Irradiated Atmospheres. III. Radiative-convective-mixing Equilibrium for Nongray Picket-fence Model
Astrophysical Journal 984:2 (2025)
Abstract:
The nongray picket-fence model predicts more accurately the temperatures in low-density regions compared to semigray models. This study investigates how the vertical-mixing and convection fluxes modify the picket-fence model. The usual radiative-convective-equilibrium is now extended to radiative-convective-mixing-equilibrium. The temperature profile, characterized by an increase with pressure in the upper region and an inversion in the lower, is influenced by Rosseland opacity, spectral bands, and chemical composition. The atmosphere consists of five distinct layers: a pseudo-adiabatic zone shaped by mixing flux, two convective layers driven by convective flux with a smaller adiabatic gradient, and two radiative layers. In scenarios with lower Rosseland opacity, vertical mixing significantly reduces the width of temperature inversion, counteracting the cooling effect of the convective layers and driving the deep convective layer inward. The convective flux lowers the upper temperature and expands the upper convective layer. In the low-Rosseland-opacity five-band model, these fluxes significantly cool the midatmosphere when temperature increases with pressure, enlarging the pseudo-adiabatic region. Without TiO/VO, the pseudo-adiabatic region shrinks, indicating that TiO/VO enhances the mixing effect. Moreover, less mixing intensity is essential to maintain a stable five-layer structure. Therefore, future studies of chemical equilibrium with multifrequency atmospheric opacity should clearly define the constraints on vertical mixing.Self-limited tidal heating and prolonged magma oceans in the L 98-59 system
(2025)
Irradiated Atmospheres. II. Interplay between Scattering and Vertical-mixing-induced Energy Transport
Astrophysical Journal 984:1 (2025)
Abstract:
Scattering is crucial for the atmospheric thermal profiles. The energy transport by vertical mixing plays an essential role in the greenhouse or anti-greenhouse effect. This work explores the interaction between scattering and vertical mixing, specifically whether these processes enhance or mitigate each other’s effects on atmospheric temperature. The interaction between mixing flux and scattering is nonlinear. Our calculations indicate that thermal scattering intensifies the greenhouse effects caused by vertical mixing in the middle atmosphere but reduces them in the lower layers. In the middle atmosphere, increased vertical mixing enhances the warming effect of thermal scattering while diminishing the cooling effect of visible scattering. In the lower atmosphere, it enhances the anti-greenhouse effect linked to visible scattering and diminishes the greenhouse effect produced by thermal scattering. The combined influence of thermal scattering and vertical mixing on the lower atmosphere’s greenhouse effect is weaker than their separate impacts, akin to 1 + 1 < 2. It is also interesting to note that the joint effect may also influence chemistry and cloud formation, altering the thermal structure.
The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape
arXiv:2504.19872 [astro-ph.EP]
Abstract:
The "cosmic shoreline", a semi-empirical relation that separates airless worlds from worlds with atmospheres as proposed by Zahnle & Catling (2017), is now guiding large-scale JWST surveys aimed at detecting rocky exoplanet atmospheres. We expand upon this framework by revisiting the shorelines using existing hydrodynamic escape models applied to Earth-like, Venus-like, and steam atmospheres for rocky exoplanets, and we estimate energy-limited escape rates for CH4 atmospheres. We determine the critical instellation required for atmospheric retention by calculating time-integrated atmospheric mass loss. Our analysis introduces a new metric for target selection in the Rocky Worlds DDT and refines expectations for rocky planet atmosphere searches in Cycle 4. Exploring initial volatile inventory ranging from 0.01% to 1% of planetary mass, we find that its variation prevents the definition of a unique clear-cut shoreline, though non-linear escape physics can reduce this sensitivity to initial conditions. Additionally, uncertain distributions of high-energy stellar evolution and planet age further blur the critical instellations for atmospheric retention, yielding broad shorelines. Hydrodynamic escape models find atmospheric retention is markedly more favorable for higher-mass planets orbiting higher-mass stars, with carbon-rich atmospheres remaining plausible for 55 Cancri e despite its extreme instellation. Dedicated modeling efforts are needed to better constrain the escape dynamics of secondary atmospheres, such as the role of atomic line cooling, especially for Earth-sized planets. Finally, we illustrate how density measurements can be used to statistically test the existence of the cosmic shorelines, emphasizing the need for more precise mass and radius measurements.
The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape
ArXiv 2504.19872 (2025)