Apsidal Motion as a Window into Stellar Interiors

The apsidal motion in close eccentric binaries has long been known as a powerful means to unveil the internal structure of stars. It originates mostly from the tidal interactions that occur between the two stars through the internal stellar structure constant $k_2$, a measure of the star’s inner density profile. In this review, we present the formalism of apsidal motion, accounting for additional contributions from general relativity and third body. We present the observational methods to derive its rate in binaries. We describe how binaries in which the general relativistic contribution dominates can be used as a test of general relativity, how apsidal motion can be used to constrain spin-orbit misalignment, and how, in non-eclipsing binaries, it can be used to constrain stellar masses. We present recent studies using apsidal motion to probe the interiors of stars: in massive stars, stellar models assuming standard prescriptions for parameters predict stars with too low a density contrast between their core and envelope compared to what observations suggest; a discrepancy not observed in low- and intermediate-mass stars. Only significantly large internal mixing allows the reconciliation between observed and modelled $k_2$, pointing toward the need for more efficient core boundary mixing in massive stars.