Testing magnetospheric accretion as an H$\alpha$ emission mechanism of embedded giant planets: The case study for the disk exhibiting meridional flow around HD 163296

Recent high-sensitivity observations reveal that accreting giant planets embedded in their parentalcircumstellar disks can emit Hα at their final formation stages. While the origin of such emission isnot determined yet, magnetospheric accretion is currently a most plausible hypothesis. In order totest this hypothesis further, we develop a simplified, but physical-based model and apply it to ourobservations taken toward HD 163296 with Subaru/SCExAO+VAMPIRES. We specify under whatconditions, embedded giant planets can undergo magnetospheric accretion and emit hydrogen lines. Wefind that when stellar accretion rates are high, magnetospheric accretion becomes energetic enough toself-regulate the resulting emission. On the other hand, if massive planets are embedded in disks withlow accretion rates, earlier formation histories determine whether magnetospheric accretion occurs.We explore two different origins of hydrogen emission lines (magnetospheric accretion flow heated byaccretion-related processes vs planetary surfaces via accretion shock). The corresponding relationshipsbetween the accretion and line luminosities dictate that emission from accretion flow achieves higherline flux than that from accretion shock and the flux decreases with increasing wavelengths (i.e., fromHα to Paβ and up to Brγ). Our observations do not detect any point-like source emitting Hα and areused to derive the 5σ detection limit. The observations are therefore not sensitive enough, and reliableexamination of our model becomes possible if observational sensitivity will be improved by a factor often or more. Multi-band observations increase the possibility of efficiently detecting embedded giantplanets and carefully determining the origin of hydrogen emission lines.