Abstract.We study the possibility of the detection of the low amplitude long (P ) period perturbative effect of a distant third companion on the motion of a close binary. We give a new, more accurate analytical formula for this kind of perturbation affecting the moments of the times of minima in eclipsing binaries. The accuracy of this formula is tested by numerical integrations carried out for several initial configurations. We also describe a numerical method based on a non-linear Levenberg-Marquardt algorithm which makes it possible to separate this dynamical effect from the pure geometrical light-time effect in the eclipsing O−C diagram. The capabilities of this new method are demonstrated by the analysis of numerically simulated O−Cs for test systems having physical parameters very similar to Algol and IU Aur. The results show that the above mentioned effect would be detectable in these systems nowadays, observing almost each minima events in a 1-2 year-long interval.

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.

HD 181068 is the brighter of the two known triply eclipsing hierarchical triple stars in the Kepler field. It has been continuously observed for more than 2 years with the Kepler space telescope. Of the nine quarters of the data, three have been obtained in short-cadence mode, that is one point per 58.9 s. Here we analyse this unique dataset to determine absolute physical parameters (most importantly the masses and radii) and full orbital configuration using a sophisticated novel approach. We measure eclipse timing variations (ETVs), which are then combined with the single-lined radial velocity measurements to yield masses in a manner equivalent to double-lined spectroscopic binaries. We have also developed a new light curve synthesis code that is used to model the triple, mutual eclipses and the effects of the changing tidal field on the stellar surface and the relativistic Doppler-beaming. By combining the stellar masses from the ETV study with the simultaneous light curve analysis we determine the absolute radii of the three stars. Our results indicate that the close and the wide subsystems revolve in almost exactly coplanar and prograde orbits. The newly determined parameters draw a consistent picture of the system with such details that have been beyond reach before.

Aims. Time-series spot modelling was used to follow the longitude changes of active regions responsible for the light variability of FK Com between 1987Com between −2004. Methods. The photometric data are analysed in the time-series mode of a spot modelling code. A scenario of one polar and two low-latitude active regions (hereafter spots, for simplicity) depicts the light variations very well. The role of the polar spot remains unclear because photometry in general does not provide direct latitudinal surface resolution, however, Doppler imaging results of FK Com also show very high latitude or even polar spots besides the low-latitude ones. We also used a light-curve inversion method to confirm some of the results. Results. The two low-latitude spots slowly migrate around 90• and 270• longitudes with quasiperiods of 5.8 and 5.2 years. The spots prefer to stay alternately on one or the other, but on the same hemisphere of the star, with a separation of typically 90−140• . We monitored a flip-flop in the light curve of FK Comae in 1999. The two low-latitude spots, being ≈140−180• from each other during the season, gradually decreased until they both practically vanished. Shortly thereafter, two new spots appeared and started to grow. One of the new spots was near the location of the old one, whereas the other turned up 90• shifted in longitude; consequently, the activity as a whole was shifted to the other hemisphere of the star. We followed a phase jump in 1997, when the two low-latitude spots got closer in longitude and finally merged, or else one of them vanished. A new spot appeared soon, shifted by 100• in longitude, but the activity remained on the same hemisphere. Conclusions. The difference between flip-flops and phase jumps is demonstrated. The derived longitude changes of activity centres may allow us to better constrain the theoretical modelling on the time-behaviour of stellar magnetic activity.