Hot-Jupiter radius inflation

Hot-Jupiter radius inflation is the unexpectedly large radius of some strongly irradiated giant exoplanets compared with ordinary cooling and contraction models at the inferred age. A giant planet loses internal energy through its exoplanet atmosphere; slowing that loss or depositing additional energy sufficiently deep can keep its interior hotter and more extended.

Atmospheric opacity and day-night heat redistribution affect the boundary condition seen by the interior. Analytic irradiated-atmosphere work shows why deep temperatures depend on global transport as well as incident power, while also illustrating the difficulty of explaining observed radii by simple opacity changes alone.^[ref] An expanded radius is thus a constraint on the thermal history, rather than direct evidence for one unique heating mechanism.

Delayed cooling preserves a young giant planet's large radius by reducing the escape of internal energy. Enhanced atmospheric opacity, an irradiation-maintained outer radiative blanket, and composition gradients that inhibit convection can slow Kelvin-Helmholtz contraction. These mechanisms retain existing heat rather than supplying a new deep heat source.

A stabilizing composition gradient can suppress large overturning motions while permitting double-diffusive convection in small layers separated by interfaces. If heat loss is less efficient than in a single well-mixed adiabat, the planet retains more entropy and contracts more slowly. This is a proposed delayed-cooling contribution to hot-Jupiter radius inflation, with an effectiveness that depends on the gradient and layer structure.

A giant planet can also remain inflated when power is deposited sufficiently deep to alter its internal energy budget. Candidate sources include tidal heating, Joule heating by wind-driven currents, and dissipation of circulation-driven mechanical energy. The depth and efficiency of deposition matter, as discussed in models of hot-Jupiter heating.

Winds in a weakly ionized exoplanet atmosphere can drive electric currents through a planetary magnetic field. Their Ohmic heating is a proposed power source for hot-Jupiter radius inflation. A model must determine the electrical conductivity, the complete current paths and the depth at which the power is deposited.^[ref]

In a nonrelativistic, isotropically conducting fluid, let $\mathbf{v}$ be its velocity, $\mathbf{E}$ the laboratory electric field, $\mathbf{B}$ the magnetic field, $\mathbf{J}$ the current density and $\sigma >0$ the electrical conductivity. The simple resistive Ohm's law isThe irreversible heat production per unit volume and time is thereforeThe laboratory electrical power $\mathbf{J}\cdot \mathbf{E}$ alone also contains mechanical work by the Lorentz force:Thus identifying $\mathbf{J}\cdot \mathbf{E}$ directly with resistive heat requires an appropriate rest frame or a vanishing mechanical-work term. The total deposited power is $L_{\mathrm{Ohm}}=\int q_{\mathrm{Ohm}}dV$. A large value confined to optically thin upper layers need not maintain the deep interior's entropy; magnetic braking and current closure also limit what a prescribed wind can supply.