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The formation of close binaries has been an open question for decades. Alarge fraction of close binaries are in triple systems, suggesting that theirformation may be associated with the Kozai-Lidov mechanism. However, thispicture remains under debate because the configurations of many observedtriples are unlikely to trigger the Kozai-Lidov mechanism. In this paper, weuse the close binary samples, including eclipsing, spectroscopic, andastrometric binaries, from Gaia Data Release 3 to investigate the mysteriousconnection between inner binaries and their wide tertiaries. We show that thewide tertiary (at $10^3$-$10^4$ AU) fraction increases with decreasing orbitalperiods 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 thefield wide binary fraction. Furthermore, there is a tentative excess at$\sim10^4$ AU for tertiaries of eclipsing binaries. Using the $v$-$r$ angledistributions, we show that wide tertiaries have isotropic orientations withrespect to the inner binaries, and the co-planar orbits can be ruled out. Theinferred eccentricity distribution of wide tertiaries is consistent($<1\sigma$) with being thermal ($f(e)\propto e$), similar to wide binaries atsimilar separations. The dynamical unfolding scenario is disfavored because itpredicts highly eccentric wide tertiaries, which is inconsistent with ourfindings. 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 atthese large initial separations and large tertiary separations.

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