The gravitational-instability dynamo in young self-gravitating protoplanetary disks under non-ideal MHD, net vertical magnetic flux, and realistic thermodynamics

In massive young protoplanetary disks, spiral density waves driven by gravitational instability (GI) act as a dynamo, amplifying magnetic fields to near-thermal strength and thereby altering the disk's turbulence, accretion rate, and fragmentation behavior. This dynamo has so far been established only under idealizations: ideal MHD or Ohmic resistivity in global models, and ambipolar diffusion in local shearing boxes, both with prescribed cooling and zero net magnetic flux. The open problem, stated in the work that confirmed the dynamo globally (Deng, Mayer & Latter 2020), is to determine how the GI dynamo behaves and reshapes the disk when these idealizations are removed: with ambipolar diffusion and the Hall effect plus realistic ionization profiles, with a net vertical (poloidal) magnetic flux, and with realistic radiative thermodynamics; and to establish its two key consequences — whether the resulting magnetic fields promote or suppress gravitational fragmentation into bound clumps, and whether the accompanying magnetically driven outflow is robust and what role it plays in disk accretion and ejection. Follow-up work has answered parts of this agenda: the dynamo survives ambipolar diffusion in local models (Riols et al. 2021), and magnetized fragmentation has been shown to produce long-lived low-mass clumps (Deng, Mayer & Helled 2021; Kubli, Mayer & Deng 2023). The Hall-effect regime, the net-vertical-flux regime (a promised sequel study never appeared), radiation-MHD treatment of the dynamo, global non-ideal models, and any characterization of the outflow remain open as of August 2026.

Background

A protoplanetary disk — the rotating gas and dust cloud around a young star — is gravitationally unstable when it is massive and cool enough that self-gravity overcomes pressure and differential rotation. The standard measure is the Toomre parameter $Q$: instability sets in when $Q\lesssim 1$–$1.5$ (with $Q\propto c_s\Omega/\Sigma$, where $c_s$ is the sound speed, $\Omega$ the orbital frequency, and $\Sigma$ the surface density). This is expected in the earliest, embedded stages of star formation (Class 0/I objects, i.e. protostars still surrounded by infalling envelope material), when the disk may hold a substantial fraction of the stellar mass. A marginally unstable disk does not necessarily fragment: if cooling is slow, it settles into a quasi-steady, spiral-dominated turbulent state called gravitoturbulence, which transports angular momentum outward and drives accretion onto the star. Most simulations of this state use a prescribed cooling law, quantified by a parameter $\beta$ giving the cooling time in units of the local orbital time. If cooling is fast (small $\beta$), spiral arms can collapse into bound clumps — the disk-instability channel of giant-planet formation.

Magnetic fields introduce a second actor. The best-known magnetic process in disks is the magnetorotational instability (MRI), an instability of a weakly magnetized differentially rotating fluid that generates turbulence; but the MRI requires sufficient ionization, and young disks are cold and poorly ionized. In weakly ionized gas three non-ideal magnetohydrodynamic (MHD) effects supplement ideal MHD: Ohmic resistivity (collision-based slippage of field lines through the gas, which diffuses away field), ambipolar diffusion (drift of field lines tied only to the sparse charged species, an anisotropic and nonlinear diffusion), and the Hall effect (a dispersive term, acting only on electrons, whose sign depends on the orientation of the magnetic field relative to the rotation axis and which can amplify or damp fields depending on polarity). Each is measured by an Elsasser number, the ratio of magnetic to (non-ideal) diffusion forces; the ambipolar Elsasser number $Am$ is the number commonly quoted. A further key physical variable is the net vertical flux: a large-scale poloidal (vertical) magnetic field threading the disk, as opposed to a field with zero mean threading, which exists only as turbulence. Net vertical flux enables magnetic braking (removal of disk angular momentum along connected field lines) and centrifugally driven disk winds (outflows launched along field lines that carry away angular momentum) in other disk regimes, and may qualitatively change both the dynamo and the outflow.

The interaction between GI and magnetic fields was first explored in low-resolution global simulations by Fromang et al. (2004), which focused on the MRI. Riols & Latter then showed, in vertically stratified local 'shearing-box' simulations (a comoving patch of disk with periodic/shear-periodic boundaries), that gravitoturbulence is itself a dynamo — a mechanism amplifying magnetic field — that builds fields to near-thermal strength (plasma beta, the ratio of gas to magnetic pressure, $\beta_{\rm pl}\lesssim 10$) even in highly resistive gas, via spiral-wave-induced vertical circulation rolls acting together with differential rotation. Deng, Mayer & Latter (2020) confirmed this in fully global three-dimensional simulations using the meshless finite mass (MFM) method, a Lagrangian particle-based hydrodynamic technique in which mass is exchanged between discrete cells, and found the saturated state is hotter with weaker 'flocculent' spirals, that accretion is enhanced by factors of several through Maxwell stress (the magnetic contribution to angular-momentum transport), that an outflow accompanies the accretion, and that Ohmic resistivity does not quench the dynamo. However, these runs used ideal MHD (plus a small Ohmic suite) and prescribed $\beta$-cooling, and no net vertical flux. The authors identified the urgent next steps: realistic ionization profiles and non-ideal MHD (ambipolar diffusion and the Hall effect), different magnetic flux configurations especially a large-scale poloidal field, and — through these — an understanding of how the dynamo affects fragmentation into clumps and whether the magnetically mediated outflow is robust.

