Rotational modulations are observed on brown dwarfs and directly imaged exoplanets, but the underlying mechanism is not well understood. Here, we analyze Jupiter's rotational light curves at 12 wavelengths from the ultraviolet (UV) to the mid-infrared (mid-IR). Peak-to-peak amplitudes of Jupiter's light curves range from sub percent to 4% at most wavelengths, but the amplitude exceeds 20% at 5 µm, a wavelength sensing Jupiter's deep troposphere. Jupiter's rotational modulations are primarily caused by discrete patterns in the cloudless belts instead of the cloudy zones. The lightcurve amplitude is dominated by the sizes and brightness contrasts of the Great Red Spot (GRS), expansions of the North Equatorial Belt (NEB), patchy clouds in the North Temperate Belt (NTB) and a train of hot spots in the NEB. In reflection, the contrast is controlled by upper tropospheric and stratospheric hazes, clouds, and chromophores in the clouds. In thermal emission, the small rotational variability is caused by the spatial distribution of temperature and opacities of gas and aerosols; the large variation is caused by the NH 3 cloud holes and thin-thick clouds. The methaneband light curves exhibit opposite-shape behavior compared with the UV and visible wavelengths, caused by wavelength-dependent brightness change of the GRS. Light-curve evolution is induced by periodic events in the belts and longitudinal drifting of the GRS and patchy clouds in the NTB. This study suggests several interesting mechanisms related to distributions of temperature, gas, hazes, and clouds for understanding the observed rotational modulations on brown dwarfs and exoplanets.
Global nonhydrostatic atmospheric models are becoming increasingly important for studying the climates of planets and exoplanets. However, such models suffer from computational difficulties due to the large aspect ratio between the horizontal and vertical directions. To overcome this problem, we developed a global model using a vertically implicit correction (VIC) scheme in which the integration time step is no longer limited by the vertical propagation of acoustic waves. We proved that our model, based on the Athena++ framework and its extension for planetary atmospheres—SNAP (Simulating Nonhydrostatic Atmospheres on Planets), rigorously conserves mass and energy in finite-volume simulations. We found that traditional numerical stabilizers such as hyperviscosity and divergence damping are not needed when using the VIC scheme, which greatly simplifies the numerical implementation and improves stability. We present simulation results ranging from 1D linear waves to 3D global circulations with and without the VIC scheme. These tests demonstrate that our formulation correctly tracks local turbulent motions, produces Kelvin–Helmholtz instability, and generates a super-rotating jet on hot Jupiters. Employing this VIC scheme improves the computational efficiency of global simulations by more than two orders of magnitude compared to an explicit model and facilitates the capability of simulating a wide range of planetary atmospheres both regionally and globally.
<ul> <li aria-level="1">Introduction</li> </ul> <p>&#160;&#160;Moist convection is ubiquitously present in Jupiter&#8217;s atmosphere albeit the least understood. Many fundamental questions regarding planetary atmospheres are closely related to moist convection. For example, lightning events are more frequently detected in Jupiter&#8217;s belts where the visible layer is dryer and cloudless [1, 2, 3]; chemically inert vapor like ammonia is not uniformly mixed well below its condensation level. To address those puzzles, we create a new Jovian atmospheric model (SNAP) [4], using the vertical-implicit-correction (VIC) scheme [5]. The VIC scheme greatly improves the computational efficiency for simulations with a large horizontal-to-vertical aspect ratio. For a typical synoptic-scale simulation, the efficiency is improved by about 2 orders of magnitudes. We present a beta-plane simulation relevant to Jupiter&#8217;s regimes with condensation of water and ammonia to study jet and vortex formations in the mid-latitude. Several cyclones, resembling hurricanes in Earth's atmosphere, are found at the interfaces of eastward jets and westward jets in the water cloud layers. Our simulation is the first nonhydrostatic 3D Jovian atmosphere model that explicitly resolves moist convection.&#160;</p> <ul> <li aria-level="1">Model Description</li> </ul> <p>&#160;&#160;SNAP is developed on top of the framework of Athena++, which is a finite volume astrophysics code [4, 6]. In our recent work, a VIC scheme is implemented into the model [5]. The VIC scheme solves diagnostic variables (i.e., density, velocities, and total energy) of Euler equations by implicitly treating the vertical flux divergence. This treatment greatly relaxes the Courant-Friedrichs-Lewy (CFL) condition in the vertical direction, allowing larger time steps for large horizontal-to-vertical aspect ratio simulations. The detailed description and test cases are present in Ref [5].</p> <ul> <li>Jupiter Beta-Plane Simulation</li> </ul> <p>&#160; We present the result of Jupiter&#8217;s beta-plane simulations. The initial condition is set as a uniform moist adiabat across the horizontal plane with water vapor and ammonia vapor. The heavy element abundances are chosen to be 3 times of solar value. We use a linear body cooling scheme to simplify the radiative transfer in Jupiter&#8217;s upper troposphere (i.e., above 1 bar pressure level). The bottom temperature is relaxed back to the initial value to mimic the internal heat flux in the real situation. Winds are allowed to evolve in the troposphere freely but are damped in the stratosphere. We tried two scenarios, one with latent heat release from water and ammonia and one without.&#160;</p> <p>&#160; Multiple eastward and westward jets are produced in both cases. Fig 1, the result of the moist case, shows that two giant cyclonic storms (i.e., radius ~ 1000 km) are also formed at jets&#8217; interfaces where the eastward jets are in the south, and westward jets are in the north. Such regions are belts in Jupiter&#8217;s atmosphere where the fluid motion is cyclonic. In the dry case, we find that, although latent heat is removed from the system (i.e., excluding water and ammonia vapors), there are still multiple jets with the same order of magnitude zonal wind speed, but cyclones vanish. Thus, resembling hurricanes on Earth [7], latent heat from the moist convection supplies the energy to form cyclones in Jupiter&#8217;s atmosphere.&#160;</p> <p><img src="data:image/png;base64, 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