We produce and analyse eclipse time variation (ETV) curves for some 2600 Kepler binaries. We find good to excellent evidence for a third body in 222 systems via either the light-travel-time (LTTE) or dynamical effect delays. Approximately half of these systems have been discussed in previous work, while the rest are newly reported here. Via detailed analysis of the ETV curves using high-level analytic approximations, we are able to extract system masses and information about the three-dimensional characteristics of the triple for 62 systems which exhibit both LTTE and dynamical delays; for the remaining 160 systems, we give improved LTTE solutions. New techniques of pre-processing the flux time series are applied to eliminate false positive triples and to enhance the ETV curves. The set of triples with outer orbital periods shorter than ∼2000 d is now sufficiently numerous for meaningful statistical analysis. We find that (i) there is a peak near i_m ≃ 40° in the distribution of the triple versus inner binary mutual inclination angles that provides strong confirmation of the operation of Kozai–Lidov cycles with tidal friction; (ii) the median eccentricity of the third-body orbits is e₂ = 0.35; (iii) there is a deficit of triple systems with binary periods ≲1 d and outer periods between ∼50 and 200 d which might help guide the refinement of theories of the formation and evolution of close binaries; and (iv) the substantial fraction of Kepler binaries which have third-body companions is consistent with a very large fraction of all binaries being part of triples.

We report eclipse timing variation analyses of 26 compact hierarchical triple stars comprised of an eccentric eclipsing (‘inner’) binary and a relatively close tertiary component found in the Kepler field. We simultaneously fit the primary and secondary O − C curves of each system for the light-traveltime effect (LTTE), as well as dynamical perturbations caused by the tertiary on different time-scales. For the first time, we include those contributions of three-body interactions which originate from the eccentric nature of the inner binary. These effects manifest themselves both on the period of the triple system, P₂, and on the longer ‘apse-node’ time-scale. We demonstrate that consideration of the dynamically forced rapid apsidal motion yields an efficient and independent tool for the determination of the binary orbit's eccentricity and orientation, as well as the 3D configuration of the triple. Modelling the forced apsidal motion also helps to resolve the degeneracy between the shapes of the LTTE and the dynamical delay terms on the P₂ time-scale, due to the strong dependence of the apsidal motion period on the triple's mass ratio. This can lead to the independent determination of the binary and tertiary masses without the need for independent radial velocity measurements. Through the use of our analytic method for fitting O − C curves, we have obtained robust solutions for system parameters for the 10 most ideal triples of our sample, and only somewhat less robust, but yet acceptable, fits for the remaining systems. Finally, we study the results of our 26 system parameter fits via a set of distributions of various physically important parameters, including mutual inclination angle, and mass and period ratios.

The aim of this paper is to search for evidences for the presence of unseen companions in some eclipsing binary systems using their O–C diagrams. A total of 8507 times of minima (6890 visual and 1617 photographic or photoelectric ones) of 18 systems have been collected from the remarkable database of late Dieter Lichtenknecker (Lichtenknecker 1988) and from other more recent papers. Assuming that light-time effect (LITE) is responsible for the periodic components on the O–C diagrams sets of orbital parameters were derived using Kopal's (1978) method. In some cases (AB And, TV Cas, XX Cep, AK Her) the resulting orbital parameters and masses of the hypothetical third components are physically acceptable. Other systems show good evidence for multiplicity, but the available data sets are not suited to compute reliable solutions (W Del, U Peg, AT Peg, ST Per). For RT And, XZ And, OO Aql, Y Cam, RS CVn, CQ Cep, U CrB and MR Cyg) an unambigous identification of third components is not possible. In the cases of TW Cas and SW Lac we could not find any LITE solution at all.

The Kepler satellite reveals details of the oscillations patterns of an evolved star in an exotic triple-star system.