How rotation rate influences the phase curve of hot Jupiters: theory and observations

Hot Jupiters are highly irradiated Jupiter-sized planets in extremely close synchronous orbits around their host stars. Despite their size and proximity to the star, which makes them relatively easy to observe, direct observations of their atmospheres are difficult. Therefore, interpreting indirect observations is crucial to understanding their global atmospheric circulation. Here, we aim to test the hypothesis that systematically varying the rotation rate of hot Jupiters influences their atmospheric circulation and resulting phase curves. We used DYNAMICO (Dubos et al, 2015), a 3d General Circulation Model (GCM) that uses an energy-conserving Hamiltonian to solve fluid dynamics equations on a rotating sphere. To test our hypothesis, we modelled benchmark hot Jupiter HD209458b and then Kepler 5b, WASP103b, and WASP121b. We used PICASO (Robbins-Blanch et al., 2022), a 3d state-of-the-art radiative transfer code, to model the phase curves in JWST NIRCam filters for 3.6 μm and 4.5 μm wavelengths. We also used GGChem (Woitke et al., 2018) to check if chemical species can condense into clouds composed of quartz and forsterite, unlike clouds in the Solar System.

Our simulations show that the general atmospheric circulation can be divided into two circulation regimes: rotational and divergent. The rotational regime is characteristic of models with fast rotation rates (between one and 40 times the nominal rotation rate). These models exhibit rotationally dominated circulation, which produces a narrow and weak eastward jet. Its speed drops from 3km/s to 0.3km/s and its width decreases with increasing rotation rate. These weak jets transport less heat from the substellar point, and therefore the synthetic phase curves have a large amplitude (the ratio of the planetary to stellar flux is around 3 × 10⁻⁵) and little to no offset. On the other hand, the divergent regime is characteristic of slow rotators. There, the divergent (overturning) circulation dominates, so the temperature across the planet is more homogenised, therefore, the synthetic phase curves exhibit 3 times smaller amplitudes than in the rotational regime and large offsets (of the order of tens of degrees).

Our results for HD209458b suggest that differences in the shapes and offsets of the phase curve are most prominent in the 4.5 μm band. However, our model underestimates the amplitude of the phase curves by half (the synthetic value is around 5 × 10⁻⁴ compared to 1 × 10⁻³ for the observed one). Even though our model includes accounts for the complex interplay between a planet’s physical characteristics (size, mass, period, etc.) and its chemical composition (metallicity and opacity), it is still idealised. It is yet to be extended to high atmosphere (10⁻⁶ bar), with possible weak temperature inversion, longer radiative timescales and high-altitude clouds.

 

Dubos, T., Dubey, S., Tort, M., Mittal, R., Meurdesoif, Y. and Hourdin, F. DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility. 2015. Geoscientific Model Development. 8: 3131-3150.

Robbins-Blanch, N., Kataria, T., Batalha, N. and Adams, D. J. Cloudy and Cloud-free Thermal Phase Curves with PICASO: Applications to WASP-43b. 2022. The Astrophysical Journal. 930: 93-102. 

Woitke, P., Helling, Ch., Hunter, G. H., Millard, J. D., Turner,  G. E., Worters, M., Blecic, J., and Stock, J. W. Equilibrium chemistry down to 100 K. Impact of silicates and phyllosilicates on carbon/oxygen ratio. 2018. Astronomy & Astrophysics. 614.