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On the validity of the super-particle approximation of planetesimals in simulations of gravitational collapse

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Dynamics of Discs and Planets

The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At best one can simulate a few million particles numerically as opposed to the several trillion meter-sized particles expected in a real protoplanetary disc. Therefore, single particles are often used as super-particles to represent a distribution of many smaller particles. However, the super- particle approximation is not always valid when applied to planetesimal formation because the system can be marginally collisional (of order one collision per particle per orbit). The super-particle approximation is valid only when the system is collisionless. In many recent numerical simulations this is not the case and the approach leads to spurious results and enhanched clumping. We present new results from numerical simulations of planetesimal formation through gravitational instability. A scaled system is studied that does not require the use of super-particles. We find that the scaled particles can indeed be used to model the initial phases of clumping if the porperties of the scaled particles are chosen such that all important timescale in the system are equivalent to what is expected in a real protoplanetary disc. This method is explained in detail in this paper and we give constraints on the number of particles that one has to use in order to achieve numerical convergence. In order to illustrate this we simplify the system: the evolution of particles is studied in a local shearing box; the particle- particle interactions such as gravity, physical collisions, and gas drag are solved directly but a constant background shear flow without any feedback from the particles is assumed. We compare this new method to the standard super-particle approach and find significant discrepancies in both the require- ment for gravitational collapse and the resulting clump statistics. Our study shows that the formation of planetesimals in a trubulent disk is much harder than previously reported.

This talk is part of the Isaac Newton Institute Seminar Series series.

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