  We study the magnetic and tidal interactions of a gas-giant exoplanet with
its host star and with its exomoons, and focus on their retention. We briefly
revisit the scaling law for planetary dynamo in terms of its mass, radius and
luminosity. Based on the virial theorem, we construct an evolution law for
planetary magnetic field and find that its initial entropy is important for the
field evolution of a high-mass planet. We estimate the magnetic torques on
orbit arising from the star-planet and planet-moon magnetic interactions, and
find that it can compensate tidal torques and bypass frequency valleys where
dynamical-tide response is ineffective. For exomoon's retention we consider two
situations. In the presence of a circumplanetary disk (CPD), by comparison
between CPD's inner and outer radii, we find that planets with too strong
magnetic fields or too small distance from its host star tend not to host
exomoons. During the subsequent CPD-free evolution, we find, by comparison
between planet's spindown and moon's migration timescales, that hot Jupiters
with periods of several days are unlikely to retain large exomoons, albeit they
could be surrounded by rings from the debris of tidally disrupted moons. In
contrast, moons, if formed around warm or cold Jupiters, can be preserved.
Finally, we estimate the radio power and flux density due to the star-planet
and planet-moon magnetic interactions and give the upper limit of detection
distance by FAST.
