Hydrodynamic Model of H$\alpha$ Emission from Accretion Shocks of Proto-Giant Planet and Circumplanetary Disk

Recent observations have detected excess H$\alpha$ emission from young stellar systems with an age of several Myr such as PDS 70. One-dimensional radiation-hydrodynamic models of shock-heated flows that we developed previously demonstrate that planetary accretion flows of $>$ a few ten km s${}^{-1}$ can produce H$\alpha$ emission. It is, however, a challenge to understand the accretion process of proto-giant planets from observations of such shock-originated emission because of a huge gap in scale between the circumplanetary disk (CPD) and the microscopic accretion shock. To overcome the scale gap problem, we combine two-dimensional, high-spatial-resolution global hydrodynamic simulations and the one-dimensional local radiation hydrodynamic model of the shock-heated flow. From such combined simulations for the protoplanet-CPD system, we find that the H$\alpha$ emission is mainly produced in localized areas on the protoplanetary surface. The accretion shocks above CPD produce much weaker H$\alpha$ emission (approximately 1-2 orders of magnitude smaller in luminosity). Nevertheless, the accretion shocks above CPD significantly affect the accretion process onto the protoplanet. The accretion occurs at a quasi-steady rate, if averaged on a 10-day timescale, but its rate shows variability on shorter timescales. The disk surface accretion layers including the CPD-shocks largely fluctuate, which results in the time-variable accretion rate and H$\alpha$ luminosity of the protoplanet. We also model the spectral emission profile of the H$\alpha$ line and find that the line profile is less time-variable, despite the large variability in luminosity. High-spectral resolution spectroscopic observation and monitoring will be key to reveal the property of the accretion process.