The Two-Dimensional Structure of Circumplanetary Disks and their Radiative Signatures

TL;DR

The paper develops and applies a self-consistent two-dimensional RAD+ framework that couples the DIAD disk structure model with the RADMC-3D radiative transfer code to predict the vertical and radial structure of circumplanetary disks (CPDs) and their radiative signatures. It shows that CPDs are geometrically thick and hot, with $H/R\sim0.1-0.25$, and that planetary irradiation and viscosity shape two distinct $\tau=1$ surfaces, producing complex temperature distributions and observable SEDs that depend on $\dot{M}$, $M_p$, infall geometry, and viewing angle. The work identifies regimes of gravitational stability ($Q\gtrsim10^3$) and a thermal instability upper limit around $\dot{M}\sim60\,M_J\,\mathrm{Myr}^{-1}$, constraining feasible accretion rates and informing expectations for future JWST/ELT observations. By mapping how radiative signatures respond to system parameters, the study provides a framework to infer CPD and planet properties from multi-wavelength observations, advancing our understanding of giant planet formation and CPD physics.

Abstract

During their formative stages, giant planets are fed by infalling material sourced from the background circumstellar disk. Due to conservation of angular momentum, the incoming gas and dust collects into a circumplanetary disk that processes the material before it reaches the central planet itself. This work investigates the complex vertical structure of these circumplanetary disks and calculates their radiative signatures. A self-consistent numerical model of the temperature and density structure of the circumplanetary environment reveals that circumplanetary disks are thick and hot, with aspect ratios $H/R\sim0.1-0.25$ and temperatures approaching that of the central planet. The disk geometry has a significant impact on the radiative signatures, allowing future observations to determine critical system parameters. The resulting disks are gravitationally stable and viscosity is sufficient to drive the necessary disk accretion. However, sufficiently rapid mass accretion can trigger a thermal instability, which sets an upper limit on the mass accretion rate. This paper shows how the radiative signatures depend on the properties of the planetary system and discuss how the system parameters can be constrained by future observations.

Figures (21)

• Figure 1: Dust Opacities. The dust opacities for different compositions. The silicate component of the dust (black) is composed of 50 olivine (red) and 50 pyroxene (green). The carbon component is entirely graphite (blue). The total opacity of the dust is the sum of the silicate and carbon components, with the silicate opacity weighted by the silicate fraction $f_{\rm Si}$ and the carbon opacity weighted by $(1-f_{\rm Si})$. The dust grains have a power-law size distribution $n(a)\propto a^{-3.5}$ with a minimum size of 0.005 and a maximum size of 100. Note that the opacity is given in terms of per unit mass of dust.
• Figure 2: Disk Radial Structure. The central temperature, surface temperature, aspect ratio, and surface density versus radius for different mass accretion rates. The mass accretion rates are shown in different colors. In the top two panels, the gray region shows where the dust sublimates at $T\geq\qty{1400}{K}$. The variations in the disk aspect ratio at large distances results from Monte Carlo noise in the temperature. The dashed lines in the third panel show the scale height if the disk were isothermal at the central temperature. The total masses of these disks are $M_p=\qtylist{7.9e-6; 1.8e-5; 4.0e-5; 8.1e-5;1.7e-4}{M_J}$ for $\dot{M}=\qtylist{0.1;0.3;1;3;10}{M_J\per\mega yr}$, respectively.
• Figure 3: Disk Density Structure. The disk density (dust and gas) as calculated by our RAD+ model. The black line indicates the "boundary" of the disk, outside of which the density is zero by construction. The white dashed line shows where $Z=H$, the white dotted line shows where the vertical optical depth to viscous heating $\tau_\nu=1$, and the white dash-dot line shows where the radial optical depth to the planet $\tau_p=1$. The system parameters are given by the fiducial values (Table \ref{['tab:canonvals']}). The solid white lines are isotherms at $T=\qtylist{100;250;500;1000}{K}$. The black dashed line shows where $Z=R$.
• Figure 4: Disk Temperature Structure. The vertical temperature structure of the disk at 5;10;50;100R_p. The height is shown in units of the (isothermal) scale height, defined to be $H\equiv\sqrt{(2k_BT_c)/(\Omega^2\mu m_p)}$, where $T_c$ is the central temperature and $\Omega=\sqrt{GM_p/R^3}$ is the Keplerian angular orbital frequency. For $\dot{M}=\qty{0.1}{M_J\per\mega yr}$, $R_X>\qty{5}{R_p}$, and so that line does not appear. The gray region indicates where $T\geq\qty{1400}{K}$ and where dust will sublimate.
• Figure 5: Disk Temperature Structure. The disk density (dust and gas) as calculated by our numerical RAD+ model. The black line indicates the "boundary" of the disk, outside of which the density is zero. The system parameters are given by the fiducial values (Table \ref{['tab:canonvals']}). The white lines show the snowlines of dust, C$_2$H$_2$, and H$_2$O.