Comparison of planetary H\alpha-emission models: A new correlation with accretion luminosity

TL;DR

This paper develops a new theoretical model linking accretion luminosity and H-alpha emission in accreting planets, revealing that previous estimates significantly underestimated the accretion rates needed for observed H-alpha signals.

Contribution

The study introduces a detailed shock-based model for planetary accretion, providing revised $L_{acc}$--$L_{H extalpha}$ relationships that differ from stellar-based correlations.

Findings

Revised $L_{acc}$ estimates are 10-100 times higher for a given $L_{H extalpha}$.

Ly-$ extalpha$ carries a large fraction of $L_{acc}$, explaining detection rarity.

Different emission mechanisms dominate at varying accretion rates.

Abstract

Accreting planets have been detected through their hydrogen-line emission, specifically H$\alpha$. To interpret this, stellar-regime empirical correlations between the H$\alpha$ luminosity $L_\mathrm{H\alpha}$ and the accretion luminosity $L_\mathrm{acc}$ or accretion rate $\dot{M}$ have been extrapolated to planetary masses, however without validation. We present a theoretical $L_\mathrm{acc}$--$L_\mathrm{H\alpha}$ relationship applicable to a shock at the surface of a planet. We consider wide ranges of accretion rates and masses and use detailed spectrally-resolved, non-equilibrium models of the postshock cooling. The new relationship gives a markedly higher $L_\mathrm{acc}$ for a given $L_\mathrm{H\alpha}$ than fits to young stellar objects, because Ly-$\alpha$, which is not observable, carries a large fraction of $L_\mathrm{acc}$. Specifically, an $L_\mathrm{H\alpha}$ measurement needs ten to 100 times higher $L_\mathrm{acc}$ and $\dot{M}$ than previously predicted, which may explain the rarity of planetary H$\alpha$ detections. We also compare the $\dot{M}$--$L_\mathrm{H\alpha}$ relationships coming from the planet-surface shock or implied by accretion-funnel emission. Both can contribute simultaneously to an observed H$\alpha$ 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 $L_\mathrm{acc}$--$L_\mathrm{line}$ relationships for several other hydrogen lines.