Were the Obliquities in DI Herculis Excited by an Unseen Tertiary Companion?

The eclipsing binary DI Herculis has garnered interest for several decades because of an apparent disagreement between the observed and calculated values of the apsidal precession rate. The problem was resolved when both stars were found to have high obliquities, but the reason for the high obliquities is unknown. Here, we investigate the possibility that the obliquities are (or were) excited by an unseen tertiary star. Obliquity excitation in the current orbital configuration can be ruled out with existing data; any tertiary star that is sufficiently close or massive to overcome the strong spin-orbit coupling of the binary would have been detected through various dynamical effects. It remains possible that the orbit of DI Herculis was initially wider and the obliquity was excited during high-eccentricity tidal migration driven by a tertiary companion, but in this scenario it would be difficult to explain why the observed spin rates are much faster than the pseudo-synchronous rate. In addition, inward migration is most likely to arise when the mass of the perturbing star is comparable to the binary mass, and such a bright tertiary would have been detected in imaging or spectroscopic data. Alternative explanations that do not invoke a tertiary star should be sought for the large obliquities in DI Herculis.