# An empirically-derived formula for the shape of planet-induced gaps in protoplanetary disks

## TL;DR

This paper derives an empirical formula for the shape of planet-induced gaps in protoplanetary disks using hydrodynamics simulations, enabling quick generation of synthetic disk profiles for various planetary and disk parameters.

## Contribution

It introduces a novel empirical formula for the surface density profile of gaps in protoplanetary disks, based on extensive numerical simulations across key parameters.

## Key findings

- Excellent agreement between the formula and numerical gaps across parameter space.
- The formula accurately predicts gap depth and width for a wide range of planet masses.
- A user-friendly code is provided for synthetic disk profile generation.

## Abstract

This study uses numerical hydrodynamics calculations and a novel method for densely sampling parameter space to measure the precise shape of a gap opened by a planet in a gaseous disk, as a function of planet-to-star mass ratio, disk Mach number, and disk viscosity. Formulas for gap depth and width are determined, which are combined to form a complete formula for surface density as a function of radius in the disk. This new analytical formula is compared with numerically-derived gaps opened by planets ranging from very low masses up to a few times Jupiter's mass, and excellent agreement is found over a wide range of parameter space relevant to planet-disk interactions. A simple-to-use code is presented to rapidly generate synthetic disk profiles.