On the terminal spins of accreting stars and planets: boundary layers

Abstract

ABSTRACT 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-break-up speeds. However, accretion cannot proceed on to planets and stars in the same way that accretion proceeds through the disc. For example, the magneto-rotational instability cannot operate in the region between the nearly Keplerian disc 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 ∼0.4−0.6 times the Keplerian rate at the surface the rate at which angular momentum is transported inwards through the boundary layer by waves decreases by ∼1−3 orders of magnitude depending on the gas sound speed. 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 break-up speed.