OGLE 2004-BLG-254: a K3 III Galactic bulge giant spatially resolved by a single microlens

14 pages, 8 figures, accepted for publication in A&A (04/09/2006)Aims. We present an analysis of OGLE 2004-BLG-254, a high-magnification (A? ? 60) and relatively short duration (t_E? 13.2 days) microlensing event in which the source star, a Bulge K-giant, has been spatially resolved by a point-like lens. We seek to determine the lens and source distance, and provide a measurement of the linear limb-darkening coefficients of the source star in the I and R bands. We discuss the derived values of the latter and compare them to the classical theoretical laws, and furthermore examine the cases of already published microlensed GK-giants limb-darkening measurements. Methods: . We have obtained dense photometric coverage of the event light curve with OGLE and PLANET telescopes, as well as a high signal-to-noise ratio spectrum taken while the source was still magnified by A ? 20, using the UVES/VLT spectrograph. We have performed a modelling of the light curve, including finite source and parallax effects, and have combined spectroscopic and photometric analysis to infer the source distance. A Galactic model for the mass and velocity distribution of the stars has been used to estimate the lens distance. Results: . From the spectrum analysis and calibrated color-magnitude of the event target, we found that the source was a K3 III Bulge giant, situated at the far end of the Bulge. From modelling the light curve, we have derived an angular size of the Einstein ring ?_E? 114 ?as, and a relative lens-source proper motion ? = ?_E/t_E? 3.1 mas/yr. We could also measure the angular size of the source, ?_*? 4.5 ?as, whereas given the short duration of the event, no significant constraint could be obtained from parallax effects. A Galactic model based on the modelling of the light curve then provides us with an estimate of the lens distance, mass and velocity as D_L? 9.6 kpc, M? 0.11 M? and v ? 145~km s-1 (at the lens distance) respectively. Our dense coverage of this event allows us to measure limb darkening of the source star in the I and R bands. We also compare previous measurements of linear limb-darkening coefficients involving GK-giant stars with predictions from ATLAS atmosphere models. We discuss the case of K-giants and find a disagreement between limb-darkening measurements and model predictions, which may be caused by the inadequacy of the linear limb-darkening law