The BANANA Project. VII. High Eccentricity Predicts Spin-Orbit Misalignment in Binaries

The degree of spin-orbit alignment in a population of binary stars can be determined from measurements of their orbital inclinations and rotational broadening of their spectral lines. Alignment in a face-on binary guarantees low rotational broadening, while alignment in an edge-on binary maximizes the rotational broadening. In contrast, if spin-orbit angles ($\psi$) are random, rotational broadening should not depend on orbital inclination. Using this technique, we investigated a sample of 2{,}727 astrometric binaries from Gaia DR3 with F-type primaries and orbital periods between 50 and 1000 days (separations 0.3--2.7~au). We found that $\psi$ is strongly associated with $e$, the orbital eccentricity. When $e<0.15$, the mean spin-orbit angle is $\langle\psi\rangle = 6.9_{-4.1}^{+5.4}$\,degrees, while for $e>0.7$, it rises to $\langle\psi\rangle = 46_{-24}^{+26}$\,degrees. These results suggest that some binaries are affected by processes during their formation or evolution that excite both orbital eccentricity and inclination.