Apsidal motion in massive binaries

TL;DR

Apsidal motion in close eccentric massive binaries provides a Newtonian leverage to probe stellar interiors, linking the rate $\dot{\omega}$ to the internal structureConstant $k_2$ and the density profile. The paper surveys methods to measure and interpret $\dot{\omega}$ from photometry and spectroscopy, and shows that standard 1D models underpredict $k_2$, with enhanced mixing (turbulent diffusion) and non-perturbative 3D modeling (MoBiDICT) delivering closer agreement with observations. It also presents a novel, model-dependent approach to derive masses for non-eclipsing double-line binaries by combining $\dot{\omega}$ with radii and $k_2$ from evolutionary models, illustrated on HD 93205 and HD 165052. The work underscores the need for more systems and a deeper understanding of mixing physics to fully exploit apsidal motion as a probe of massive-star interiors and evolution, acknowledging Rodolfo Barba's contributions in this domain.

Abstract

One of the most efficient and reliable observational technique allowing to probe the internal structure of a star is the determination of the apsidal motion in close eccentric binaries. This secular precession of the binary orbit's major axis depends on the tidal interactions occurring between the two stars. Its rate is directly related to the internal structure of the stars, in particular their inner density profile. Combining radial velocity and light curve data over a long timescale, the apsidal motion rate can be constrained, together with the fundamental parameters of the stars. Confrontation of observational parameters to stellar models then allows us to constrain the internal structure of stars. This powerful technique has been known for years but has been seldom applied to massive stars. I highlight its interest and reveal recent results concerning several massive binaries. While standard stellar models predict stars having a smaller internal stellar structure constant, that is to say, stars having a smaller density contrast, than expected from observations, I demonstrate that the addition of mixing inside the models helps to solve, at least partially, this discrepancy. Studies with the non-perturbative code MoBiDICT showed that the perturbative model assumption is not justified in highly distorted stars, in which cases the apsidal motion is underestimated, exacerbating even more the need for enhanced mixing inside the models. But what happens if the binary is a double-line spectroscopic but non-eclipsing binary? In that case, we indeed have no estimate of the masses and radii of the stars. Surprisingly, the apsidal motion equations combined with the binary' spectroscopic observations allow us to derive the masses of the stars, in a model-dependent way. Rodolfo Barbá contributed to the development of this original method that I bring out.

Figures (17)

• Figure 1: Definition of the orbital elements of a binary system. The argument of periastron, $\omega$, is the angle between the line of nodes and the line of apsides, and the true anomaly, $\phi$, is the angle between the line of apsides and the position of the primary star; Both are measured in the orbital plane.
• Figure 2: Apsidal motion period as a function of the orbital period. Upper panel: individual observed systems coming from the literature baroch21baroch22claret21marcussen22rauw16rosu20brosu22arosu22brosu23torres10wolf06wolf08wolf10. Only the primaries are plotted, colour-coded by their mass. Figure taken from rosu24b. Lower left panel: study of hong16. Credit: Figure 6 of hong16. Lower right panel: study of zasche19zasche20. Credit: zasche20, reproduced with permission © ESO.
• Figure 3: Nine theoretical lightcurves colour-coded by the assumed value of $\omega$. All other parameters are identical ($e=0.134$, $i=68.6^\circ$, and the stars have the same $m, R$, and $T_\mathrm{eff}$). Figure from rosu21.
• Figure 4: Left panel: Time difference between secondary and primary minima of the eclipses as a function of the orbital cycle for V541 Cyg. Figure from baroch21. Middle panel: Same for V459 Cas. Figure from baroch21. Right panel: Phase difference between the secondary and primary minima as a function of time for CPD-41$\circ$ 7742. Figure from rosu22b.
• Figure 5: Measured RVs of the primary (filled dots) and secondary (open dots) stars of HD 152248, and best-fit RV curves (blue and red). Data from struve44hill74penny99rosu20b. Figure from rosu21.