Analysis of Spin-Orbit Misalignment in Eclipsing Binary DI Herculis

TL;DR

This paper develops a method using gravity darkening to determine the full 3D spin orientation of stars in DI Herculis, explaining its anomalous apsidal precession by constraining the stellar spin axes.

Contribution

It introduces a novel approach combining gravity darkening and archival photometry to measure the 3D spin angles of binary stars, addressing limitations of previous projection-only measurements.

Findings

Stellar spins in DI Her are nearly orthogonal to the orbital plane.

The method constrains spin axes to be close to the sky plane.

The approach accounts for long-term spin precession effects.

Abstract

Eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow apsidal precession, below the rate predicted by the general relativity. Recent measurements of the Rossiter-McLauglin 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 the 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 of 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 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 spread over several decades we are able to constrain the unknown spin angles in DI Her with this method, finding that 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.