Oligarchic growth of protoplanets in an expanding planetesimal ring

In the standard planet formation scenario, planetesimals have been assumed to form throughout the protoplanetary disk and to be smoothly distributed in the radial direction except for the snowline. Planetesimal evolution theory is also investigated based on this assumption. Recently, however, simulations of gas and dust evolution have shown that planetesimals form only in radially limited locations, such as gas pressure bumps and snowlines, and are concentrated in ring-like regions.  On the other hand, simulations starting from protoplanets arranged in a narrow annulus successfully reproduced the mass distribution of terrestrial planets in the solar system. The evolution process of planetesimals distributed in a ring is crucial to understanding planet formation theory. However, the evolution of planetesimal rings has not been studied in detail.

 

We investigate the evolution of a  planetesimal ring (Kambara & Kokubo 2025). We systematically change the initial conditions and investigate the dependence on them.

Figure 1.  Snapshots of one of the simulations on a--e plane (Kambara & Kokubo 2025).  The blue dots represent planetesimals, and red circles represent protoplanets more massive than 1000 times of the initial mass. The ratios of the circles' radii correspond to the ratios of the particles' radii.

 

 Figure 1 shows snapshots from one of the simulations. In the simulations, protoplanets undergo oligarchic growth while the ring expands. Protoplanets keep the orbital separation due to orbital repulsion. This is a typical outcome of oligarchic growth. Protoplanets' mass and orbital separation between adjacent protoplanets in the ring can be predicted by the oligarchic growth model and the surface density after ring expansion. The ring width and protoplanets' mass weakly depend on the initial ring width. When we fix the initial ring width, protoplanets get heavier and the ring expands faster in a more massive ring. We do not find any simulations that reproduce a narrow protoplanet ring which is thought to be favorable to reproduce the solar system. We can use our results as an initial condition of giant impact stage and test if  planetesimal rings can succesfully  reproduce the solar system planets and exoplanets.