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[ascl:1206.011] Double Eclipsing Binary Fitting

The parameters of the mutual orbit of eclipsing binaries that are physically connected can be obtained by precision timing of minima over time through light travel time effect, apsidal motion or orbital precession. This, however, requires joint analysis of data from different sources obtained through various techniques and with insufficiently quantified uncertainties. In particular, photometric uncertainties are often underestimated, which yields too small uncertainties in minima timings if determined through analysis of a χ2 surface. The task is even more difficult for double eclipsing binaries, especially those with periods close to a resonance such as CzeV344, where minima get often blended with each other.

This code solves the double binary parameters simultaneously and then uses these parameters to determine minima timings (or more specifically O-C values) for individual datasets. In both cases, the uncertainties (or more precisely confidence intervals) are determined through bootstrap resampling of the original data. This procedure to a large extent alleviates the common problem with underestimated photometric uncertainties and provides a check on possible degeneracies in the parameters and the stability of the results. While there are shortcomings to this method as well when compared to Markov Chain Monte Carlo methods, the ease of the implementation of bootstrapping is a significant advantage.

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