[Paper Review] Thanatology in Protoplanetary Discs: the combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones

Geoffroy Lesur, Matthew W. Kunz+1 more|Feb 17, 2014

Astrophysics and Star Formation StudiesPhysics and Astronomy68 references142 citations

TL;DR

This study presents the first 3D numerical simulations of protoplanetary discs including all three non-ideal magnetohydrodynamic effects—Ohmic dissipation, ambipolar diffusion, and the Hall effect—demonstrating that the Hall effect can revive magnetically dead zones by generating a dominant azimuthal magnetic field and large-scale Maxwell stress in the midplane. The result is a substantial increase in disc scale height and efficient angular momentum transport without requiring magnetically driven outflows, even at accretion rates ≤10⁻⁷ M☉ yr⁻¹.

ABSTRACT

Protoplanetary discs are poorly ionised due to their low temperatures and high column densities, and are therefore subject to three "non-ideal" magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the Hall effect. The existence of magnetically driven turbulence in these discs has been a central question since the discovery of the magnetorotational instability. Early models considered Ohmic diffusion only and led to a scenario of layered accretion, in which a magnetically "dead" zone in the disc midplane is embedded within magnetically "active" surface layers at distances ~1-10 au from the central protostellar object. Recent work has suggested that a combination of Ohmic dissipation and ambipolar diffusion can render both the midplane and surface layers of the disc inactive and that torques due to magnetically driven outflows are required to explain the observed accretion rates. We reassess this picture by performing three-dimensional numerical simulations that include, for the first time, all three non-ideal MHD effects. We find that the Hall effect can generically "revive" dead zones by producing a dominant azimuthal magnetic field and a large-scale Maxwell stress throughout the midplane, provided the angular velocity and magnetic field satisfy Omega.B > 0. The attendant large magnetic pressure modifies the vertical density profile and substantially increases the disc scale height beyond its hydrostatic value. Outflows are produced, but are not necessary to explain accretion rates <10^{-7} Msun/yr. The flow in the disc midplane is essentially laminar, suggesting that dust sedimentation may be efficient. These results demonstrate that, if the MRI is relevant for driving mass accretion in protoplanetary discs, one must include the Hall effect to obtain even qualitatively correct results.

Motivation & Objective

• To reassess the role of non-ideal MHD effects in magnetically dead zones of protoplanetary discs, particularly the interplay of Ohmic dissipation, ambipolar diffusion, and the Hall effect.
• To determine whether magnetically driven outflows are necessary to explain observed accretion rates in protoplanetary discs.
• To investigate the nonlinear evolution of the magnetorotational instability (MRI) when all three non-ideal MHD effects are included simultaneously.
• To evaluate the impact of the Hall effect on the vertical structure and turbulence in the disc midplane, especially under conditions of low ionization.
• To test whether the Hall effect can generate sufficient Maxwell stress to drive accretion in the absence of outflows or active surface layers.

Proposed method

• Performs three-dimensional, unstratified shearing box simulations using the Pluto code with a high-resolution grid (up to 128×32×32) to resolve small-scale dynamics.
• Implements Ohmic dissipation, ambipolar diffusion, and the Hall effect via source terms in the MHD equations, with careful treatment of boundary conditions to prevent numerical instabilities.
• Uses a monotonized centered slope limiter and second-order Runge-Kutta time integration to ensure numerical stability and reduce artificial dissipation.
• Applies conservative finite-volume methods with HLL Riemann solvers to handle shocks and discontinuities, particularly in Hall-MHD and ambipolar diffusion regimes.
• Validates the implementation against known linear and nonlinear benchmarks, including the Hall-MRI zonal field state and ambipolar-MRI growth rates.
• Analyzes the magnetic field structure, stress profiles, and vertical density profiles to assess the degree of turbulence and accretion efficiency.

Experimental results

Research questions

• RQ1 Can the Hall effect revive magnetically dead zones in protoplanetary discs when Ohmic and ambipolar diffusion are also present?
• RQ2 Does the Hall effect generate sufficient Maxwell stress in the disc midplane to drive accretion without requiring magnetically driven outflows?
• RQ3 How does the inclusion of all three non-ideal MHD effects alter the vertical structure and scale height of the disc compared to models with only Ohmic or ambipolar diffusion?
• RQ4 What is the role of the Hall effect in modifying the magnetic field topology and promoting large-scale azimuthal fields in the midplane?
• RQ5 Can the observed accretion rates in T Tauri systems (≤10⁻⁷ M☉ yr⁻¹) be explained by midplane turbulence driven solely by the Hall effect, without outflows?

Key findings

• The Hall effect can generically revive dead zones by producing a dominant azimuthal magnetic field and large-scale Maxwell stress in the disc midplane when Ω·B > 0.
• The resulting magnetic pressure significantly increases the disc scale height beyond its hydrostatic value, altering the vertical density structure.
• Accretion rates ≤10⁻⁷ M☉ yr⁻¹ can be sustained without requiring magnetically driven outflows, as the Hall effect alone provides sufficient angular momentum transport.
• The flow in the disc midplane remains essentially laminar, suggesting that dust sedimentation may proceed efficiently in such regions.
• The Hall effect dominates the non-ideal MHD physics in the midplane, rendering Ohmic and ambipolar diffusion subdominant for turbulence generation.
• Numerical validation confirms accurate recovery of known linear growth rates for ambipolar-MRI (γ_theory = 0.171, γ_sim = 0.17) and successful reproduction of Hall-MRI zonal field structures.