Hybrid methods in planetesimal dynamics: Formation of protoplanetary systems and the mill condition

TL;DR

This paper introduces a hybrid algorithm combining direct N-body and Fokker-Planck methods to simulate protoplanetary system formation, revealing insights into planetesimal interactions, fragmentation effects, and an upper mass limit known as the mill condition.

Contribution

The work presents a novel hybrid simulation approach for planetesimal dynamics, integrating high-accuracy N-body and statistical methods, and investigates the impact of fragmentation and gas drag on protoplanetary mass limits.

Findings

No gap formation terminates protoplanetary accretion.

Fragmentation controls mass loss during planet formation.

Universal upper mass limit (mill condition) depends on star distance.

Abstract

The formation and evolution of protoplanetary discs remains a challenge from both a theoretical and numerical standpoint. In this work we first perform a series of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoane and Spurzem 2011 (henceforth Paper I) that combines the advantages of high accuracy of direct-summation N-body methods with a statistical description for the planetesimal disc based on Fokker-Planck techniques. We then address the formation of planets, with a focus on the formation of protoplanets out of planetesimals. We find that the evolution of the system is driven by encounters as well as direct collisions and requires a careful modelling of the evolution of the velocity dispersion and the size distribution over a large range of sizes. The simulations show no termination of the protoplanetary accretion due to gap formation, since the distribution of the planetesimals is only subjected to small fluctuations. We also show that these features are weakly correlated with the positions of the protoplanets. The exploration of different impact strengths indicates that fragmentation mainly controls the overall mass loss, which is less pronounced during the early runaway growth. We prove that the fragmentation in combination with the effective removal of collisional fragments by gas drag sets an universal upper limit of the protoplanetary mass as a function of the distance to the host star, which we refer to as the mill condition.