Lava planets are a class of rocky exoplanets that orbit so close to their star that parts of their surface are molten. Indeed, dayside temperatures can be hot enough to maintain a rock vapour atmosphere detectable through transit and eclipse spectroscopy, as well as phase curves. Theoretical studies of lava planets and their relatively volatile sodium atmospheres have been published for CoRot-7b, Kepler-10b, 55 Cnc-e, KIC 12556548, and HD 219134b. These studies utilized a 1D model that solves for the flow of mass, momentum, and energy from the hot dayside to the cold nightside.
Now, Giang Nguyen and colleagues, studied K2-141b, the highest signal-to-noise lava planet discovered to date, as its phase variations have been measured by K2, Spitzer and possibly in the future with the James Webb Space Telescope (JWST). They use essentially the same model as the above studies, but they employed more accurate surface temperature calculations. They consider three compositional end-members for the atmosphere: 1) pure sodium (Na), due to its high volatility, 2) silicon monoxide (SiO), or 3) pure silica (SiO2) due to their abundance in the crust of rocky planets. These three cases bracket the range of plausible atmospheric compositions.
They then compared how pure Na, SiO, or SiO2 atmospheres would impact future observations.
For that they used the model to determine the steady-state flow of a pure Na, SiO, and SiO2 atmosphere for lava planet K2-141b. Atmospheric pressure, wind velocity, and temperature for the three cases are shown in fig 2 below. Na is the most volatile molecule, making the Na atmosphere the thickest of the three with the maximum pressure at the subsolar point of 13.8 kPa. The Na atmosphere fully condenses out at 𝜃 = 102° where wind speed can reach up to 2.3 km/s. The atmospheric temperature of Na can drop to near zero before fully collapsing.
SiO is not as volatile as Na making the SiO atmosphere thinner with a maximum pressure of 5.25 kPa. The wind, however, accelerates much faster than the Na case with velocities reaching up to 2.2 km/s and the atmosphere condenses out at 𝜃 = 92°. The temperature also drops much faster. Running the model for SiO2 produces the thinnest atmosphere with a maximum pressure of 240 Pa and collapses at 𝜃 = 89°. The wind is slower with a maximum speed of 1.75 km/s but the SiO2 atmosphere is much warmer as the temperature remains above 1500 K.
Evaporation and condensation rates vary significantly between the Na, SiO, and SiO2 cases. Although Na and SiO have similar evaporation rates near the subsolar point, the SiO atmosphere starts to condense sooner than its Na counterpart. The evaporation rates for the three scenarios are shown in Fig. 3.
Besides this, they have shown that the significantly less volatile SiO2 atmosphere may be easier to observe due to the extreme geometry of this system. Transit spectroscopy of K2-141b is possible due to its proximity to its star which make dayside regions accessible at the start and end of transit, and leads to large acceleration throughout transit.
They also note that the extreme orbit of K2-141b leads to significant changes in radial velocity over the course of the transit.
Their calculated return flow of SiO2 through the magma ocean is slow (10-⁴ m/s), so mass balance can be easily achieved. This supports a steady-state silicate flow whereas the volatile Na atmosphere would be limited by the return flow through the magma ocean.
If we assume the composition of K2-141b to be similar to the Bulk Silicate Earth, then there is 100x more silicate material than Na, by mass. However, their results showed that the mass transport required for a steady-state flow of Na is much greater than the 10-⁴ m/s provided by the SiO2 magma ocean. This implies that a more realistic Na atmosphere is much thinner than what they predicted before because the steady-state flow cannot be sustained, leading to the “evolved” state. Also, any precipitation that falls beyond the magma ocean shore (𝜃 > 79°) must be brought back to maintain mass conservation. This may occur via solid state flow analogous to glaciers on Earth, or via isostatic adjustment. If mass is transported back too slowly, the resulting mass imbalance could lead to reorientation of the planetary spin.
According to researchers, although K2-141b is an especially good target for atmospheric observation, their results regarding atmospheric dynamics, replenishment via the magma ocean, and transit geometry may apply to other lava planets.
References: T. Giang Nguyen, Nicolas B. Cowan, Agnibha Banerjee, John E. Moores, “Modelling the atmosphere of lava planet K2-141b: implications for low and high resolution spectroscopy”, ArXiv, pp. 1-8 2020. https://arxiv.org/abs/2010.14101
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