# Pileups and Migration Rates for Planets in Low Mass Disks

## TL;DR

This paper studies how low-mass planets interact with viscous disks, revealing a pileup effect behind the planet that influences migration rates and can be observed in protoplanetary disks.

## Contribution

It provides the first detailed 2D hydrodynamical simulations of pileup effects in low-mass disks and introduces a new Type-II migration rate model.

## Key findings

- Disk material piles up behind planets, acting as a leaky dam.
- Simulation results match theoretical predictions for moderate gap depths.
- Current theory is insufficient for very deep gaps, indicating areas for further research.

## Abstract

We investigate how planets interact with viscous accretion disks, in the limit that the disk is sufficiently low mass that the planet migrates more slowly than the disk material. In that case, the disk's surface density profile is determined by the disk being in viscous steady state (VSS), while overflowing the planet's orbit. We compute the VSS profiles with 2D hydrodynamical simulations, and show that disk material piles up behind the planet, with the planet effectively acting as a leaky dam. Previous 2D hydrodynamical simulations missed the pileup effect because of incorrect boundary conditions, while previous 1D models greatly overpredicted the pileup due to the neglect of non-local deposition. Our simulations quantify the magnitude of the pileup for a variety of planet masses and disk viscosities. We also calculate theoretically the magnitude of the pileup for moderately deep gaps, showing good agreement with simulations. For very deep gaps, current theory is inadequate, and we show why and what must be understood better. The pileup is important for two reasons. First, it is observable in directly imaged protoplanetary disks, and hence can be used to diagnose the mass of a planet that causes it or the viscosity within the disk. And second, it determines the planet's migration rate. Our simulations determine a new Type-II migration rate (valid for low mass disks), and show how it connects continuously with the well-verified Type-I rate.