Radiation Hydrodynamics of Self-gravitating Protoplanetary Disks: I. Direct Formation of Gas Giants via Disk Fragmentation

TL;DR

This study demonstrates that gravitational instability in self-gravitating protoplanetary disks, when modeled with global 3D radiation hydrodynamics and high resolution, can produce planetary-mass fragments rather than predominantly brown-dwarf-mass clumps. By varying disk mass and opacity and employing an M1 radiation transport within a meshless finite-mass framework, the authors show that fragmentation probability increases with mass and decreased opacity due to enhanced cooling, while non-fragmenting disks settle into gravito-turbulence with $\alpha \sim \beta_{\mathrm{cool}}^{-1}$. The initial masses of fragments typically lie in $\sim$0.3–10 $M_J$, consistent with forming gas giants, and scale with a local analytical estimate based on the Toomre wavelength and local surface density, yielding a log-normal distribution of $m_{\mathrm{frag}}/M_{\mathrm{analytical}}$ centered near $\sim1.3$. These results strengthen the case that GI can directly form gas-giant planets under realistic cooling conditions and motivate future work on fragment evolution, migration, and observable signatures, including the roles of irradiation and magnetic fields.

Abstract

Gravitational instability (GI) has long been considered a viable pathway for giant planet formation in protoplanetary disks (PPDs), especially at wide orbital separations or around low-mass stars where core accretion faces significant challenges. However, a primary drawback is that disk fragmentation from GI was generally found to produce over-massive clumps, typically in the mass range of brown dwarfs, although most numerical studies adopted simplified cooling prescriptions or with limited numerical resolution. We conduct a suite of global three-dimensional radiation hydrodynamics (RHD) simulations of self-gravitating PPDs using the meshless finite-mass (MFM) method. By implementing radiation transport via the M1 closure and systematically varying disk mass and opacity, we show that increasing disk mass and lowering opacity promote fragmentation by enhancing radiative cooling. Non-fragmenting disks settle into a gravito-turbulent state with low-order spiral structures and effective angular momentum transport characterized by $α\sim β_\mathrm{cool}^{-1}$. In fragmenting disks, a subset of gravitationally bound clumps survives as long-lived fragments. Their initial masses form a consistent distribution around $Σ\cdotλ_\mathrm{T} \cdot 2 (c_s/Ω_\mathrm{K})$ (with $λ_T$ the Toomre wavelength), corresponding to $\sim 0.3 - 10\,M_\mathrm{J}$ in our simulations, consistent with being gas giants. These results demonstrate that GI can produce planet-mass fragments under more realistic conditions, reinforcing it as a viable gas giant formation pathway and motivating further studies of fragment evolution and observational signatures.

Figures (14)

• Figure 1: The gas surface density maps at the end of the simulations as labelled in the upper left. The box size is $225\,\mathrm{AU}\times225\,\mathrm{AU}$, and a scale bar of 100 AU is included.
• Figure 2: Time-averaged radial profiles of $\Sigma$, $T$, $\tau_\mathrm{mid}$, $\beta_\mathrm{cool}$, $Q$ in all the simulations. Profiles of the three non-fragmented disks, i.e., m13k1, m13k5, and m15k5, are time-averaged during the last $1\,\mathrm{kyr}$ of the simulation ($4-5\,\mathrm{kyr}$) to capture the GI-saturated quasi-steady state. Profiles of fragmented disks, i.e., m15k1, m17k1, m17k5, m20k1, and m20k5, are time-averaged during the last $0.1\,\mathrm{kyr}$ before the first clumps in these simulations emerge to capture the instantaneous disk properties generating the fragmentation. Black circles indicate locations of the first clumps in the fragmented disks.
• Figure 3: Time-averaged Fourier amplitudes of the gas density in the $3$ non-fragmented disks during the $4-5\mathrm{kyr}$. Labels at the upper left corner of each panel indicate the names of these simulation runs. We cover the radius range $35\,\mathrm{AU}<R<100\,\mathrm{AU}$ to exclude the effect of disk outer boundaries. Ticks of $m=1,2,3,4,5,6$ are additionally denoted to show the exact values of the dominated $m$ modes.
• Figure 4: Time-averaged Reynolds stress profiles (top left), gravitational stress profiles (top right), viscous $\alpha$ profiles (bottom left) and $\alpha$-$\beta_\mathrm{cool}^{-1}$ relation (bottom right) in the $3$ non-fragmented disks during the $4-5\mathrm{kyr}$.
• Figure 5: Temporal evolution of the clump mass $m_\mathrm{clump}$ (left column) and virial parameter $\alpha_\mathrm{vir}$ (right column) in m15k1, m17k1, m20k1, m17k5, and m20k5. Labels in the upper left of all rows indicate the names of five simulation runs. Each line demonstrates the evolution of an individual clump. Solid lines represent the fragments among all clumps, and dotted lines represent all other clumps.