Title:
Flipping spins in mass transferring binaries and origin of spin-orbit
misalignment in binary black holes

Abstract:
Close stellar binaries are prone to undergo a phase of stable mass
transfer in which a star loses mass to its companion. Assuming that the
donor star loses mass along the instantaneous interstellar axis, we
derive the orbit-averaged equations of motion describing the evolution
of the donor rotational angular momentum vector (spin) which accompanies
the transfer of mass. We consider: (i) a model in which the mass
transfer rate is constant within each orbit and (ii) a phase-dependent
rate in which all mass per orbit is lost at periapsis. In both cases, we
find that the ejection of $\gtrsim 30$ per cent of the donor's initial
mass causes its spin to nearly flip onto the orbital plane of the
binary, independently of the initial spin-orbit alignment. Moreover, we
show that the spin flip due to mass transfer can easily dominate over
tidal synchronisation in any giant stars and main-sequence stars with
masses $\sim1.5$ to $5\msun$. Finally, the general equations of motion,
including tides, are used to evolve a realistic population of massive
binary stars leading to the formation of binary black holes. Assuming a
strong core-envelope coupling, the resulting tilt of the first-born
black hole typically reduces its spin projection onto the orbit normal
by a factor $\sim\mathcal{O}(0.1)$. This result supports previous
studies in favour of an insignificant contribution to the effective spin
projection, $\chi_\text{eff}$, in merging binary black holes.