Dust Dynamics in a Gravitationally Unstable Disc

The Role of Drag and Gravity on Dust Concentration in a Gravitationally Unstable Disc

Sahl Rowther, Rebecca Nealon, Farzana Meru, James Wurster, Hossam Aly, Richard Alexander, Ken Rice, Richard A. Booth

Abstract

We carry out three dimensional smoothed particle hydrodynamics simulations to study the role of gravitational and drag forces on the concentration of large dust grains (St > 1) in the spiral arms of gravitationally unstable protoplanetary discs, and the resulting implications for planet formation.

We find that both drag and gravity play an important role in the evolution of large dust grains. If we include both, grains that would otherwise be partially decoupled will become well coupled and trace the spirals. For the dust grains most influenced by drag (with Stokes numbers near unity), the dust disc quickly becomes gravitationally unstable and rapidly forms clumps with masses between 0.15 - 6 Earth masses. A large fraction of clumps are below the threshold where runaway gas accretion can occur. However, if dust self-gravity is neglected, the dust is unable to form clumps, despite still becoming trapped in the gas spirals. When large dust grains are unable to feel either gas gravity or drag, the dust is unable to trace the gas spirals. Hence, full physics is needed to properly simulate dust in gravitationally unstable discs.

Dust trapping of large grains in spiral arms of discs stable to gas fragmentation could explain planet formation in very young discs by a population of planetesimals formed due to the combined roles of drag and gravity in the earliest stages of a disc's evolution. Furthermore, it highlights that gravitationally unstable discs are not just important for forming gas giants quickly, it can also rapidly form Earth mass bodies.

Testing the Impact of Different Physics

The spiral arms in a gravitationally unstable protoplanetary disc are regions of both pressure maxima and gravitational potential minima. Thus, both the drag and gravitational force can influence the motion of dust.

To investigate the role of drag and gravity on the dust dynamics, we perform four simulations with different physics. The evolution of the dust in each simulation is shown in Figure 1 and described below.

Full Physics (top left) - The dust feels the drag force, and the gravitational force due to the gas and dust. The dust rapidly drifts towards and concentrates in the spiral arms, eventually forming gravitationally bound clumps.
No Dust Self-Gravity (top right) - The dust no longer feels the gravity of other dust particles. The evolution of the dust is similar to the Full Physics simulation, except the dust can no longer clump together.
Drag Only (bottom left) - The dust only feels the drag force. The absence of gravity prevents the dust from tracing the gas spiral arms as before.
Gravity Only (bottom right) - The dust only feels the gravity of gas and dust. Although the dust initially forms spiral structures, the absence of the drag force causes the dust to quickly decouple from the gas resulting in a smooth dust disc.

Neither drag nor gravity on their own is enough to trap dust. Their combined influence is necessary for the dust to become trapped in the gas spirals.

Figure 1: The evolution of large dust grains (St ~ 4) in a gravitationally unstable disc. Each panel shows the same simulation setup. The only difference between the four panels is the physics.

Rapid Formation of Earth-Mass Clumps

The results presented here show that planet formation through gravitational instability may not be limited to just giant planets.

The spiral arms of gravitationally unstable discs provide conditions that favour dust concentration which rapidly collapses to form numerous Earth mass clumps. The mass distribution of the clumps formed in the Full Physics simulation is shown in Figure 2.

The short timescale at which the Earth mass clumps form could help explain how some of the observed discs exhibit ring & gap structure (often associated with evidence of planet formation) despite being less than a million years old.