Formation of intermediate-mass planets via magnetically controlled disk fragmentation


Intermediate-mass planets, from super-Earth to Neptune-sized bodies, are the most common types of planet in the Galaxy1. The prevailing theory of planet formation—core accretion2—predicts the existence of substantially fewer intermediate-mass giant planets than have been observed3,4. The competing mechanism for planet formation—disk instability—can produce massive gas giant planets on wide orbits, such as HR 87995, by direct fragmentation of the protoplanetary disk6. Previously, fragmentation in magnetized protoplanetary disks has been considered only when the magneto-rotational instability is the driving mechanism for magnetic field growth7. However, this instability is naturally superseded by the spiral-driven dynamo when more realistic, non-ideal magneto-hydrodynamic conditions are considered8,9. Here, we report on magneto-hydrodynamic simulations of disk fragmentation in the presence of a spiral-driven dynamo. Fragmentation leads to the formation of long-lived bound protoplanets with masses that are at least one order of magnitude smaller than in conventional disk instability models10,11. These light clumps survive shear and do not grow further owing to the shielding effect of the magnetic field, whereby magnetic pressure stifles the local inflow of matter. The outcome is a population of gaseous-rich planets with intermediate masses, while gas giants are found to be rarer, in qualitative agreement with the observed mass distribution of exoplanets.

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Fig. 1: Global and local flow and magnetic field structures in the disk midplane.
Fig. 2: The mass evolution of protoplanets identified via their gravitationally bound components.
Fig. 3: The frequency of planets of different masses.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The latest version of the GIZMO code is made available by its author, P. Hopkins, at


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H.D. acknowledges support from the Swiss National Science Foundation via an Early Postdoctoral Mobility Fellowship. We are grateful to D. Lin and G. Ogilvie for stimulating discussions. We also thank the Swiss National Supercomputing Center for their continued support as users of the PizDaint supercomputer, on which all the simulations were performed.

Author information




H.D. planned the study and carried out the simulations. H.D. and L.M. conceived the analysis, which was carried out by H.D. H.D., L.M. and R.H. interpreted the results and wrote the manuscript.

Corresponding author

Correspondence to Hongping Deng.

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The authors declare no competing interests.

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Peer review informationNature Astronomy thanks Aaron Boley and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Disk midplane density of the HD fragmentation simulation at 100 yr.

Two clumps at 4 and 6 o’clock are formed with masses of 0.128MJ and 0.042MJ, respectively. The over-dense region near 8 o’clock is not gravitationally bound.

Extended Data Fig. 2 Density profiles around two roughly Neptune-mass protoplanets (about 0.04MJ) in GI-HD clump (HD-cl2 at 100 yr) and GI-MHD clump (MHD-cl1 at 290 yr).

The cooling timescale beyond the 10−9 g cm−3 region is longer than 50 local orbits. This justifies turning off cooling in the clump’s core region (see Methods subsection “Thermodynamics of simulations”). However, we note that only regions with a typical density above about 10−8 g cm−3 are gravitationally bound.

Extended Data Fig. 3 Disk density maps in the resolution test of the HD simulation summarized in Table 1.

We employed four times more particles in the test than the HD simulation of Table 1. Also in this case, all the clumps are disrupted after 400 yr.

Extended Data Fig. 4 Magnetic energy to kinetic energy ratio in the co-moving frame of MHD-cl1 at 290 yrs.

(See also the lower panels of Fig. 1.) The dashed circle indicates the Hill radius of the protoplanet in MHD-cl1, 0.3 au. The magnetic energy dominates the kinetic energy outside the Hill sphere, thus controlling the dynamics of the flow.

Extended Data Fig. 5 The refilling rate of material within the Hill sphere of a Neptune-mass protoplanet.

The refilling rate is defined as the new mass, as a fraction of the total, that enters the Hill sphere of the protoplanet every year. The calculation is performed for HD-cl2 (100–170 yr) and MHD-cl1 (200–440 yr) (see Fig. 2) using snapshots taken every 3 yr. The spikes of the yellow curve are caused by encounters with spiral density waves.

Extended Data Fig. 6 Clump migration.

The heliocentric distance of the clumps/protoplanets (see Fig. 2) suggests both inwards and outwards migration can happen due to gravito-turbulence.

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Deng, H., Mayer, L. & Helled, R. Formation of intermediate-mass planets via magnetically controlled disk fragmentation. Nat Astron (2021).

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