4 Discussion and conclusions

The three stage weighted MPA has been developed especially for simultaneous multichannel photometric observations. The new method has been tested successfully using two groups of artificially generated data with varying noise levels. The light curve model for the first group was constructed arbitrarily. The model for the second group was built using real-life multichannel photometric measurements as a template. Here are the main conclusions which can be drawn from our experiments:

1.

The MPA allows one to take into account all available data in a uniform and most informative way. It works correctly with different light curves and different noise levels in different channels. It incorporates easily data sets with missing values in some particular channels;

2.

The theoretically predicted improvement in detection capabilities and in estimation precision of the multichannel method was proved using simple simulations. The use of the new method for real data sets will be described elsewhere;

3.

It is possible to construct multichannel variants for all stages of the periodicity search. The grid search and the final period refinement can be done in the framework of standard least squares estimation. The only difference is the use of combined sums of squares. All the new methods described above can easily be implemented by introducing minor extensions to available software;

4.

We point out that the interpretation of the PDM spectra is somewhat more complicated than that of the classical power spectra. Thus, we derived the general formula for spurious periods (Eq. (19)) to help the identification of the correct periods among the ghosts.

In this paper only a single period case is treated. Multiperiodic light curves and especially coupled periods will complicate the analysis significantly. We can expect that multichannel methods will still give some edge over standard single channel methods.

The proposed method can also be used for searching hidden periodicities in the variations of spectral line profiles (if we use all wavelength pixels of the observed spectra as different photometric channels). It will detect periods even when equivalent widths remain stable and only the spectral profiles change. This kind of time series spectroscopy can reveal even low level periodic disturbances (say, from invisible companions etc.).

Acknowledgements

The work of Jaan Pelt was supported by the Estonian Science Foundation grant 2628. The authors thank Dr. Rudolf Dümmler and Dr. Andrei Berdyugin for checking the text, and the anonymous referee for his valuable comments.