  Circumplanetary disks (CPDs) control the growth of planets, supply material
for satellites to form, and provide observational signatures of young forming
planets. We have carried out two dimensional hydrodynamical simulations with
radiative cooling to study CPDs, and suggested a new mechanism to drive the
disk accretion. Two spiral shocks are present in CPDs, excited by the central
star. We find that spiral shocks can at least contribute to, if not dominate
the angular momentum transport and energy dissipation in CPDs. Meanwhile,
dissipation and heating by spiral shocks have a positive feedback on
shock-driven accretion itself. As the disk is heated up by spiral shocks, the
shocks become more open, leading to more efficient angular momentum transport.
This shock driven accretion is, on the other hand, unsteady on a timescale of
months/years due to production and destruction of vortices in disks. After
being averaged over time, a quasi-steady accretion is reached from the planet's
Hill radius all the way to the planet surface, and the disk
$\alpha$-coefficient characterizing angular momentum transport due to spiral
shocks is $\sim$0.001-0.02. The disk surface density ranges from 10 to 1000 g
cm$^{-2}$ in our simulations, which is at least 3 orders of magnitude smaller
than the "minimum mass sub-nebula" model used to study satellite formation;
instead it is more consistent with the "gas-starved" satellite formation model.
Finally, we calculate the millimeter flux emitted by CPDs at ALMA and EVLA
wavelength bands and predict the flux for several recently discovered CPD
candidates, which suggests that ALMA is capable of discovering these accreting
CPDs.
