Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt

TL;DR

This paper investigates how different initial disk density profiles affect terrestrial planet formation and asteroid belt excitation, concluding that a single profile cannot explain both the Earth/Mars mass ratio and asteroid belt dynamics, supporting the need for a separate depletion mechanism.

Contribution

It demonstrates that no single initial disk density profile can simultaneously reproduce the terrestrial planets' structure and asteroid belt excitation, emphasizing the necessity of additional processes like the Grand Tack.

Findings

Shallow density gradients produce asteroid belt excitation but result in overly massive Mars analogs.

Steep density gradients match the Earth/Mars mass ratio but leave the asteroid belt too cold.

A separate depletion mechanism is required to explain the asteroid belt's current state.

Abstract

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.