Magnetospheric accretion is an important process for a wide range of astrophysical systems, and may play a role in the formation of gas giant planets. Extending the formalism describing stellar magnetospheric accretion into the planetary regime, we d
emonstrate that magnetospheric processes may govern accretion onto young gas giants in the isolation phase of their development. Planets in the isolation phase have cleared out large gaps in their surrounding circumstellar disks, and settled into a quasi-static equilibrium with radii only modestly larger than their final sizes (i.e., $ r sim 1.4 r_{rm final}$). Magnetospheric accretion is less likely to play a role in a young gas giants main accretion phase, when the planets envelope is predicted to be much larger than the planets Alfven radius. For a fiducial 1 M$_J$ gas giant planet with a remnant isolation phase accretion rate of $dot{M}_{odot} =$ 10$^{-10} M_{odot}{rm yr}^{-1}=10^{-7}M_{J}{rm yr}^{-1}$, the disk accretion will be truncated at $sim 2.7r_J$ (with $r_J$ is Jupiters radius) and drive the planet to rotate with a period of $sim$7 hours. Thermal emission from planetary magnetospheric accretion will be difficult to observe; the most promising observational signatures may be non-thermal, such as gyrosynchrotron radiation that is clearly modulated at a period much shorter than the rotation period of the host star.
This work investigates the short wavelength stability of the magnetopause between a rapidly-rotating, supersonic, dense accretion disc and a slowly-rotating low-density magnetosphere of a magnetized star. The magnetopause is a strong shear layer with
rapid changes in the azimuthal velocity, the density, and the magnetic field over a short radial distance and thus the Kelvin-Helmholtz (KH) instability may be important. The plasma dynamics is treated using non-relativistic, compressible (isentropic) magnetohydrodynamics. It is necessary to include the displacement current in order that plasma wave velocities remain less than the speed of light. We focus mainly on the case of a star with an aligned dipole magnetic field so that the magnetic field is axial in the disc midplane and perpendicular to the disc flow velocity. However, we also give results for cases where the magnetic field is at an arbitrary angle to the flow velocity. For the aligned dipole case the magnetopause is most unstable for KH waves propagating in the azimuthal direction perpendicular to the magnetic field which tends to stabilize waves propagating parallel to it. The wave phase velocity is that of the disc matter. A quasi-linear theory of the saturation of the instability leads to a wavenumber ($k$) power spectrum $propto k^{-1}$ of the density and temperature fluctuations of the magnetopause, and it gives the mass accretion and angular momentum inflow rates across the magnetopause. For self-consistent conditions this mass accretion rate will be equal to the disc accretion rate at large distances from the magnetopause.
