Flow Regimes in Hot Jupiter Atmospheres: Insights from Anelastic Models

TL;DR

This paper addresses how irradiation drives complex 3D flows in Hot Jupiter atmospheres beyond hydrostatic GCMs by solving the full anelastic Navier–Stokes and heat equations in a rotating spherical shell. Using the MagIC code, it maps 124 models across a broad range of Rayleigh numbers and stratification to identify flow regimes and quantify heat redistribution via entropy advection and Reynolds stresses. It finds four regime classes, with strong stratification producing fast prograde equatorial jets (up to km s$^{-1}$) and slow radial flows, and shows that both eastward and westward hotspot shifts can arise from entropy advection alone, depending on depth; this offers a magnetic-free explanation for retrograde phase offsets observed in some systems. The results highlight depth-dependent phase curves and emphasize the importance of anelastic, 3D dynamics for interpreting exoplanet IR observations, extending beyond traditional GCM assumptions.

Abstract

Hot Jupiters are Jupiter-sized exoplanets with close-in orbits, characterized by extreme day-night temperature contrasts due to synchronous rotation. These planets offer unique observational opportunities through transit photometry, transmission spectroscopy, and infrared (IR) phase curve analysis, which reveal information about heat redistribution and atmospheric dynamics. Complementary to common generalized circulation models (GCMs), we introduce a more comprehensive approach using the anelastic fluid equations that fully capture the three-dimensional nature of the emerging non-linear flows. We identify various non-linear flow regimes and analyze the heat distribution when irradiation and thermal advection reach equilibrium. Eastward zonal winds can reach velocities comparable to the planetary rotation (up to several kilometers per second), while slower radial flows, though less prominent, contribute significantly to heat advection and can cause both eastward and westward hotspot shifts. The efficiency of day-to-night heat redistribution and the positioning of brightness maxima are shown to depend strongly on pressure and the interplay of advective and radiative processes. These findings improve our understanding of the diversity observed in the IR phase curves and suggest a non-magnetic mechanism for retrograde hotspot shifts. By extending the scope of traditional GCM models, our work demonstrates the usefulness of anelastic models in capturing the complex, multidimensional dynamics of irradiated exoplanetary atmospheres.

Figures (12)

• Figure 1: Statistics of characteristic HJ properties. Top panel: Mass-radius diagram. Middle panel: Depth for a hundredfold pressure increase relative to planet radius. Bottom panel: Ratio of the isothermal Brunt-Väisälä and the rotation frequency $N_T/\Omega$. The size of the symbols is scaled with the planetary radius, while the color indicates the equilibrium temperature.
• Figure 2: Overview of parameter regimes and types of solution. The three left panels show the location of the four solution types, indicated by different symbols, in the $Ra$/$A$ parameter space for three different Ekman numbers. We classify the solutions into linear (triangles), partially unstable (pentagons), turbulent (circles) and super-laminar (stars). The symbol size is scaled with the Ekman number and the symbol color indicates the stratification $\hbox{A}$. The center panel shows the characteristic non-dimensional poloidal $U_{pol}$ and toroidal flow amplitudes $U_{tor}$scaled to provide Rossby numbers $\hbox{Ro}=U/(D\Omega)$. The right hand plot shows the zonality of the toroidal flow.
• Figure 3: Flow solutions classified by spherical surface plots of $u_r$, $u_\theta$, $u_\phi$ and the nonaxisymmetric part of $u_\phi^\prime$ at $r/r_o=0.95$
• Figure 4: Like Fig. \ref{['instab1']} but for higher relative stratification.
• Figure 5: Like Fig. \ref{['instab1']} but for the two configurations found in the super laminar regime.