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 misalignment between the stellar spin and the disc angular momentum axes .
The gravitational torque on the disc from an inclined binary companion makes the disc precess around the binary axis , while the star-disc interaction torque due to the rotation-induced stellar quadrupole tends to make 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 ( e.g. , with decreasing disc mass ) such that the two precession frequencies cross each other .
This “ secular resonance ” behaviour can be understood in a simple , geometric way from the precession dynamics of spin and disc angular momenta .
We derive the general conditions for such resonance crossing to occur , and find that they can be satisfied for very reasonable protostar-disc-binary parameters .
The evolution of star-disc inclination is also significantly affected by mass accretion from the disc onto the central star and by magnetic star-disc interaction torques , which can either promote or reduce star-disc misalignment , as well as by the possible damping of disc-binary inclination due to viscous dissipation of disc warps .
In general , as long as the initial binary-disc inclination is not too small ( greater than a few degrees ) , a variety of star-disc misalignment angles can be generated within the lifetimes of protoplanetary discs ( \sim 10 Myrs ) .
We discuss the implications of our results for the observations of stellar spin orientations in binaries , for the alignments/misalignments of protostellar discs and debris discs relative to their host stars , and for the observed stellar obliquities in exoplanetary systems .
In particular , if hot Jupiters are produced by the secular Lidov-Kozai effect induced by an external stellar companion present in the protostellar phase , 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 and hot Jupiters may still be produced during the protoplanetray disc phase .