[Paper Review] Constraining the properties of the potential embedded planets in the disk around HD 100546

Max Ackermann Pyerin, Timmy N. Delage+4 more|arXiv (Cornell University)|Oct 7, 2021

Astrophysics and Star Formation StudiesPhysics and Astronomy53 references13 citations

TL;DR

This study constrains the masses and orbital radii of two embedded planets in the protoplanetary disk around HD 100546 using self-calibrated ALMA 0.9 mm dust continuum observations. By combining hydrodynamic simulations (FARGO3D) with synthetic observations (RADMC-3D), the best-fit model identifies an inner planet at 13 au with 8 MJup and an outer planet at 143 au with 3 MJup, requiring a self-similar, exponentially tapered gas surface density profile to reproduce the faint outer ring's low brightness relative to the inner ring.

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 $M_1 = 8 M_{ m{Jup}}$ and an outer planet located at $r_2 = 143\,$au with a mass $M_2 = 3 M_{ m{Jup}}$ 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.

Motivation & Objective

• To constrain the masses and orbital separations of potential embedded planets in the HD 100546 protoplanetary disk.
• To determine whether one or two planets are required to reproduce the observed substructures, particularly the faint outer ring.
• To investigate the disk's initial gas surface density profile necessary to match the observed brightness ratio between inner and outer rings.
• To evaluate the detectability of such planets with current ALMA and direct imaging instruments.

Proposed method

• Self-calibrated 0.9 mm ALMA observations of HD 100546 were used to extract dust continuum emission and identify substructures.
• Hydrodynamic simulations of gas and dust were performed using the FARGO3D code, modeling planet-disk interactions with varying planet masses and orbital radii.
• Synthetic observations were generated from simulation outputs using the RADMC-3D code to simulate ALMA-like imaging conditions.
• The model outputs were compared with real ALMA data by analyzing image morphology and radial brightness profiles.
• A self-similar, exponentially tapered power-law initial gas surface density profile was tested and found necessary to reproduce the faint outer ring.
• Model fitting was performed iteratively by varying disk viscosity (α), planet masses, and orbital locations to minimize deviation from observed radial profiles.

Experimental results

Research questions

• RQ1 What planet masses and orbital radii best reproduce the observed substructures in the HD 100546 disk, particularly the faint outer ring?
• RQ2 Can a two-planet model explain both the inner and outer rings, or is a single planet sufficient?
• RQ3 What initial disk gas surface density profile is required to match the observed brightness ratio between the inner and outer rings?
• RQ4 How does disk viscosity (α) affect the inferred planet masses and model fit quality?
• RQ5 Are the predicted planet masses detectable with current ALMA or direct imaging instruments?

Key findings

• The best agreement between synthetic and ALMA observations is achieved with an inner planet at 13 au and a mass of 8 MJup, and an outer planet at 143 au and a mass of 3 MJup, with a deviation of less than 3σ in the normalized radial profile.
• The initial gas surface density profile must follow a self-similar, exponentially tapered power law to reproduce the low brightness of the outer ring relative to the inner ring.
• For a disk viscosity of α = 10⁻³, the outer planet mass is estimated at 3 MJup; for lower viscosity (α = 10⁻⁴), the mass is estimated at 1.7 MJup.
• The model successfully reproduces the outer ring's lack of azimuthal asymmetries, supporting the planet-induced pressure trap mechanism.
• The inferred planet masses are below the current ALMA detection limit (33 MJup for a 4 Myr-old system), making direct detection unlikely with existing instrumentation.
• The results are consistent with previous findings from scattered-light imaging (spiral arms at ~100 au) and molecular line observations (companion at ~15 AU), supporting the presence of two massive planets.