The mystery in Gaia DR3 triples: occurrence rates, orientations, and eccentricities of wide tertiaries around close binaries

The formation of close binaries has been an open question for decades. A large fraction of close binaries are in triple systems, suggesting that their formation may be associated with the Kozai-Lidov mechanism. However, this picture remains under debate because the configurations of many observed triples are unlikely to trigger the Kozai-Lidov mechanism. In this paper, we use the close binary samples, including eclipsing, spectroscopic, and astrometric binaries, from Gaia Data Release 3 to investigate the mysterious connection between inner binaries and their wide tertiaries. We show that the wide tertiary (at $10^3$-$10^4$ AU) fraction increases with decreasing orbital periods of the inner binaries. The wide tertiary fraction of eclipsing binaries (a median orbital period of $0.41$ day) is $2.33\pm0.11$ times higher than the field wide binary fraction. Furthermore, there is a tentative excess at $\sim10^4$ AU for tertiaries of eclipsing binaries. Using the $v$-$r$ angle distributions, we show that wide tertiaries have isotropic orientations with respect to the inner binaries, and the co-planar orbits can be ruled out. The inferred eccentricity distribution of wide tertiaries is consistent ($<1\sigma$) with being thermal ($f(e)\propto e$), similar to wide binaries at similar separations. The dynamical unfolding scenario is disfavored because it predicts highly eccentric wide tertiaries, which is inconsistent with our findings. For the Kozai-Lidov mechanism to be effective for wide tertiaries at $>10^3$ AU, the initial separations of the inner binaries need to be $>3$ AU. Future theoretical investigations are needed to explore the parameter space at these large initial separations and large tertiary separations.