Circumplanetary Disks are Rare around Planets at Large Orbital Radii: A Parameter Survey of Flow Morphology around Giant Planets

Abstract: We investigate how the formation and structure of circumplanetary disks (CPDs) varies with planet mass and protoplanetary disk aspect ratio. Using static mesh refinement and a near-isothermal equation of state, we perform a small parameter survey of hydrodynamic simulations with parameters appropriate for disk-embedded protoplanets at moderate to large orbital radii. We find that CPD formation occurs along a continuum, with ``diskiness'' increasing smoothly with planetary mass and decreasing disk aspect ratio. As expected from disk hydrostatic equilibrium arguments, the transition from envelope-dominated to disk-dominated structures is determined to first order by the ratio of the planetary Hill sphere radius to the disk scale height, but planets need to be significantly super-thermal to host classical rotationally supported CPDs. The circularization radius of inflowing gas (as a fraction of the Hill sphere radius) shows an approximately quadratic power-law scaling with the ratio of planetary mass to the thermal mass. Compared to more physically complete radiation hydrodynamic simulations, our runs almost maximize the possibility for classical CPD formation, and hence define a plausible necessary condition for CPDs. The low abundance of detected CPDs in disks where planetary companions are inferred from substructure data may be due to a combination of the large scale height of the protoplanetary disk, and a low frequency of sufficiently massive protoplanets. Unless their CPDs cool below the local protoplanetary disk temperature, most of the wide-orbit giant planet population will be embedded in quasi-spherical envelopes that are hard to detect. Disks, and satellite systems, are more likely to form around smaller orbital separation planets.

• The paper investigates circumplanetary disk (CPD) formation around giant planets at large orbital radii using hydrodynamic simulations, varying parameters like planetary mass and protoplanetary disk aspect ratio to understand flow morphology.
• Numerical results indicate CPD formation depends predictably on planetary mass and disk aspect ratio, with their observed rarity attributed to large disk scale heights and the scarcity of sufficiently massive planets needed to sustain classical disks.
• This study emphasizes the need to integrate temperature effects, angular momentum, and radiation hydrodynamics more realistically in future CPD models to address observational challenges and refine satellite system formation theories.

Investigating the Rarity of Circumplanetary Disks Around Giant Planets at Large Orbital Radii

This paper conducts a detailed study concerning the formation and structure of circumplanetary disks (CPDs) around giant planets, particularly those positioned at substantial orbital radii. The authors employ hydrodynamic simulations under a near-isothermal condition to understand how different parameters such as the planetary mass and protoplanetary disk aspect ratio affect CPD morphology.

Study Overview

The paper systematically examines how the so-called "diskiness" of CPDs evolves with planetary mass and the aspect ratio of the surrounding protoplanetary disk. It uses a static mesh refinement technique for simulations, which allows a focus on hydrodynamic scenarios where protoplanets are embedded within disks at moderate-to-large orbital radii. The research distinguishes itself by exploring the continuum of CPD formation and transitioning from envelope-dominated to disk-dominated morphologies. This transition is analyzed primarily through the lens of the ratio between the planetary Hill sphere radius and the disk scale height, emphasizing the necessity for a planet to be significantly super-thermal to support a rotating CPD.

Key Findings

The numerical results underscore several critical insights:

• CPD Morphology: The formation of CPDs progresses predictably with increasing planetary mass and decreasing disk aspect ratio, confirming theoretical expectations. Notably, the angular momentum of inflowing gas—and consequently the emergence of disk-like structures—are dictated by a quadratic power-law relation involving the planetary mass relative to thermal mass.
• CPD Rarity: The low observation distribution of CPDs, even in planets inferred to exist through disk substructures, is attributed to the combination of large disk scale heights and the scarcity of sufficiently massive planets to sustain classical CPDs. Additionally, unless the CPDs successfully cool below the local disk temperature, they are likely to remain in hard-to-detect spherical envelopes.
• Simulation Boundaries: The near-isothermal state used in simulations aimed to provide an almost maximal condition for possible CPD formation. Comparisons with more intricate radiation hydrodynamics models suggest that while necessary for CPD formation, these conditions only depict near-ideal scenarios seldom found in real observed environments.

Implications and Future Directions

This study has significant implications for the theoretical modeling and observational strategies of CPD and satellite system formation. Practically, it stresses the observational challenges posed by the CPDs' embedding in quasi-spherical envelopes at wide orbital radii. Theoretically, it highlights the importance of integrating temperature effects and angular momentum considerations more realistically in future simulation models.

The work also suggests that more sophisticated simulations incorporating radiation effects, magnetic fields, and longer cooling timeframes could offer further insights into CPD dynamics, particularly for environments differing significantly from the near-isothermal condition. Furthermore, understanding the implications of planetary migration on CPD structure within varying disk atmospheres (region-specific H/R) could refine models of satellite system formation, both in our solar system and exoplanetary realms.

In conclusion, this study advances the comprehension of the delicate equilibrium between disk properties and planetary mass in shaping the CPD landscape, thus providing a basis for future explorations of circumplanetary environments.