Constraining the properties of the potential embedded planets in the disk around HD 100546

TL;DR

This study uses high-resolution ALMA observations and numerical modeling to constrain the properties of potential embedded planets in the HD 100546 disk, revealing two planets at specific locations and masses that explain the observed rings.

Contribution

It provides the first detailed modeling of the HD 100546 disk with embedded planets, constraining their masses and positions based on observed substructures.

Findings

Inner planet at 13 au with 8 Jupiter masses

Outer planet at 143 au with 3 Jupiter masses

Disk density profile follows an exponentially tapered power law

Abstract

Context. The protoplanetary disk around the star HD 100546 displays prominent substructures in the form of two concentric rings. Recent observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) have revealed these features with high angular resolution and have resolved the faint outer ring well. This allows us to study the nature of the system further. Aims. Our aim is to constrain some of the properties of potential planets embedded in the disk, assuming that they induce the observed rings and gaps. Methods. We present the self-calibrated $0.9\,$mm ALMA observations of the dust continuum emission from the circumstellar disk around HD 100546. These observations reveal substructures in the disk that are consistent with two rings, the outer ring being much fainter than the inner one. We reproduced this appearance closely with a numerical model that assumes two embedded planets. We varied planet and disk parameters in the framework of the planet-disk interaction code FARGO3D and used the outputs for the gas and dust distribution to generate synthetic observations with the code RADMC-3D. Results. From this comparison, we find that an inner planet located at $r_1 = 13\,$au with a mass $M_1 = 8 M_{\rm{Jup}}$ and an outer planet located at $r_2 = 143\,$au with a mass $M_2 = 3 M_{\rm{Jup}}$ leads to the best agreement between synthetic and ALMA observations (deviation less than $3\sigma$ for the normalized radial profiles). To match the very low brightness of the outer structure relative to the inner ring, the initial disk gas surface density profile needs to follow an exponentially tapered power law (self-similar solution), rather than a simple power-law profile.