Fig. 1 Ionization parameter–temperature relation based on the data in Picogna et al. (2019) . 3.2 Diagnostics The relativestrength of the magnetic field can be expressed with the dimensionless plasma parameter β : which is the ratio of thermal pressure over magnetic pressure. In order to evaluate the nonideal MHD effects (ohmic diffusion) on possible MRI activity, the notion of an ohmic Elsasser number Λ Ω ( Turner et al. 2007 ) is useful: Here v A is the Alfvén velocity and η the ohmic diffusion coefficient. Generally, MRI is considered to be suppressed for Λ Ω ≲ 1. The integrated mass-loss rate caused by the wind is computed by the expression and the disk region is excluded from the range in θ . Here, v R denotes the radial velocity component of the flow. 3.3 EUVand X-ray heating Following the approach of Owen et al. (2010 , 2012 , 2013 ), X-ray heating was provided by using a fitted ionization parameter - temperature relation T = f ( ξ ), taken from Picogna et al. (2019) . In addition to the previously studied models, the temperature curves depend on the local column density, as shown in Fig. 1 . Knowing the dependence of the temperature on the local variables, we traced rays from the inner simulation boundary radially outward up to column densities of 5 × 10 22 cm −2 . Within this range, the temperatures were set corresponding to the locally computed ionization parameter using the fitted relation f ( ξ ). With intermediate column densities, the temperature is linearly interpolated. The temperature adjustment was only invoked when the temperature computed by the ionization model was