Efficiency of Hydrodynamic Atmospheric Escape in Hot Jupiters and Super Earths

TL;DR

We address how radiative cooling, especially via $\mathrm{H}_3^+$ and Ly$\alpha$, reduces the energy budget available to drive EUV-induced atmospheric escape from hot Jupiters and sub-Neptunes. To do this, we develop a flexible 1D photochemical-hydrodynamic model that couples hydrogen/helium chemistry with hydrodynamics, conduction, and bolometric heating/cooling under a solar-like EUV spectrum scaled by orbital distance. Our results show that $\mathrm{H}_3^+$ cooling can substantially limit the outflow, with conduction enhancing cooling at larger stellocentric distances and cooler, more molecular outflows arising for lower-mass planets, implying molecular cooling is crucial for atmospheric retention in those cases. The framework provides a path to evaluate energy-limited escape versus radiative losses across planetary masses and separations, highlighting the importance of molecular processes in shaping planetary atmospheres.

Abstract

We develop a flexible one-dimensional code to model the escape of hydrogen and helium from a hot Jupiter as a result of photoionization from extreme-ultraviolet (EUV) radiation. We include stellar spectrum heating and ionization, radiative cooling by Lyman-$α$ and H$_3^+$, heat conduction, tidal gravity, a H-He reaction network, and account for the secondary ionization of species by photoelectrons. For a fiducial hot Jupiter, we uncover a three-layer structure: an H$_3^+$-cooled layer of molecular hydrogen at the base, enveloped by a Lyman-$α$-cooled layer of neutral hydrogen, which transitions into an ionized wind layer that is cooled by adiabatic expansion. The highest spectral energy photons are deposited in the molecular layer, where, after accounting for energy loss via photoelectrons and ionization, H$_3^+$ is a substantial radiative coolant. We run a grid of models, varying the distance of our fiducial planet from the star. We find that heat conduction at the base starts to have an effect at distances $\gtrsim 0.2$ au, increasing the H$_3^+$ cooling relative to the EUV input flux. At increasing stellocentric distances, the outflow becomes increasingly more neutral. The neutral hydrogen starts to decouple from the ionized outflow, free-streaming out. In pure H-He mini-Neptune/super-Earth simulations, the outflows are significantly cooler, allowing molecules to survive throughout the outflow, pointing toward the likely importance of molecular cooling in determining whether these planets can maintain massive atmospheres. The analysis in this paper provides a framework for understanding the impact of molecular radiative cooling on atmospheric outflows.

Figures (1)

• Figure 1: Illustration of a staggered grid with uneven spacing. The staggered grid cells are centered at the regular grid cell boundaries. The ghost cells are shaded in gray.