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Efficiency of O–C diagrams as diagnostic tools for long-term period variations - I. Wind-driven mass loss and magnetic braking

Context. The credibility of an O–C diagram analysis is investigated when long-term processes are examined in binary systems. The morphology of period and O–C diagrams is thoroughly explored when mass loss and magnetic braking, induced by stellar winds, drive the orbital evolution of late-type detached binaries. Conditions are specified that determine which process dominates. Aims. Our objective is to determine the minimum time intervals that observations are expected to span for a physical mechanism to be detectable by means of an O–C diagram analysis. Computations for various values that account for the noise level and the orbital period are performed to find out to which degree these affect the inferred intervals. Methods. Generalized u J − u P relations that govern the orbital evolution of a binary system are set and solved analytically to determine in a closed form the period and the function expected to represent the respective O–C variations. Semi-empirical relations adapting mass loss and magnetic braking processes for single cool stars are adopted and properly modified to be consistent with the latest observational constraints. A standard Newton-Raphson numerical procedure is then employed to estimate the minimum temporal range over which a specific mechanism is rendered measurable.