Magnetospheric Accretion as a Source of H$\alpha$ Emission from Proto-planets around PDS 70

Advances in high-resolution imaging have revealed H$\alpha$ emission separated from the host star. It is generally believed that the emission is associated with forming planets in protoplanetary disks. However, the nature of this emission is still not fully understood. Here we report a modeling effort of H$\alpha$ emission from the planets around the young star PDS 70. Using standard magnetospheric accretion models previously applied to accreting young stars, we find that the observed line fluxes can be reproduced using a range of parameters relevant to PDS 70b and c, with the mean mass accretion rate of log(${\rm \dot{M}}$) = $-8.0\pm0.6$ M$_{\rm Jup}$ yr$^{-1}$ and $-8.1\pm0.6$ M$_{\rm Jup}$ yr$^{-1}$ for PDS 70b and PDS 70c, respectively. Our results suggest that H$\alpha$ emission from young planets can originate in the magnetospheric accretion of mass from the circumplanetary disk. We find that empirical relationships between mass accretion rate and H$\alpha$ line properties frequently used in T Tauri stars are not applicable in the planetary mass regime. In particular, the correlations between line flux and mass accretion rate underpredict the accretion rate by about an order of magnitude, and the width at the 10% height of the line is insensitive to the accretion rate at ${\rm \dot{M}}$ $< 10^{-8}$ M$_{\rm Jup}$ yr$^{-1}$.