Problem Statement

Determine how the spiral-driven gravitational-instability dynamo behaves, and how it reshapes young massive self-gravitating disks, once the idealizations of the confirming simulations are removed — a single coupled program whose parts jointly answer: does magnetism control the evolution of gravitoturbulent disks?

Specifically, for self-gravitating protoplanetary (protostellar) disks in the gravitoturbulent state:

1. Dynamo under realistic non-ideal physics: establish the growth, saturation amplitude, and geometry of the GI dynamo when ambipolar diffusion and the Hall effect are included with realistic ionization profiles — beyond the ideal-MHD/Ohmic treatments done globally and the ambipolar-only, zero-net-flux local treatment — and in global disk models rather than only shearing boxes.
2. Dynamo under net vertical flux: determine how a net vertical (large-scale poloidal) magnetic field threading the disk modifies the GI dynamo, including whether it suppresses, enhances, or reorganizes the field amplification identified in the zero-net-flux case (the regime explicitly deferred by Riols et al. 2021 as paper II, which never appeared).
3. Dynamo under realistic thermodynamics: establish whether the dynamo and its saturation survive when the prescribed beta-cooling is replaced by radiative transfer (including stellar irradiation), the regime in which disk fragmentation is now being studied but only without magnetic fields.
4. Consequence for fragmentation: quantify whether the saturated dynamo and its associated magnetic stresses promote or suppress gravitational fragmentation — the formation, initial masses, and survival of bound clumps — and how this depends on the ionization, flux, and thermodynamic regimes of items 1–3.
5. Consequence for outflows: robustly characterize the magnetically driven outflow accompanying GI-dynamo accretion (its launching mechanism, mass and energy fluxes, and numerical robustness), and determine its role in the disk's accretion/ejection balance.

Items 1–3 set the saturated magnetic state whose stresses and pressures control items 4–5. Item 4's dependence is on the ionization, flux, and thermodynamic regimes established in items 1–3 — ambipolar-plus-Hall at both Hall polarities, net vertical flux versus its zero-net-flux counterpart, and radiative transfer with stellar irradiation versus prescribed cooling.

References

1. Deng, H., Mayer, L., & Latter, H. 2020, 'Global Simulations of Self-gravitating Magnetized Protoplanetary Disks', The Astrophysical Journal 891(2), 154. DOI: 10.3847/1538-4357/ab77b2 (arXiv:2001.08693). https://doi.org/10.3847/1538-4357/ab77b2
2. Riols, A., Xu, W., Lesur, G., Kunz, M. W., & Latter, H. 2021, 'Gravito-turbulence and dynamo in poorly ionized protostellar discs – I. Zero-net-flux case', Monthly Notices of the Royal Astronomical Society 506(1), 1407–1426. DOI: 10.1093/mnras/stab1637 (arXiv:2106.03607). https://doi.org/10.1093/mnras/stab1637
3. Deng, H., Mayer, L., & Helled, R. 2021, 'Formation of intermediate-mass planets via magnetically controlled disk fragmentation', Nature Astronomy 5, 440–444. DOI: 10.1038/s41550-020-01297-6. https://doi.org/10.1038/s41550-020-01297-6
4. Kubli, N., Mayer, L., & Deng, H. 2023, 'Characterizing fragmentation and sub-Jovian clump properties in magnetized young protoplanetary discs', Monthly Notices of the Royal Astronomical Society 525(2), 2731–2749. DOI: 10.1093/mnras/stad2478 (arXiv:2303.04163). https://doi.org/10.1093/mnras/stad2478
5. Ni, Y., Deng, H., & Bai, X.-N. 2025, 'Radiation Hydrodynamics of Self-gravitating Protoplanetary Disks. I. Direct Formation of Gas Giants via Disk Fragmentation', The Astrophysical Journal 995(1), 96. DOI: 10.3847/1538-4357/ae16a4 (arXiv:2510.19915). https://doi.org/10.3847/1538-4357/ae16a4
6. Helled, R., Schib, O., Reinhardt, C., Kubli, N., Mayer, L., Mordasini, C., & Cugno, G. 2026, 'Giant Planet Formation by Disk Instability', arXiv:2604.09042. https://arxiv.org/abs/2604.09042
7. Riols, A., & Latter, H. 2019, 'Gravitoturbulent dynamos in astrophysical discs', Monthly Notices of the Royal Astronomical Society 482(3), 3989–4008. DOI: 10.1093/mnras/sty2804 (arXiv:1810.06589). https://doi.org/10.1093/mnras/sty2804
8. Riols, A., & Latter, H. 2016, 'Gravitoturbulence in magnetized protostellar discs', Monthly Notices of the Royal Astronomical Society 460(2), 2223–2237. DOI: 10.1093/mnras/stw1112 (arXiv:1605.01873). https://doi.org/10.1093/mnras/stw1112
9. Fromang, S., Balbus, S. A., Terquem, C., & De Villiers, J.-P. 2004, 'Evolution of Self-Gravitating Magnetized Disks. II. Interaction between Magnetohydrodynamic Turbulence and Gravitational Instabilities', The Astrophysical Journal 616(1), 364–375. DOI: 10.1086/424829. https://doi.org/10.1086/424829