= Intrinsic planetary luminosity
{title2=$L_{\rm int}$}
The intrinsic planetary luminosity $L_{\rm int}$ is the power supplied by interior cooling, contraction, nuclear reactions if present, or internal heating, excluding reflected or passively reradiated stellar light. For fixed <mass> and no accretion or nuclear source, global <conservation of energy> gives $L_{\rm int}=Q_{\rm deep}-d(U+\Omega)/dt$, where $Q_{\rm deep}$ is any additional power deposited in the interior, such as <tidal heating> or <Joule heating>. For $Q_{\rm deep}=0$ and a gas-supported quasi-static sphere of fixed <specific-heat ratio> $\gamma$ and negligible surface <pressure>, the <stellar virial theorem> gives $\Omega=-3(\gamma-1)U$, hence
$$
L_{\rm int}=-\frac{3\gamma-4}{3(\gamma-1)}\frac{d\Omega}{dt}.
$$
For a dynamically stable gas-supported model take $\gamma>4/3$. For $\gamma=5/3$ this is half the gravitational release. Degenerate giants require a different internal energy reservoir; the half-factor is not universal.
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