Three-Dimensional Ocean Dynamics and Detectability of Tidally Locked Lava Worlds

Abstract

Tidally locked lava planets are hot, rocky worlds on close-in orbits with a permanent molten dayside. With JWST, their surfaces and atmospheres are beginning to be revealed. This work investigates 3D magma-ocean dynamics, derives scaling laws for the resulting ocean heat transport (OHT), and predicts its detectability. For the first time, the ocean circulation driven by the intense momentum and mass exchanges with the supersonic atmosphere is considered in addition to that by thermal forcing. The wind forcing turns out to overwhelmingly dominate the other two mechanisms, driving ocean currents reaching $\sim$100 m s$^{-1}$ and greatly expanding the latitudinal extent of the Matsuno-Gill response. Despite these extreme flow speeds, scaling analysis and 3D simulations consistently demonstrate that magma-ocean circulation alone does not produce an observable hotspot offset. This inefficiency arises because basin geometry and circulation structure fundamentally constrain zonal heat redistribution, suppressing large-scale longitudinal transport even under vigorous flow.

Figures (9)

• Figure 1: Drivers of ocean circulation on tidally locked lava worlds. (a) Surface temperature with a substellar temperature of 3000 K and a nightside temperature of 50 K. The ocean boundary, defined by the 2000 K liquidus, is indicated by the black contour. (b) Evaporation and condensation rates, with maxima of 0.1 and $-$0.05 kg m$^{-2}$ s$^{-1}$, respectively; positive values correspond to evaporation (mass loss) and negative values to condensation (mass gain). (c) Horizontal wind stress, directed radially outward from the substellar point, peaking at approximately 120 N m$^{-2}$ near $\pm$40$^\circ$ in both longitude and latitude.
• Figure 2: Ocean circulation driven by various forcings. Panels (a–i) show results driven by thermal forcing (a), evaporative forcing (b), wind forcing scaled by 0.001 (c), 0.01 (d), 0.05 (e), 0.1 (f), 0.5 (g), and 1 (h), and all forcings (i). Arrows represent vertically integrated horizontal flow over the upper 10 m (m$^2$ s$^{-1}$), and colors represent vertical velocity at the base of the upper 10 m layer (m s$^{-1}$). In each panel, the meridional extents set by the equatorial Rossby deformation radius, $L_{\beta} = \sqrt{\sqrt{\Delta b D_o}/{\beta}}$, and the Rhines scale, $L_{\rm Rhines} = \sqrt{U/\beta}$, are indicated by gray dashed and solid lines, respectively. Here $\Delta b$ is the horizontal buoyancy contrast, $\beta$ is the meridional derivative of the Coriolis parameter, $D_o$ and $U$ are the characteristic magma ocean depth and horizontal current speed in the upper 10 m, respectively. A reference vector indicating the arrow length is shown in the bottom right corner of each panel.
• Figure 3: 3D temperature structure and basin shape, and SSH driven by thermal (a), evaporative (b), wind (c), and all forcings (d). In each panel, colors indicate temperature, contours represent SSH (contour intervals of 1 m in (a), 4 m in (b), and 15 m in (c) and (d)), and gray shading masks the magma ocean basin. The surface temperature and SSH fields are projected onto the top plane as functions of longitude and latitude. A zonal–vertical temperature slice along the equator is projected onto the back plane, and a meridional–vertical slice along 50$^{\circ}$W is projected onto the right plane. For clarity, only the upper 1800 m is shown.
• Figure 4: Examination of scaling laws under thermal-driven (left), evaporation-driven (middle), and wind-driven (right) conditions. From top to bottom, panels show horizontal velocity ($U$, black squares and lines) and SSH difference ($\Delta \eta$, red crosses and lines); thermocline depth ($D$, black squares and lines) and magma ocean depth ($D_o$, red crosses and lines), with the corresponding $\pm1\sigma$ intervals indicated by error bars; and OHT divergence ($H$) as functions of forcing amplitude. Under wind-driven conditions, no scaling law is shown for $\Delta \eta$ because the surface velocity is forced by wind stress rather than by a pressure gradient. In all panels, markers represent mean values within the magma ocean obtained from the 3D simulations, while solid lines indicate predictions from scaling laws.
• Figure 5: Detectability index, $\log(\mathcal{P})$, under a range of stellar, planetary, and atmospheric conditions. From left to right, panels show $\log(\mathcal{P})$ as a function of planetary radius $R_p/R_E$ and substellar temperature $T_{\rm sub}$ for stellar mass ratios of $M_{\star}/M_{\odot} = 0.2$, 1, and 5, respectively. Here, $R_p$ and $R_E$ denote the radii of the lava planet and Earth, $M_\star$ and $M_{\odot}$ denote the stellar and solar mass. In each panel, blue and orange contours orrespond to Na and SiO vapor atmospheres, respectively, and the shaded regions indicate regimes in which lava OHT is detectable, defined by $\log(\mathcal{P})>0$.