Exoplanet atmosphere

An exoplanet atmosphere controls the planet's spectrum, heat redistribution, chemistry, clouds, and atmospheric escape.

An irradiated planetary atmosphere receives stellar energy from above while internal heat emerges from below. Their competition creates radiative, convective, and sometimes thermally inverted regions.

A semi-grey atmosphere uses separate mean visible and infrared opacities. Their ratio $\gamma ={\kappa }_{\mathrm{vis}}/{\kappa }_{\mathrm{IR}}$ controls where stellar energy is deposited.

The irradiation temperature is defined from the incident stellar flux, commonly by $T_{\mathrm{irr}}=T_{\ast }\sqrt{R_{\ast }/a}$ before redistribution and albedo factors are applied.

The internal effective temperature parametrizes the intrinsic cooling luminosity of a planet through $F_{\mathrm{int}}=\sigma T_{\mathrm{int}}^4$.

An atmospheric thermal inversion is a region where temperature increases outward. In a strongly irradiated atmosphere it can arise when shortwave opacity exceeds thermal infrared opacity and stellar energy is absorbed high in the atmosphere.

The radiative-convective boundary is where radiative transport first requires a temperature gradient steeper than the adiabatic gradient, causing convection below.

During secondary eclipse the planet passes behind its star. The lost system light measures the planet-star flux ratio from reflected starlight and planetary thermal emission.

Geometric albedo compares a body's full-phase brightness with that of a flat, perfectly diffusing reference disc of the same cross-section.

Bond albedo is the fraction of total incident power reflected in all directions and over all wavelengths.

A Lambertian surface has direction-independent radiance. A perfectly reflecting Lambertian patch receiving normal flux $F$ emits specific intensity $I=F/\pi$ into its outward hemisphere.

For blackbody star and planet, the monochromatic thermal eclipse depth is

An exoplanet transmission spectrum measures the wavelength-dependent area blocked as starlight passes tangentially through the atmosphere during transit.

For an isothermal ideal-gas atmosphere, $H=k_{B}T/(\mu m_{H}g)$. A strong transmission feature spanning $N_H$ scale heights has approximate transit-depth amplitude $2R_p{N}_{H}H/R_{\ast }^2$.

If extinction scales as $\sigma \propto {\lambda }^{\gamma }$, an isothermal hydrostatic atmosphere has $d{R}_p/d\log \lambda =\gamma H$. The measured continuum slope can therefore estimate atmospheric temperature when gravity and mean molecular mass are known.

An exoplanet emission spectrum is the wavelength-dependent thermal radiation emerging from the planet. Vertical temperature gradients turn opacity differences into absorption or emission features.

Atmospheric escape removes gas from a planet through thermal motion, hydrodynamic outflow, photochemistry, and interactions with stellar radiation and plasma.

For particles of mass $m$ at radius $r$ and temperature $T$, the Jeans escape parameter isLarge $\lambda$ gives weak tail escape, while order-unity $\lambda$ indicates hydrodynamic blow-off.

For exobase number density $n_e$ and $v_{\mathrm{th}}=\sqrt{2k_{B}T/m}$, the collisionless Jeans number flux is

Hydrodynamic atmospheric escape is a collisional transonic outflow in which bulk gas carries multiple species away. It replaces the hydrostatic Jeans-tail description when gravity is weak compared with thermal energy.