  (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.
