Prograde spin-up during gravitational collapse

Abstract

Asteroids, planets, stars in some open clusters, as well as molecular clouds appear to possess a preferential spin-orbit alignment, pointing to shared processes that tie their rotation at birth to larger parent structures. We present a new mechanism that describes how collections of particles or 'clouds' gain a prograde rotational component when they collapse or contract while subject to an external, central force. The effect is geometric in origin, as relative shear on curved orbits moves their shared center-of-mass slightly inward and toward the external potential during a collapse, exchanging orbital angular momentum into aligned (prograde) rotation. We perform illustrative analytical and N-body calculations to show that this process of prograde spin-up proceeds quadratically in time ($\delta L_\mathrm{rot} \propto t^2$) until the collapse nears completion. The total rotational gain increases with the size of the cloud prior to its collapse: $\delta L_\mathrm{rot}/L_\mathrm{H} \propto (R_\mathrm{cl}/R_\mathrm{H})^5$, and typically with distance to the source of the potential ($L_\mathrm{H}\propto r_0)$. For clouds that form at the interface of shear and self-gravity ($R_\mathrm{cl} \sim R_\mathrm{H}$), prograde spin-up means that even setups with large initial retrograde rotation collapse to form prograde-spinning objects. Being a geometric effect, prograde spin-up persists around any central potential that triggers shear, even those where the shear is strongly retrograde. We highlight an application to the Solar System, where prograde spin-up can explain the frequency of binary objects in the Kuiper belt with prograde rotation.