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The Schönberg-Chandrasekhar limit is the largest mass fraction that an approximately isothermal inert core can have while remaining matched in hydrostatic and thermal equilibrium to a hydrogen-rich envelope. For a simple isothermal core and polytropic envelope,Because a helium core has larger mean molecular weight than its hydrogen-rich envelope, the limiting fraction is typically near ten per cent. Once shell burning grows the core beyond this limit, no neighboring equilibrium with an isothermal core exists: the core contracts and heats by Kelvin-Helmholtz contraction, the hydrogen-burning shell brightens, and the envelope expands rapidly toward a red giant.

For uniform density, Kelvin-Helmholtz contraction releases binding energy $|U|=3G{M}^2/(5R)$. If mass and luminosity are constant and stellar heating is negligible at 90 au, the contraction age isEnergy conservation, $L=-dU/dt$, givesThe virial theorem places roughly half of the released gravitational energy into internal heat. Including that effect gives $t_{\mathrm{KH}}\simeq 3G{M}^2/(10RL)$ and $\dot{R}\simeq -10L{R}^2/(3G{M}^2)$.

Young giant planets retain high formation entropy and radiate gravitational and thermal energy as they contract. Their infrared self-luminosity, especially at wide angular separation from a young nearby star, made the first directly imaged exoplanets much easier to detect than mature reflected-light planets. The inferred brightness depends on whether formation followed a high-entropy hot start or a low-entropy cold start.

By $10^{10}$ years, deuterium burning and most rapid Kelvin-Helmholtz contraction have ended. The intrinsic luminosity is governed mainly by the remaining interior entropy and ionic heat capacity, slow contraction supported by partially degenerate electrons, and the atmospheric opacity that controls escape of heat. Composition-dependent processes such as helium rain can add energy. For an irradiated planet, absorbed and reradiated starlight may dominate the observed luminosity, but it does not equal the planet's intrinsic cooling luminosity.