High-Eccentricity Migration with Disk-Induced Spin-Orbit Misalignment: a Preference for Perpendicular Hot Jupiters

High-eccentricity migration is a likely formation mechanism for many observed hot Jupiters, particularly those with a large misalignment between the stellar spin axis and orbital angular momentum axis of the planet. In one version of high-eccentricity migration, an inclined stellar companion excites von Zeipel-Lidov-Kozai (ZLK) eccentricity oscillations of a cold Jupiter, and tidal dissipation causes the planet's orbit to shrink and circularize. Throughout this process, the stellar spin can evolve chaotically, resulting in highly misaligned hot Jupiters. Previous population studies of this migration mechanism have assumed that the stellar spin is aligned with the planetary orbital angular momentum when the companion begins to induce ZLK oscillations. However, in the presence of a binary companion, the star's obliquity may be significantly excited during the dissipation of its protoplanetary disk. We calculate the stellar obliquities produced in the protoplanetary disk phase and use these to perform an updated population synthesis of ZLK-driven high-eccentricity migration. We find that the resulting obliquity distribution of HJ systems is predominantly retrograde with a broad peak near 90$^\circ$. The distribution we obtain has intriguing similarities to the recently-observed preponderance of perpendicular planets close to their host stars.