Orbital evolution of planetesimals in gaseous disks

TL;DR

This paper derives analytical formulas for the orbital evolution of planetesimals with large eccentricities and inclinations in gaseous disks, extending previous models to later stages of planet formation.

Contribution

It provides new analytical expressions for orbital element changes applicable to bodies with large eccentricities and inclinations, relevant for advanced planet formation stages.

Findings

Formulas valid for $1-e^2 \\ll 1$ and $i \\ll H/a$

Formulas applicable for $i \\gg H/a$

Potential implications for satellite capture in circumplanetary disks

Abstract

Planets are formed from collisional growth of small bodies in a protoplanetary disk. Bodies much larger than approximately $1$\,m are mainly controlled by the gravity of the host star and experience weak gas drag; their orbits are mainly expressed by orbital elements: semimajor axes $a$, eccentricities $e$, and inclinations $i$, which are modulated by gas drag. In a previous study, $\dot a$, $\dot e$, and $\dot i$ were analytically derived for $e \ll 1$ and $i \ll H/a$, where $H$ is the scale height of the disk. Their formulae are valid in the early stage of planet formation. However, once massive planets are formed, $e$ and $i$ increase greatly. Indeed, some small bodies in the solar system have very large $e$ and $i$. Therefore, in this paper, I analytically derive formulae for $\dot a$, $\dot e$, and $\dot i$ for $1-e^2 \ll 1$ and $i \ll H/a$ and for $i \gg H/a$. The formulae combined from these limited equations will represent the results of orbital integration unless $e \geq 1$ or $i > \pi - H/a$. Since the derived formulae are applicable for bodies not only in a protoplanetary disk but also in a circumplanetary disk, I discuss the possibility of the capture of satellites in a circumplanetary disk using the formulae.