Towards a global model for planet formation in layered MHD wind-driven discs: A population synthesis approach to investigate the impact of low viscosity and accretion layer thickness

TL;DR

The paper develops a population synthesis framework for planet formation in layered MHD wind-driven discs, where accretion occurs in a laminar surface layer and two Type II migration regimes (viscosity-dominated and wind-driven) govern giant planet evolution. By varying the accretion-layer thickness Σ_active and other disc initial conditions, the study demonstrates that the resulting planet populations exhibit substantial shifts in the mass-distance distribution, including in-situ giant formation for thin layers and widespread hot Jupiters for thick layers, while maintaining compatibility with observed demographics at intermediate layer properties. Key findings include a strong dependence of the giant-planet cutoff mass and migration history on Σ_active, a persistent planetary desert near ~10–20 M⊕ driven by runaway gas accretion, and the ability to reproduce some observed Hot-to-Cold Jupiter ratios only within a limited range of layer thicknesses. The work highlights wind-driven Type II migration as a plausible contributor to close-in giant planets and identifies gap-opening, envelope accretion physics, and the layer’s cooling and heating as critical aspects shaping planetary architectures in MHD-wind discs. It also notes that fully matching the observed exoplanet population will require incorporating additional physics and performing multi-embryo simulations for direct statistical comparison.

Abstract

Planet formation is inherently linked to protoplanetary disc evolution, which recent developments suggest is driven by magnetised winds rather than turbulent viscosity. We study planet formation in magnetohydrodynamic (MHD) wind-driven discs, assuming accretion occurs in a laminar surface layer above a weakly turbulent midplane. Our goal is to assess the global consequences of recent hydrodynamical results, including inefficient midplane heating and the existence of two Type II migration regimes: slow viscosity-dominated and fast wind-driven migration. We perform single-embryo planetary population syntheses with varying initial disc conditions (i.e. disc mass, size and angular momentum transport), and embryo starting locations, testing different prescriptions for the accretion layer thickness $Σ_\text{active}$. Thin ($\lesssim0.01\mathrm{g\,cm^{-2}}$) or fast ($\gtrsim12\%$ sonic velocity) accretion layers result in slow, viscosity-dominated regime which strongly limits the extent of Type II migration. For thick ($\gtrsim1\mathrm{g\,cm^{-2}}$) or slow ($\lesssim3\%$ sonic velocity) accretion layers, fast wind-driven Type II migration occurs frequently, leading to long-range inward migration that sets in once planets reach masses sufficient to block the accreting layer. Disk-limited gas accretion is also strongly affected by deep and early gap opening, limiting maximum giant planet masses. These effects strongly influence the final mass-distance distribution. For thin layers, giant planets form nearly in situ once they have entered Type II migration, which happens already at a few Earth masses, while thick layers lead to numerous migrated Hot Jupiters. Overall, we find that while the global properties of the emerging planet population are strongly modified relative to classical viscous discs, key properties of the observed population can be reproduced within this new paradigm.

Figures (8)

• Figure 1: Sketch of the global framework explored in this work. Disc evolution through angular momentum extraction by an MHD wind with additional low-level internal and external photoevaporation with accretion occurring in layers at the disc surface. Low-mass planets remain embedded and undergo Type I migration. Growing planets eventually open a gap and transition to Type II migration. Initially, the fast accretion layer bypasses the planet, which migrates due to Lindblad torques from the gap (viscosity-dominated regime) while still accreting. At higher masses, the planet fully blocks the flow, entering wind-driven Type II migration, where it is pushed by the outer gap replenished by the accretion flow.
• Figure 2: Time evolution of an exemplary disc evolution (see Table \ref{['tab:exemplary_disc']} for the parameter choice). The left panel shows the evolution of the gas surface density. The evolution of the pebble and dust surface density evolution is shown in the middle panel and the right panel shows the time evolution of the midplane temperature. Note that the sudden change in dust surface density is related to the change from drift limited size (outer disc) to fragmentation limited size (inner disc).
• Figure 3: Migration rate as a function of orbital distance and planetary mass for the exemplary disc evolution at 3 Myrs (see Sect. \ref{['subsubsec:exempl_disc_evo']}). The cyan line marks the transition from Type I to Type II migration through gap opening. The pink line denotes the transition into the wind-driven Type II migration regime. The left panel shows the migration map for $\Sigma_\mathrm{active}=0.1\,\mathrm{g/cm^2}$ and the right panel shows the migration map for $\Sigma_\mathrm{active}(0.08\times c_\mathrm{s})$.
• Figure 4: Map showing the reduced surface density in the gap as a function of planetary mass for the exemplary disc evolution at 1 Myr (see Sect. \ref{['subsubsec:exempl_disc_evo']}), calculated using Eq. \ref{['eq:kanag_gap_depth']}. The cyan line corresponds to the gap opening mass with the criterion $\Sigma_\mathrm{gap}/\Sigma_\mathrm{unp} = 0.5$. We show pebble isolation mass formulas from Bitsch2018 and Ataiee2018 in green and black and the red line corresponds to the thermal mass criterion.
• Figure 5: Formation tracks compiled from 100 individual single embryo simulations ($M_\mathrm{emb}=10^{-2}\,\mathrm{M_\oplus}$) with varying initial locations $r_\mathrm{start}$ spaced uniform in log between $0.05\,\mathrm{au}$ and $40\,\mathrm{au}$ for our exemplary disc discussed in Section \ref{['subsubsec:exempl_disc_evo']}. Tracks are coloured by migration regime. Time evolution of the planet's accretion rate (core and envelope) and migration rate are shown as an example for a planet with $r_\mathrm{start}\simeq20\,\mathrm{au}$.