Star-Disc-Binary Interactions in Protoplanetary Disc Systems and Primordial Spin-Orbit Misalignments

We study the interactions between a protostar and its circumstellar disc under the influence of an external binary companion to determine the evolution of the mutual stellar spin - disc misalignment angle. The gravitational torque on the disc from an inclined binary makes the disc precess around the binary axis, while the star-disc interaction torque due to the rotation-induced quadrupole makes the stellar spin and the disc angular momentum axes precess around each other. A significant star-disc misalignment angle can be generated from a small initial value as the star-disc system evolves in time such that the two precession frequencies cross each other. This ``secular resonance'' behavior can be understood in a geometric way from the precession dynamics of spin and disc angular momenta. We derive the conditions for such resonance to occur, and find that they can be satisfied for reasonable protostar-disc-binary parameters. The evolution of star-disc inclination is also affected by mass accretion and by magnetic star-disc interaction torques, which can either promote or reduce star-disc misalignment. In general, as long as the initial binary-disc inclination is greater than a few degrees, a variety of star-disc misalignment angles can be generated within the disc lifetimes. We discuss the implications of our results for the stellar spin orientations in binaries, for the alignments/misalignments of protostellar discs and debris discs, and for the stellar obliquities in exoplanetary systems. In particular, if hot Jupiters are produced by the Kozai effect induced by an external stellar companion, then it is likely that ``primordial'' star-disc misalignments are already generated by the star-disc-binary interactions. Even for systems where the Kozai effect is suppressed, misaligned planets may still be produced during the protoplanetary disc phase.