Absolute dimensions of solar-type eclipsing binaries II. V636 Centauri: A 1.05 M⊙ primary with an active, cool, oversize 0.85 M⊙ secondary

Context. The influence of stellar activity on the fundamental properties of stars around and below 1 M-circle dot is not well understood. Accurate mass, radius, and abundance determinations from solar-type binaries exhibiting various levels of activity are needed for a better insight into the structure and evolution of these stars. Aims. We aim to determine absolute dimensions and abundances for the solar-type detached eclipsing binary V636 Cen, and to perform a detailed comparison with results from recent stellar evolutionary models. Methods. uvby light curves and uvby beta standard photometry were obtained with the Stromgren Automatic Telescope, radial velocity observations with the CORAVEL spectrometer, and high-resolution spectra with the FEROS spectrograph, all at ESO, La Silla. State-of-the-art methods were applied for the photometric and spectroscopic analyses. Results. Masses and radii that are precise to 0.5% have been established for the components of V636 Cen. The 0.85 M-circle dot secondary component is moderately active with starspots and Ca II Pi and K emission, and the 1.05 M-circle dot primary shows signs of activity as well, but at a much lower level. We derive a [Fe/H] abundance of -0.20 +/- 0.08 and similar abundances for Si, Ca, Ti, V, Cr, Co, and Ni. Corresponding solar-scaled stellar models are unable to reproduce V636 Cen, especially its secondary component, which is similar to 10% larger and similar to 400 K cooler than predicted. Models adopting significantly lower mixing-length parameters l/H-p remove these discrepancies, seen also for other solar-type binary components. For the observed [Fe/H], Claret models for l/H-p = 1.4 (primary) and 1.0 (secondary) reproduce the components of V636 Cen at a common age of 1.35 Gyr. The orbit is eccentric (e = 0.135 +/- 0.001), and apsidal motion with a 40% relativistic contribution has been detected. The period is U = 5 270 +/- 335 yr, and the inferred mean central density concentration coefficient, log(k(2)) = -1.61 +/- 0.05, agrees marginally with model predictions. The measured rotational velocities, 13.0 +/- 0.2 (primary) and 11.2 +/- 0.5 (secondary) km s(-1), are in remarkable agreement with the theoretically predicted pseudo-synchronous velocities, but are about 15% lower than the periastron values. Conclusions. V636 Cen and 10 other well-studied inactive and active solar-type binaries suggest that chromospheric activity, and its effect on envelope convection, is likely to cause radius and temperature discrepancies, which can be removed by adjusting the model mixing length parameters downwards. Noting this, the sample may also lend support to theoretical 2D radiation hydrodynamics studies, which predict a slight decrease of the mixing length parameter with increasing temperature/mass for inactive main sequence stars. More binaries are, however, needed for a description/calibration in terms of physical parameters and level of activity.