4 Conclusions

In this paper we examined the possibility of detecting certain kind of perturbations, which are manifesting themselves on a very short time scale (even during a yearly observing window of the eclipsing variable), but usually omitted due to their low amplitude. This question naturally has different aspects. These are as follows:

• There are only a few known systems where the amplitude of the dynamical term in the O-C exceeds significantly the present observational accuracy. We can easily estimate the maximum-value of the P'/P ratio which is necessary to fulfill this condition. Supposing that the three components have equal masses, and the third body revolves in a circular orbit, according to Eq. (72) the amplitude may exceed the 10^-3 day limit, if P'/P<40P, at least when the two orbits are perpendicular to each other. If the outer orbit has significant eccentricity (say e'=0.50), or the system consists of stars with different masses, then this limit in the function of the mutual inclination may even grow up to $P'/P\approx150P$. From that point of view the two systems for which the numerical integrations were carried out in this paper are placed near the limit of the detectability, as for Algol $P'/P\approx83P$, while for IU Aur the same value is $P'/P\approx91P$.

  The three presently known closest eclipsing triple systems are $\lambda$ Tau ( $P'/P\approx2.11P$), DM Per ( $P'/P\approx13.17P$), and VV Ori ( $P'/P\approx54.41P$) (see e.g. the catalogue of Chambliss 1992). In the cases of the latter two binaries unfortunately only a very few times of minima observations can be found in the literature, although we could expect the largest effects at these stars. On the other hand, we have to note that as the amplitude of the light time-effect decreases with P'^2/3, at these stars already the detection of the pure geometrical effect is also a challenge. In the most interesting case of $\lambda$ Tau, the amplitude of the perturbative terms may be larger with an order of magnitude than that of the light-time terms. Furthermore, at this system due to the large amount of proximity our initial assumptions may loose their validity.

• The second aspect is mainly a technical question. It refers to the observing strategy. This was written already in the conclusion of Borkovits et al. (2002), but, for the sake of the completeness, we repeat it. In order to have any chance for the detection of this phenomenon frequent and accurate timings are necessary. It is desirable to cover a few revolutions of the distant object as densely as possible. The shorter the time interval of such coverage, the smaller the apse-node time scale or secular variations in the orbital elements which could modify the results.
• Finally, the mathematical modelling of perturbations are necessary in order to extract all information from the observations.

In this paper we concentrated mainly on this third item. We calculated a new analytical formula which gives the long period perturbations of the times of minima in eclipsing binaries. We found that this formula is very similar to the earlier expression of Mayer (1990), nevertheless, some errors are corrected. Using this expression we developed a numerical method to separate this dynamical effect from the pure geometrical light time effect. We tested the capabilities of our model by the analysis of numerically simulated O-C curves. In the case of the test runs for outer orbits with moderate eccentricity, significantly better solutions were found than in the larger eccentricity cases.

Naturally the next step would be the application of the method for observed O-C diagrams of real systems. Unfortunately, up to now there are not any O-C diagrams with sufficient accuracy for the possible target systems. This is why we plan to observe some of the few such systems in the near future to collect as many new times of minima as possible.