Title: Protostellar spin-up and fast rotator formation through binary star formation

Abstract: (Edited) Many fast rotator stars (rotation periods of < 2 days) are found in unresolved binaries with separations of tens of au. This correlation leads to the question of whether the formation of binary stars inherently produces fast rotators. We aim to understand whether the formation of companions plays a role in spinning up stars. We use magneto-hydrodynamical simulations to study the formation of multiple star systems from turbulent and non-turbulent protostellar cores. We track the angular momentum accreted by individual star and inner disc systems by using a sink particle technique. We run a resolution study to extrapolate protostellar properties. We find in all simulations that the primary star can experience spin-up events that are correlated with the formation of companions. The primary star can spin up by up to 84% of its pre-fragmentation angular momentum and by up to 18% of its pre-fragmentation mass-specific angular momentum. The mechanism for the spin-up is gravitational disc instabilities in the circumstellar disc around the primary star, leading to the accretion of material with high specific angular momentum. The simulations that experience the strongest disc instabilities fragment to form companions. Simulations with weaker spin-up events experience disc instabilities triggered by a companion flyby, and the disc instability in these cases does not produce further fragments. We conclude that the primary star in multiple star systems may end up with a higher spin than single stars. This is because gravitational instabilities in the circumstellar disc around the primary star can trigger a spin-up event. In the strongest spin-up events, the instability is likely to cause disc fragmentation and the formation of companions. This companion formation coupled with shorter disc lifetimes, because the companion truncates the circumstellar disc, can help produce fast rotators.