  Large Galactic stellar surveys and new generations of stellar atmosphere
models and spectral line formation computations need to be subjected to careful
calibration and validation and to benchmark tests. We focus on cool stars and
aim at establishing a sample of 34 Gaia FGK Benchmark Stars with a range of
different metallicities. The goal was to determine the effective temperature
and the surface gravity independently from spectroscopy and atmospheric models
as far as possible. Fundamental determinations of Teff and logg were obtained
in a systematic way from a compilation of angular diameter measurements and
bolometric fluxes, and from a homogeneous mass determination based on stellar
evolution models. The derived parameters were compared to recent spectroscopic
and photometric determinations and to gravity estimates based on seismic data.
Most of the adopted diameter measurements have formal uncertainties around 1%,
which translate into uncertainties in effective temperature of 0.5%. The
measurements of bolometric flux seem to be accurate to 5% or better, which
contributes about 1% or less to the uncertainties in effective temperature. The
comparisons of parameter determinations with the literature show in general
good agreements with a few exceptions, most notably for the coolest stars and
for metal-poor stars. The sample consists of 29 FGK-type stars and 5 M giants.
Among the FGK stars, 21 have reliable parameters suitable for testing,
validation, or calibration purposes. For four stars, future adjustments of the
fundamental Teff are required, and for five stars the logg determination needs
to be improved. Future extensions of the sample of Gaia FGK Benchmark Stars are
required to fill gaps in parameter space, and we include a list of suggested
candidates.
