  Recent high-sensitivity observations reveal that accreting giant planets
embedded in their parental circumstellar disks can emit H$\alpha$ at their
final formation stages. While the origin of such emission is not determined
yet, magnetospheric accretion is currently a most plausible hypothesis. In
order to test this hypothesis further, we develop a simplified, but
physical-based model and apply it to our observations taken toward HD 163296
with Subaru/SCExAO+VAMPIRES. We specify under what conditions, embedded giant
planets can undergo magnetospheric accretion and emit hydrogen lines. We find
that when stellar accretion rates are high, magnetospheric accretion becomes
energetic enough to self-regulate the resulting emission. On the other hand, if
massive planets are embedded in disks with low accretion rates, earlier
formation histories determine whether magnetospheric accretion occurs. We
explore two different origins of hydrogen emission lines (magnetospheric
accretion flow heated by accretion-related processes vs planetary surfaces via
accretion shock). The corresponding relationships between the accretion and
line luminosities dictate that emission from accretion flow achieves higher
line flux than that from accretion shock and the flux decreases with increasing
wavelengths (i.e., from H$\alpha$ to Pa$\beta$ and up to Br$\gamma$). Our
observations do not detect any point-like source emitting H$\alpha$ and are
used to derive the 5$\sigma$ detection limit. The observations are therefore
not sensitive enough, and reliable examination of our model becomes possible if
observational sensitivity will be improved by a factor of ten or more.
Multi-band observations increase the possibility of efficiently detecting
embedded giant planets and carefully determining the origin of hydrogen
emission lines.
