Transit timing variations in eccentric hierarchical triple exoplanetary systems

Abstract

Aims. We study the long-term time scale (i.e. period comparable to the orbital period of the outer perturber object) transit timing variations (TTVs) in transiting exoplanetary systems that contain another more distant (a 2 a 1 ) planetary or stellar companion. Methods. We give an analytical form of the O−C diagram (which describes such TTVs) in a trigonometric series, which is valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. Results. We show that the dependence of the O−C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the real physical parameters (i.e. masses, separations, periods) of a concrete system and only depend on dimensionless orbital elements, so can be analysed in general. We find that, for a specific transiting system, where eccentricity (e 1 ) and the observable argument of periastron (ω 1 ) are known, say, from spectroscopy, the main characteristics of that TTV, which is caused by a possible third-body can be mapped simply. Moreover, as the physical attributes of a given system only occur as scaling parameters, the real amplitude of the O−C can also be estimated for a given system, simply as a function of the m 3 /P 2 ratio. We analyse the above-mentioned dimensionless amplitudes for different arbitrary initial parameters, as well as for two particular systems, CoRoT-9b and HD 80606b. We find in general that, while the shape of the O−C strongly varies with the angular orbital elements, the net amplitude (departing from some specific configurations) depends only weakly on these elements, but strongly on the eccentricities. As an application, we illustrate how the formulae work for the weakly eccentric CoRoT-9b and the highly eccentric HD 80606b. We also consider the question of detection, as well as the correct identification of such perturbations. Finally, we illustrate the operation and effectiveness of Kozai cycles with tidal friction (KCTF) in the case of HD 80606b.

ξTauri: a unique laboratory to study the dynamic interaction in a compact hierarchical quadruple system

“…So far, the long-period effects, namely those with a period P 2 of orbit 2, have been extensively studied (e.g. Soderhjelm 1975Soderhjelm , 1982Borkovits et al 2003Borkovits et al , 2011Borkovits et al , 2015. We here focus on the ETVs, that is, on advances and delays δt LP in epochs of eclipse of orbit 1 that are due to the variations in its mean motion n 1 caused by component B.…”

“…Assuming for simplicity coplanar orbitsJ = 0 deg, we obtain (e.g. Soderhjelm 1975;Borkovits et al 2011Borkovits et al , 2015Rappaport et al 2013, which also contain terms proportional to ∝J 2 )…”

No circumbinary planets transiting the tightestKeplerbinaries – a possible fingerprint of a third star

“…To find such planets it is likely that new techniques will need to be developed. The four years of Kepler photometric data are yet to be exhaustively searched, and may still yield discoveries of misaligned planets via eclipse timing variations (Borkovits et al 2011), or transits on non-eclipsing binaries (Martin & Triaud 2014), particularly on binaries found with the BEER technique (Faigler et al 2012). A re-observation of the Kepler field by the future PLATO satellite may lead to transits on the existing sample of eclipsing binaries by new planets that have precessed into view.…”

Gaia's potential for the discovery of circumbinary planets

“…Konacki et al 2009). The method of eclipse-timing variations (ETV) is sensitive to long-period planets ( 200 days) since the ETV amplitude increases with the planet period (Borkovits et al 2011). Whilst the ETV amplitude is independent of the binary period, short-period binaries ( 50 days) are favoured since they allow us to reach the temporal precision required to detect the light travel time effect induced by a planet.…”