Magnetically driven accretion in protoplanetary discs

Abstract: We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation supporting a strong laminar Maxwell stress that is absent if the field is anti-aligned. In the anti-aligned case, we instead find evidence for bursts of turbulent stress at 5-10 au, which we tentatively identify with the non-axisymmetric Hall-shear instability. The presence or absence of these bursts depends upon the details of the adopted chemical model, which suggests that appreciable regions of actual protoplanetary discs might lie close to the borderline between laminar and turbulent behaviour. Given the number of important control parameters that have already been identified in MHD models, quantitative predictions for disc structure in terms of only radius and accretion rate appear to be difficult. Instead, we identify robust qualitative tests of magnetically driven accretion. These include the presence of turbulence in the outer disc, independent of the orientation of the vertical magnetic fields, and a Hall-mediated bi-modality in turbulent properties extending from the region of thermal ionization to 10 au.

Magnetically Driven Accretion in Protoplanetary Discs

This paper provides a detailed study of magnetically driven accretion in protoplanetary discs, spanning a radial range of 1 au to 100 au. Leveraging a series of local non-ideal magnetohydrodynamic (MHD) simulations, the study explores the influence of various non-ideal MHD effects, namely, Ohmic resistivity, the Hall effect, and ambipolar diffusion, on the accretion processes in these discs. The simulations, founded on a Minimum Mass Solar Nebula (MMSN) model, employ a net vertical magnetic field, providing insights into the dynamics of both laminar and turbulent accretion regimes.

Key Findings and Numerical Results

1. Magnitudes and Orientation Effects:
   • The study underscores the significant role of the Hall effect in influencing accretion, particularly between 1 au and 10 au. The orientation of the vertical magnetic field with respect to the angular momentum vector of the disc (i.e., the sign of $\bm{\Omega} \cdot \bm{B}$) induces significant variability in accretion rates. For $\bm{\Omega} \cdot \bm{B} > 0$, the discs support strong laminar Maxwell stress, whereas for $\bm{\Omega} \cdot \bm{B} < 0$, the study observed bursts of turbulent stress, especially around 5 au to 10 au.
2. Non-Ideal MHD Effects at Different Radii:
   • The Hall effect introduces variability in disc behavior closer in at 1 au to 10 au but has a diminished impact at larger radii (e.g., 30 au to 100 au). At these larger radii, ambipolar diffusion becomes a more dominant factor suppressing MRI-driven turbulence near the disc mid-plane.
3. Chemistry and Control Parameters:
   • The presence of such variable turbulence is closely linked to the adopted chemical model, specifically the assumptions about ionization mechanisms and non-ideal MHD coefficients. Discs may be near a threshold where their behavior could flip between laminar and turbulent states, influenced by subtle changes in ionization chemistry.

Theoretical and Practical Implications

• Disc Structure Predictions: Quantitative predictions of protoplanetary disc structure—linked to radius and accretion rate—are complicated by the large number of control parameters identified in MHD models. Nevertheless, the study outlines qualitative tests for magnetically driven accretion, such as the presence of turbulence in the outer disc independent of magnetic field orientation and Hall-mediated bi-modal turbulence in the inner disc.
• Magnetic Field Orientation: The findings highlight the necessity of considering the magnetic-field orientation in theoretical models of protoplanetary discs. This orientation affects the MRI and can lead to varied observational signatures in disc substructures.
• Future Observations and Model Refinements: Advanced telescopic technologies (e.g., ALMA) and molecular-line observations are poised to test these theoretical predictions. Observational studies could help refine models of accretion by constraining parameters like ionization levels and magnetic-field strengths.

Conclusion and Future Research Directions

The research elucidates the complexities of magnetically driven accretion processes in protoplanetary discs, emphasizing the intricate interplay between various MHD effects across different radial zones. The susceptibility of these discs to transitions between laminar and turbulent states invites further exploration, especially with an emphasis on global simulations that might capture large-scale magnetic structures and reconcile local findings.

Future research should aim to integrate these local insights into comprehensive models that can account for both localized behavior and global disc evolution. Enhanced understanding of the underlying non-ideal MHD mechanisms will advance the predictive power of disc evolution models, enriching our comprehension of planet formation processes.