Binarity, activity and metallicity among late-type stars I. Methodology and application to HD 27536 and HD 216803

We present the first in a series of papers that attempt to investigate the relation between binarity, magnetic activity, and chemical surface abundances of cool stars. In the current paper, we lay out and test two abundance analysis methods and apply them to two well-known, active, single stars, HD 27536 (G8IV-III) and HD 216803 (K5V), presenting photospheric fundamental parameters and abundances of Li, Al, Ca, Si, Sc, Ti, V, Cr, Fe, Co and Ni. The abundances from the two methods agree within the errors for all elements except calcium in \hdeen, which means that either method yields the same fundamental model parameters and the same abundances. Activity is described by the radiative loss in the Ca II H & K lines with respect to the bolometric luminosity, through the activity index R_{HK}. Binarity is established by very precise radial velocity (RV) measurements using HARPS spectra. The spectral line bisectors are examined for correlations between RV and bisector shape to distinguish between the effects of stellar activity and unseen companions. We show that HD 27536 exhibit RV variations mimicking the effect of a low-mass (m ~ 4M_J) companion in a relatively close (a ~ 1AU) orbit. The variation is strongly correlated with the activity, and consistent with the known photometric period P = 306.9 d, demonstrating a remarkable coherence between R_{HK} and the bisector shape, i.e. between the photosphere and the chromosphere. We discuss the complications involved in distinguishing between companion and activity induced RV variations.