We have presented a new approach to determine the orbital parameters of a binary in the case that one of the components is an intrinsically variable star. The method is applicable when the orbital period is considerably longer than the period(s) of the intrinsic variability. Our approach turns out to be very useful when a limited amount of data is available, i.e. when only a few nights of extensive data, that cover the intrinsic variability cycle, and a number of data points scattered throughout the orbital phase have been obtained. Such a situation typically occurs when the intrinsic variable target star of an observing run that covers the pulsational period turns out to be the component of an unknown binary. It is then often difficult to extend the data set in such a way that the orbital solution can be found without any problem. The method is also helpful when the observing run extends over the complete orbital period but when some nights are badly covered because of instrumental problems or poor atmospheric conditions.
Imbert (1987, 1994) previously suggested a method that takes into account the intrinsic variability of Cepheids in binaries when determining the orbital parameters. He achieves this by describing the pulsational radial-velocity variations by an artificial Keplerian orbit. This method only works well when the following conditions hold: the pulsation is monoperiodic, the pulsation period is well-known, and the pulsation cycles are well covered with data. It is therefore very restricted compared to our method and not applicable to most non-radial pulsators. Moreover, it assumes an artificial motion while we make use of a physically justified model. Finally, and most importantly, all observations are treated with equal importance in his method, contrary to our algorithm. The strength of our method is that it allows to use measurements of both badly and well covered cycles in a statistically justified way.
It is to be expected that the algorithm proposed here will be used more often in the near future now that it turns out that many pulsating stars belong to a multiple system (see e.g. Aerts et al. 1998b) and that known binaries turn out to have at least one variable component (Harmanec et al. 1997), the latter's intrinsic variations being neglected in the determination of the orbital solution so far.
AcknowledgementsP. De Cat acknowledges the financial support of the Belgian Fund for Joint Basic Research under Research Project No. G.0398.98.
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