Periodic Reporting for period 1 - DUSTSPEC (Sizes Matter: The Dust Size Distribution during Planet Formation)
Reporting period: 2023-01-01 to 2025-06-30
Planets form in discs of gas and dust around young stars. Within these discs, grains initially smaller than a micron will somehow have to grow into planetary sized objects. This is relatively easy at first: when two grains meet they stick, held together by inter-molecular forces. When particles reach millimeter size, however, this no longer works as well, with collisions often resulting in bouncing rather than sticking. A further complicating issue is that at these sizes, dust particles are rapidly driven towards the central star by friction with the gas. This inward drift can be extremely fast: boulders of 1 meter in size can drift into the star in 100 years, while planet formation typically takes 100,000-1,000,000 years. This 'drift-barrier' has long been a major problem in planet formation.
A promising solution is the 'streaming instability'. As it turns out, in many cases solids streaming through a gas is hydrodynamically unstable. The streaming instability feeds off the drift, creating a turbulent state with strong dust overdensities. These overdensities can subsequently collapse gravitationally into kilometer-sized 'planetesimals'. These objects are large enough to be safe from drift, and are usually strong enough not to be destroyed by collisions. Moreover, the growth time of the instability is shorter than the drift time of the dust, making sure that planetesimals form before all the solids are lost into the central star.
Dust flow in gas discs is usually studies in the simplified case where all particles have the same size. While this greatly simplifies the analysis, in reality there will always be a distribution of sizes. As it turns out, a size distribution can have important dynamical consequences. For example, a wide size distribution can completely disable the streaming instability if the size distribution is not exactly of the right form. If this behavior is generic, this means that the size distribution, which is very difficult to observe directly, can be traced through larger-scale processes in protoplanetary discs. This provides a new window on planet formation, revealing previously unseen processes.
In this project, we are letting the dust size distribution take center stage. What role does the size distribution play in growing planets? How can we perform realistic simulations of a gas-dust mixture with a size distribution? How can we compare simulation outcomes to observations of for example Solar system objects?
A promising solution is the 'streaming instability'. As it turns out, in many cases solids streaming through a gas is hydrodynamically unstable. The streaming instability feeds off the drift, creating a turbulent state with strong dust overdensities. These overdensities can subsequently collapse gravitationally into kilometer-sized 'planetesimals'. These objects are large enough to be safe from drift, and are usually strong enough not to be destroyed by collisions. Moreover, the growth time of the instability is shorter than the drift time of the dust, making sure that planetesimals form before all the solids are lost into the central star.
Dust flow in gas discs is usually studies in the simplified case where all particles have the same size. While this greatly simplifies the analysis, in reality there will always be a distribution of sizes. As it turns out, a size distribution can have important dynamical consequences. For example, a wide size distribution can completely disable the streaming instability if the size distribution is not exactly of the right form. If this behavior is generic, this means that the size distribution, which is very difficult to observe directly, can be traced through larger-scale processes in protoplanetary discs. This provides a new window on planet formation, revealing previously unseen processes.
In this project, we are letting the dust size distribution take center stage. What role does the size distribution play in growing planets? How can we perform realistic simulations of a gas-dust mixture with a size distribution? How can we compare simulation outcomes to observations of for example Solar system objects?
(1) Numerical simulations of the streaming instability. We have designed a new method to deal with a continuous size distribution in existing hydrodynamics codes. We have shown that this method performs 5-10 times better than state-of the art methods. We have implemented this method in the existing codes FARGO3D and IDEFIX. Simulations of the streaming instability show that the high density clumps are not dominated by the largest particles in the distribution, but by slightly smaller particles. Interestingly, the resulting size distribution in the clumps that may continue to collapse into planetesimals resembles a size distribution that comes out of pure coagulation simulations.
(2) Resonant drag instabilities with a size distribution. We have studied two more resonant drag instabilities, namely the settling instability and the acoustic drag instability, to see how they react to a dust size distribution. We were able to prove that the streaming instability switches off for even very narrow size distributions (0.9-1.1 cm!), but that the settling instability survives, if only at relatively small scales that could be subject to diffusion. The acoustic drag instability can survive only for specific size distributions, which could lead to projects studying the size distribution based on the presence or absence of this instability.
(3) Simulations of the settling instability. We have performed numerical simulations of the settling instability, confirming the results in the linear phase of (2). Interestingly, clumps form more readily with our improved scheme.
(2) Resonant drag instabilities with a size distribution. We have studied two more resonant drag instabilities, namely the settling instability and the acoustic drag instability, to see how they react to a dust size distribution. We were able to prove that the streaming instability switches off for even very narrow size distributions (0.9-1.1 cm!), but that the settling instability survives, if only at relatively small scales that could be subject to diffusion. The acoustic drag instability can survive only for specific size distributions, which could lead to projects studying the size distribution based on the presence or absence of this instability.
(3) Simulations of the settling instability. We have performed numerical simulations of the settling instability, confirming the results in the linear phase of (2). Interestingly, clumps form more readily with our improved scheme.
Our new integration scheme for polydisperse dust should find its way into every multi-fluid hydrodynamics code that allows pressureless dust fluids, as it is a cost-free method to greatly improve the integration over dust sizes.