Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. II. Vertical-net-flux regime

Abstract

The inner regions of protoplanetary discs, which encompass the putative habitable zone, are dynamically complex, featuring a relatively well-ionised, turbulent active zone located interior to a poorly ionised 'dead' zone. In this second paper, we investigate a model of the magnetohydrodynamic processes around the interface between these two regions, using five three-dimensional global magnetohydrodynamic simulations of discs threaded by a large-scale poloidal-net-flux magnetic field. We employ physically motivated profiles for Ohmic resistivity and ambipolar diffusion, alongside a simplified thermodynamic model comprising a cool disc and hot corona. Our results show that, first, the interface acts as a one-way barrier to inward transport of large-scale magnetic flux from the dead zone. This leads to magnetic flux depletion throughout most of the active zone, whereby it either advects inwards to the inner numerical boundary or accumulates just inside the interface. Second, two sources of strong variability emerge from the interface due to the difficulty of maintaining a constant, vertically integrated electrical current across distinct and evolving magnetic-field states. Third, despite the weak magnetothermal wind in the dead zone, a pressure maximum forms at the interface, leading to Rossby-wave-induced vortices. Fourth, unlike the model of Iwasaki et. al (2024), there is no 'transition zone' devoid of magnetic flux and magnetic winds. Instead, multiple outflow zones span all disc radii reflecting the radially varying launch conditions, with an inner turbulent wind impinging upon an outer, more laminar one. Fifth, a heated corona prevents the 'puffing up' of poloidal-net-flux, active disc regions.

Figures (31)

• Figure 1: Meridional $(R,z)$ plots of the prescribed target temperature $T_\text{eff}/T_0$ (left), ambipolar Elsässer number $\Lambda_\text{A}$ (middle) and magnetic Reynolds number $\text{R}_\text{m}$ (right) for NF-BAZ, as outlined in Section \ref{['section:inner_disc_model']}. The initial magnetic field configuration, which is defined in equation \ref{['eqn:inital_magnetic_field']}, is exhibited through certain magnetic field lines in the left panel (white arrowed lines), and the dashed black lines denote the disc--corona transition. Meanwhile, the dashed white lines delineate the following empirically derived stratified net-flux stability conditions for the MRI; R$_\text{m}\lesssim \sqrt{\beta} \sim 10^{2}$latter_vertical_2022 and $\Lambda_\text{A}\lesssim 1$bai_effect_2011simon_turbulence_2013, which is less certain. For clarity, the non-ideal MHD diffusivities are limited to $10^6$, and the Ohmic-resistive inner radial buffer region is not shown.
• Figure 2: Meridional $(R,z)$ plots of the numerical grid in the upper half-plane, showing the inner regions for NF-BAZ (left) and NF-SAZ (right), with $R_{\text{DZI}}$ normalised to $1\,\text{au}$. The inner radial edge of the domain is $R_{0}=1$ in code units, whilst the buffer zone (red region) extends to $r_{\text{buf}}$ (see Table \ref{['table:list_net_flux_global_simulations']}). The bold line denotes the disc--corona temperature transition at $|z|=4H$, beyond which the grid is geometrically stretched in the $\theta$ direction. The meshes are plotted by every eight cells in both directions for illustrative purposes.
• Figure 3: Zoomed-in rendering of an azimuthally extended model of NF-BAZ at $t_{\text{in}}=300$, comprising three components. First, a midplane cut reveals the toroidal field structure, $B_\phi$, and the small inner MRI-active zone, which extends to $R_{\text{DZI}} = 10R_0 = 1\,\text{au}$. Second, a spherical wedge, which defines the domain shape of NF-BAZ, shows the density $\rho$. Third, two magnetic field lines are traced from $R_\text{f} = 0.5\,\text{au}$ (white) and $R_\text{f} = 1.5\,\text{au}$ (black), exhibiting the highly helical field geometry essential for weak-magnetic-wind launching.
• Figure 4: Evolution of the total Maxwell $\alpha$ in the active zone for NF-BAZ (black) and NF-SAZ (red), volume-averaged over: $r\!\in\![0.5,0.7]$ au, $\theta\!\in\![z=2H, z=-2H]$ and $\phi\!\in\![0,\pi/2]$. $\alpha_\mathcal{M}$ decays as magnetic flux is depleted from the region and $t_{R=0.6\,\text{au}}$ is the number of local orbits at $R=0.6\,\text{au}$.
• Figure 5: Space--time $(\theta,t)$ diagrams along the contour $r=0.75\,\text{au}$ for the normalised azimuthally averaged toroidal field, $R\langle B_\phi \rangle_\phi$, showing similar evolution in the active zone for NF-BAZ (top) and NF-SAZ (bottom). To aid the comparison, $t_{R=0.75\,\text{au}}$ is the number of local orbits at $R=0.75\,\text{au}$.