[Paper Review] First 3-D grid-based gas-dust simulations of circumstellar disks with an embedded planet

Fabian Binkert, J. Szulágyi+1 more|arXiv (Cornell University)|Mar 18, 2021

Astrophysics and Star Formation Studies4 references4 citations

TL;DR

This study presents the first 3D grid-based hydrodynamic simulations of circumstellar disks with embedded planets, coupling gas and 1-mm dust dynamics. It reveals that planets induce vertical dust stirring, thickening the dust disk and causing ALMA-derived masses to underestimate true disk masses by up to a factor of 10, implying disks may be significantly more massive than previously assumed based on optically thin assumptions.

ABSTRACT

Substructures are ubiquitous in high resolution (sub-)millimeter continuum observations of circumstellar disks. They are possibly caused by forming planets embedded in the disk. To investigate the relation between observed substructures and young planets, we perform novel three-dimensional two-fluid (gas+1-mm-dust) hydrodynamic simulations of circumstellar disks with embedded planets (Neptune-, Saturn-, Jupiter-, 5 Jupiter-mass) at different orbital distances from the star (5.2AU, 30AU, 50AU). We turn these simulations into synthetic (sub-)millimeter ALMA images. We find that all but the Neptune-mass planet open annular gaps in both the gas and the dust component of the disk. We find that the temporal evolution of the dust density distribution is distinctly different of the gas'. For example, the planets cause significant vertical stirring of the dust in the circumstellar disk which opposes the vertical settling. This creates a thicker dust disk than disks without a planet. We find that this effect greatly influences the dust masses derived from the synthetic ALMA images. Comparing the dust disk masses in the 3D simulations and the ones derived from the 2D ALMA synthetic images, we find the former to be a factor of a few (up to 10) larger, pointing to that real disks might be significantly more massive than previously thought based on ALMA continuum images using the optically thin assumption and equation. Finally, we analyze the synthetic ALMA images and provide an empirical relationship between the planet mass and the width of the gap in the ALMA images including the effects of the beam size.

Motivation & Objective

• To investigate how embedded planets shape substructures in circumstellar disks using 3D two-fluid hydrodynamics.
• To determine the impact of planetary gravitational torques on dust distribution, particularly vertical stirring and gap formation.
• To assess the reliability of ALMA-derived dust masses when using the standard optically thin assumption.
• To establish a quantitative empirical relationship between observed ALMA gap width and planetary mass.
• To evaluate how disk properties such as turbulence and temperature affect gap morphology and observability.

Proposed method

• Performing 3D grid-based hydrodynamic simulations of circumstellar disks with embedded planets of varying masses (Neptune to 5 Jupiter masses).
• Using a two-fluid approach to model coupled gas and 1-mm dust dynamics, including dust feedback on gas.
• Simulating disks at different orbital radii (5.2 AU, 30 AU, 50 AU) to assess orbital distance effects.
• Applying radiative transfer to synthetic ALMA images from the 3D simulation outputs to mimic real observations.
• Deriving disk masses from both full 3D simulations and from 2D ALMA mock images using the standard optically thin formula.
• Fitting empirical relations between observed ALMA gap width and planetary mass, accounting for beam size and disk parameters.

Experimental results

Research questions

• RQ1 How do embedded planets affect the vertical structure and density distribution of dust in 3D circumstellar disks?
• RQ2 To what extent does vertical dust stirring by planets alter the inferred dust disk mass from ALMA observations?
• RQ3 How do gap widths in ALMA images correlate with planetary mass, and can this be used to infer planet masses from observations?
• RQ4 How do disk turbulence and temperature influence the morphology and observability of planetary gaps in dust continuum?
• RQ5 To what extent is the standard optically thin dust mass formula biased when applied to disks with embedded planets?

Key findings

• All planets except the Neptune-mass one open annular gaps in both gas and dust components, with gap width and depth evolving over time.
• The dust gap depth can initially increase and then decrease, unlike the gas gap, which steadily deepens.
• Planets induce significant vertical stirring of dust, resulting in a thicker dust disk than in planetless systems, counteracting vertical settling.
• The derived dust disk mass from ALMA mock images is systematically lower than the true 3D mass, underestimating it by a factor of 2 to 10 depending on the system.
• The discrepancy is most pronounced in systems with low-mass planets, regardless of orbital distance, indicating a general bias in standard mass estimation.
• An empirical relation between ALMA gap width and planetary mass is established, incorporating orbital radius, disk turbulence, and temperature, enabling future planet mass constraints.