On the Terminal Spins of Accreting Stars and Planets: Boundary Layers

TL;DR

This study investigates how acoustic waves generated by shear instabilities in boundary layers limit the spin rates of accreting stars and planets, providing a hydrodynamic mechanism that prevents them from reaching breakup speeds.

Contribution

First simulation-based analysis of wave-driven angular momentum transport in boundary layers of accreting stars and planets, revealing a spin-limiting mechanism.

Findings

Angular momentum transport decreases significantly at higher rotation rates.

Accretion rates and variability decrease with increasing spin.

Hydrodynamic waves can limit spin to below breakup speeds.

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-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.