Constraining the Formation of the Four Terrestrial Planets in the Solar System

TL;DR

This study uses extensive N-body simulations to investigate the formation of the four terrestrial planets, revealing that typical truncated disks cannot produce accurate analogs, and proposing specific disk properties necessary for realistic formation.

Contribution

The paper provides the first comprehensive analysis of the likelihood of forming all four terrestrial planet analogs simultaneously, highlighting the limitations of current truncated disk models and proposing new disk configurations.

Findings

Most systems contained at least three analogs, but only 17 had all four terrestrial planet analogs.

Truncated disks produce Mercury and Mars analogs that are too dynamically cold and too close to Venus and Earth.

Mercury analogs tend to be too massive, and Mars analogs are often more massive than actual Mars.

Abstract

To reproduce the orbits and masses of the terrestrial planets (analogs) of the solar system, most studies scrutinize simulations for success as a batch. However, there is insufficient discussion in the literature on the likelihood of forming planet analogs simultaneously in the same system (analog system). To address this issue, we performed 540 N-body simulations of protoplanetary disks representative of typical models in the literature. We identified a total of 194 analog systems containing at least three analogs, but only 17 systems simultaneously contained analogs of the four terrestrial planets. From an analysis of our analog systems, we found that, compared to the real planets, truncated disks based on typical outcomes of the Grand Tack model produced analogs of Mercury and Mars that were too dynamically cold and located too close to the Venus and Earth analogs. Additionally, all the Mercury analogs were too massive, while most of the Mars analogs were more massive than Mars. Furthermore, the timing of the Moon-forming impact was too early in these systems, and the amount of additional mass accreted after the event was too great. Therefore, such truncated disks cannot explain the formation of the terrestrial planets. Our results suggest that forming the four terrestrial planets requires disks with the following properties: 1) Mass concentrated in narrow core regions between ~0.7-0.9 and ~1.0-1.2 au; 2) an inner region component starting at ~0.3-0.4 au; 3) a less massive component beginning at ~1.0-1.2 au; 4) embryos rather than planetesimals carrying most of the disk mass; and 5) Jupiter and Saturn placed on eccentric orbits.