  The origin of the spins of giant planets is an open question in astrophysics.
As planets and stars accrete from discs, if the specific angular momentum
accreted corresponds to that of a Keplerian orbit at the surface of the object,
it is possible for planets and stars to be spun up to near-breakup speeds.
However, accretion cannot proceed onto planets and stars in the same way that
accretion proceeds through the disk. For example, the magneto-rotational
instability cannot operate in the region between the nearly-Keplerian disk and
more slowly-rotating surface because of the sign of the angular velocity
gradient. Through this boundary layer where the angular velocity sharply
changes, mass and angular momentum transport is thought to be driven by
acoustic waves generated by global supersonic shear instabilities and vortices.
We present the first study of this mechanism for angular momentum transport
around rotating stars and planets using 2D vertically-integrated moving-mesh
simulations of ideal hydrodynamics. We find that above rotation rates of
$\sim0.4-0.6$ times the Keplerian rate at the surface, depending on the gas
sound speed, the rate at which angular momentum is transported inwards through
the boundary layer by waves decreases by $\sim1-3$ orders of magnitude. We also
find that the accretion rate through the boundary layer decreases
commensurately and becomes less variable for faster-rotating objects. Our
results provide a purely hydrodynamic mechanism for limiting the spins of
accreting planets and stars to factors of a few less than the breakup speed.
