Basic physical parameters of a selected sample of evolved stars

We present the detailed spectroscopic analysis of 72 evolved stars, which were previously studied for accurate radial velocity variations. Using one Hyades giant and another well studied star as the reference abundance, we determine the [Fe/H] for the whole sample. These metallicities, together with the T_eff values and the absolute V-band magnitude derived from Hipparcos parallaxes, are used to estimate basic stellar parameters (ages, masses, radii, (B-V)0 and log g) using theoretical isochrones and a Bayesian estimation method. The (B-V)0 values so estimated turn out to be in excellent agreement (to within ~0.05 mag) with the observed (B-V), confirming the reliability of the T_eff-(B-V)0 relation used in the isochrones. On the other hand, the estimated log g values are typically 0.2 dex lower than those derived from spectroscopy; this effect has a negligible impact on [Fe/H] determinations. The estimated diameters theta have been compared with limb darkening-corrected ones measured with independent methods, finding an agreement better than 0.3 mas within the 1<theta<10 mas interval (or, alternatively, finding mean differences of just 6%). We derive the age-metallicity relation for the solar neighborhood; for the first time to our knowledge, such a relation has been derived from observations of field giants rather than from open clusters and field dwarfs and subdwarfs. The age-metallicity relation is characterized by close-to-solar metallicities for stars younger than ~4 Gyr, and by a large [Fe/H] spread with a trend towards lower metallicities for higher ages. In disagreement with other studies, we find that the [Fe/H] dispersion of young stars (less than 1 Gyr) is comparable to the observational errors, indicating that stars in the solar neighbourhood are formed from interstellar matter of quite homogeneous chemical composition. The three giants of our sample which have been proposed to host planets are not metal rich; this result is at odds with those for main sequence stars. However, two of these stars have masses much larger than a solar mass so we may be sampling a different stellar population from most radial velocity searches for extrasolar planets. We also confirm the previous indication that the radial velocity variability tends to increase along the RGB, and in particular with the stellar radius.