Accreting planets have been detected through their hydrogen-line emission, specifically Hα. To interpret this, stellar-regime empirical correlations between the Hα luminosity LHα and the accretion luminosity Lacc or accretion rate $\dot{M}$ have been extrapolated to planetary masses, however without validation. We present a theoretical Lacc–LHα relationship applicable to a shock at the surface of a planet. We consider wide ranges of accretion rates and masses and use detailed spectrally

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... , nonequilibrium models of the postshock cooling. The new relationship gives a markedly higher Lacc for a given LHα than fits to young stellar objects, because Lyα, which is not observable, carries a large fraction of Lacc. Specifically, an LHα measurement needs 10 to 100 times higher Lacc and $\dot{M}$ than previously predicted, which may explain the rarity of planetary Hα detections. We also compare the $\dot{M}$–LHα relationships coming from the planet-surface shock or implied by accretion-funnel emission. Both can contribute simultaneously to an observed Hα signal, but at low (high) $\dot{M}$ the planetary-surface shock (heated funnel) dominates. Only the shock produces Gaussian line wings. Finally, we discuss accretion contexts in which different emission scenarios may apply, putting recent literature models in perspective, and also present Lacc–Lline relationships for several other hydrogen lines.