2013ApJ...768..112P

The eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow apsidal precession below the rate predicted by general relativity. Recent measurements of the Rossiter-McLaughlin effect indicate that stellar spins in DI Her are almost orthogonal to the orbital angular momentum, which explains the anomalous precession in agreement with the earlier theoretical suggestion by Shakura. However, these measurements yield only projections of the spin-orbit angles onto the sky plane, leaving the spin projection onto our line of sight unconstrained. Here we describe a method for determining the full three-dimensional spin orientation of the binary components relying on the use of the gravity-darkening effect, which is significant for the rapidly rotating stars in DI Her. Gravity darkening gives rise to a nonuniform brightness distribution over the stellar surface, the pattern of which depends on the stellar spin orientation. Using archival photometric data obtained during multiple eclipses over several decades, we are able to constrain the unknown spin angles in DI Her with this method, finding that the spin axes of both stars lie close to the plane of the sky. Our procedure fully accounts for the precession of stellar spins over the long time span of observations.