Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. I. Zero-net flux regime

TL;DR

The inner regions of protoplanetary discs harbor complex interactions between MRI turbulence, non-ideal MHD diffusion, and thermodynamic stratification. The paper uses five 3D global simulations with zero-net flux to study the dead–active zone interface, revealing self-generated large-scale poloidal magnetic loops in the active zone, flux accumulation at the disc–corona transition that drives surface-layer accretion, and a vertical field morphology in the dead zone capable of launching a weak wind. It also finds a robust axisymmetric pressure maximum that sustains through several scale heights and triggers Rossby-wave instability, producing anticyclonic vortices that influence dust dynamics and angular-momentum transport. The results illuminate how magnetic flux transport, non-ideal MHD effects, and thermodynamic transitions shape the structure and evolution of the inner disc, laying groundwork for more comprehensive models including vertical-net flux, Hall physics, and dust feedback. These insights have implications for accretion variability, planetesimal formation sites, and the early evolution of planetary systems.

Abstract

The inner regions of protoplanetary discs, which encompass the putative habitable zone, are dynamically complex, featuring a well-ionised, turbulent active inner region and a poorly ionised `dead' outer region. In this first paper, we investigate a base-level model of the magnetohydrodynamic processes around the interface between these two regions, using five three-dimensional global magnetohydrodynamic simulations in the zero-net flux regime. 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, large-scale coherent poloidal magnetic field loops form in the magnetorotational instability active region. These loops lead to the accumulation of tightly wound magnetic flux at the disc-corona temperature transition, driving strong, localised accretion flows in the surface layers of the active region. Second, an axisymmetric pressure maximum, extending across multiple disc scale heights, develops as a result of outward mass transport from the active region. This, in turn, triggers the Rossby wave instability and leads to the development of anticyclonic vortices. Third, the dead zone develops magnetic field with a distinct morphology, likely resulting from the outward diffusion of the large-scale poloidal loops in the active zone. This self-consistently generated field exhibits a vertical structure that can drive accretion in the inner dead zone via a weak magnetic-pressure wind. In the second paper in the series, we extend this work to the vertical-net flux regime, where global magnetic flux transport and magnetically driven outflows become dynamically significant.

Figures (22)

• Figure 1: Meridional ($R,z$) plots of the prescribed target temperature $T_{\text{eff}}$\ref{['equation:target_temperature']} (left), ambipolar Elsässer number $\Lambda_\text{A}$ (middle), and initial magnetic Reynolds number $\text{R}_\text{m}$ (right), as described in Section \ref{['section:inner_disc_model']}. The dashed black lines in the left panel mark the disc--corona transition at $z=\pm 4H$. The dashed white lines show empirical thresholds for stratified ZNF MRI stability: R$_m\lesssim 3000$flock_turbulence_2012 and $\Lambda_\text{A}\lesssim 1$bai_effect_2011simon_turbulence_2013, which is less certain. These clearly delineate the dead--active zone interface at $R_{\text{DZI}}=4R_0=1\,\text{au}$. 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: Snapshot of ZNF-FID at $t_{\textrm{in}}=30$, showing a slice through the disc midplane embedded within a quarter-azimuthal wedge of the full domain. The toroidal magnetic field, $B_\phi$, highlights the self-consistent turbulent magnetic structures, clearly delineating the midplane location of the dead--active zone interface (black line) at $R_{\text{DZI}}=4R_0 =1$ au. Over time, a complex laminar $B_\phi$ structure extends throughout the entire dead zone (see Fig. \ref{['fig:bx3_evolution']} and Section \ref{['section:magnetic_field_structures']}). The remaining faces of the wedge show the density $\rho$, revealing the vertically stratified disc embedded into a low-density corona.
• Figure 3: Meridional $(R,z)$ plots of the normalised, azimuthally averaged toroidal field, $R\langle{B_\phi}\rangle_{\phi}$, for three snapshots of ZNF-FID: $t_{\text{in}}=0$ (left), $t_{\text{in}}=200$ (middle) and $t_{\text{in}}=700$ (right). The dashed black lines denote the disc--corona transition at $z=\pm4H$, and the dead--active zone interface is at $R=1\,\text{au}$. Note the formation of characteristic MRI-driven turbulence in the inner disc, the presence of strong tightly wound magnetic field structures in the MRI-active disc surface layers (see Section \ref{['section:vertical_accretion_structure']}), and the complex toroidal magnetic field configuration that eventually permeates the entire dead zone (see Section \ref{['section:magnetic_fields_dead_zone_overview']}).
• Figure 4: Temporal evolution of the volume-averaged total $\alpha$ (black) and Maxwell $\alpha_\mathcal{M}$ (red) in the MRI-active zone, which are larger in the higher-resolution simulation ZNF-HRES (dotted) compared to ZNF-FID (solid). The volume average is computed over the spherical wedge: $r\in[0.5,1]\,\text{au}$, $\theta \in[z=-4H, z=4H]$ and $\phi\in[0,2\pi)$.
• Figure 5: Magnetic field configuration for ZNF-FID in the active zone, averaged in azimuth and over the interval $t_{\text{in}}\in[200,700]$ to enhance the visibility of coherent field structures. The poloidal magnetic field, $\langle\mathbf{B_p}\rangle_{\phi,t}$, shown using black field lines and a LIC overlay in greyscale, forms coherent clockwise loops spanning the extent of the MRI-active region. The sign of the normalised toroidal field, $R\langle B_\phi\rangle_{\phi,t}$, (background colour) near the disc surface layers (dashed white lines), is negatively correlated with the sign of the radial magnetic field.