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

2021 
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 well resolved the faint outer ring. 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 are responsible for inducing 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 which are consistent with two rings, the outer ring being much fainter than the inner one. We reproduce this appearance closely with a numerical model that assumes two embedded planets. We vary planet and disk parameters in the framework of the planet-disk interaction code FARGO3D, and use 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 one 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.
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