Mass constraint for a planet in a protoplanetary disk from the gap width

TL;DR

This paper derives an empirical formula relating the width of gaps in protoplanetary disks to the mass of embedded planets, enabling more accurate planet mass estimates from observations.

Contribution

The authors provide a new empirical formula for gap width as a function of planet mass, disk aspect ratio, and viscosity, based on hydrodynamic simulations.

Findings

Gap width scales with the square root of planet mass.

The formula reduces uncertainties in planet mass estimates from observed gaps.

Application to HL Tau suggests specific planet masses within observed gaps.

Abstract

A giant planet creates a gap in a protoplanetary disk, which might explain the observed gaps in protoplanetary disks. The width and depth of the gaps depend on the planet mass and disk properties. We have performed two--dimensional hydrodynamic simulations for various planet masses, disk aspect ratios and viscosities, to obtain an empirical formula for the gap width. The gap width is proportional to the square root of the planet mass, -3/4 power of the disk aspect ratio and -1/4 power of the viscosity. This empirical formula enables us to estimate the mass of a planet embedded in the disk from the width of an observed gap. We have applied the empirical formula for the gap width to the disk around HL~Tau, assuming that each gap observed by ALMA observations is produced by planets, and discussed the planet masses within the gaps. The estimate of planet masses from the gap widths is less affected by the observational resolution and dust filtration than that from the gap depth.