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We study the long-term time-scale (i.e. period comaprable to the orbitalperiod of the outer perturber object) transit timing variations in transitingexoplanetary systems which contain a further, more distant (a_2>>a_1) eitherplanetary, or stellar companion.  We give an analytical form of the O-C diagram (which describes such TTV-s) intrigonometric series, valid for arbitrary mutual inclinations, up to the sixthorder in the inner eccentricity. We show that the dependence of the O-C on theorbital and physical parameters can be separated into three parts. Two of theseare independent of the real physical parameters (i.e. masses, separations,periods) of a concrete system, and depend only on dimensionless orbitalelements, and so, can be analyzed in general. We analyze these dimensionlessamplitudes for different arbitrary initial parameters, as well as for twoparticular systems CoRoT-9b and HD 80606b. We find in general, that while theshape of the O-C strongly varies with the angular orbital elements, the netamplitude (departing from some specific configurations) depends only weakly onthese elements, but strongly on the eccentricities. As an application, weillustrate how the formulae work for the weakly eccentric CoRoT-9b, and thehighly eccentric HD 80606b. We consider also the question of detection, as wellas the correct identification of such perturbations. Finally, we illustrate theoperation and effectiveness of Kozai cycles with tidal friction (KCTF) in thecase of HD 80606b.

astronomy and astrophysics

Transit timing variations in eccentric hierarchical triple exoplanetary  systems. I. Perturbations on the time-scale of the orbital period of the  perturber