Efficiency of O–C diagrams as diagnostic tools for long-term period variations

I. Wind-driven mass loss and magnetic braking

¹ Department of Astrophysics, Astronomy and MechanicsFaculty of Physics, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, 15 784 Athens, Greece
e-mail: nanouris@phys.uoa.gr; eantonop@phys.uoa.gr; elivan@phys.uoa.gr
² Technological and Educational Institute of the Ionian Islands, Kalvos Square, 29 100 Zakynthos, Greece
e-mail: tasoskalimeris@ath.forthnet.gr

Received: 14 February 2011
Accepted: 6 September 2011

Abstract

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 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.

Results. Mass loss rates comparable to or greater than −10^-9 M_⊙ yr^-1 are measurable for typical noise levels of the O–C diagrams when the data span more than a century. Magnetic braking was proved to be very sensitive on the orbital period and on the braking law adopted for inference. It is expected to be detectable in current O–C diagrams of very short-period binaries only, for others it needs at least two centuries of observations to confirm its effects safely.

Conclusions. Both wind driven mass loss and magnetic braking processes are able to drive the orbital evolution of short-period detached binaries (P_orb1d) in amounts traced on human timescales. There are also special conditions under which their strength is equalized, locking the orbital period invariable in time. Several short-period RS CVn-type binaries are fine candidates where this regime is expected to prevail.