Analyses of Multiple Balmer Emission Lines from Accreting Brown Dwarfs and Very Low Mass Stars

A planetary growth rate, a.k.a., the mass accretion rate, is a fundamental parameter in planet formation, as it determines a planet's final mass. Planetary mass accretion rates have been estimated using hydrogen lines, based on the models originally developed for accreting stars, known as the accretion flow model. Recently, Aoyama et al. (2018) introduced the accretion shock model as an alternative mechanism for hydrogen line emission. However, it remains unclear which model is more appropriate for accreting planets and substellar objects. To address this, we applied both models to archival data consisting of 96 data points from 76 accreting brown dwarfs and very low-mass stars, with masses ranging from approximately 0.02 to 0.1 $M_\sun$, to test which model best explains their accreting properties. The results showed that the emission mechanisms of 15 data points are best explained by the shock model, while 55 data points are best explained by the flow model. For the 15 data points explained by the planetary shock model, the shock model estimates up to several times higher mass accretion rates than the flow model. As this trend is more pronounced for planetary mass objects, it is crucial to determine which emission mechanism is dominant in individual planets. We also discuss the physical parameters that determine the emission mechanisms and the variability of line ratios.