Comparison of Planetary Hα-emission Models: A New Correlation with Accretion Luminosity
Yuhiko Aoyama, Gabriel-Dominique Marleau, Masahiro Ikoma, Christoph Mordasini
Abstract
Abstract Accreting planets have been detected through their hydrogen-line emission, specifically H α . To interpret this, stellar-regime empirical correlations between the H α luminosity L H α and the accretion luminosity L acc or accretion rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> have been extrapolated to planetary masses, however without validation. We present a theoretical L acc – L H α 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, nonequilibrium models of the postshock cooling. The new relationship gives a markedly higher L acc for a given L H α than fits to young stellar objects, because Ly α , which is not observable, carries a large fraction of L acc . Specifically, an L H α measurement needs 10 to 100 times higher L acc and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> than previously predicted, which may explain the rarity of planetary H α detections. We also compare the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> – L H α relationships coming from the planet-surface shock or implied by accretion-funnel emission. Both can contribute simultaneously to an observed H α signal, but at low (high) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:math> 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 acc – L line relationships for several other hydrogen lines.