Limb Darkening of a K Giant in the Galactic Bulge: PLANET Photometry of MACHO 97‐BLG‐28

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Abstract
We present the PLANET photometric data set for the binary-lens microlensing event MACHO 97-BLG-28, consisting of 696 I- and V-band measurements, and analyze it to determine the radial surface brightness profile of the Galactic bulge source star. The microlensed source, demonstrated to be a K giant by our independent spectroscopy, crossed an isolated cusp of the central caustic of the lensing binary, generating a sharp peak in the light curve that was well-resolved by dense (3-30 minute) and continuous monitoring from PLANET sites in Chile, South Africa, and Australia. This is the first time that such a cusp crossing has been observed. Analysis of the PLANET data set has produced a measurement of the square-root limb-darkening coefficients of the source star in the I and V bands; the resulting stellar profiles are in excellent agreement with those predicted by stellar atmospheric models for K giants. The limb-darkening coefficients presented here are the first derived from microlensing. They are also among the first found for normal giants by any technique and the first for any star as distant as the Galactic bulge. Modeling of our light curve for MACHO 97-BLG-28 indicates that the lensing binary has a mass ratio q = 0.23 and an (instantaneous) separation in units of the angular Einstein ring radius of d = 0.69. For a lens in the Galactic bulge, this corresponds to a typical stellar binary with a projected separation between 1 and 2 AU. If the lens lies closer (i.e., in the Galactic disk), the separation is smaller, and one or both of the lens objects is in the brown dwarf regime. Assuming that the source is a bulge K2 giant at 8 kpc, the relative lens-source proper motion is μ = 19.4 ± 2.6 km s-1 kpc-1, consistent with a disk or bulge lens. If the nonlensed blended light is due to a single star, it is likely to be a young white dwarf in the bulge, consistent with the blended light coming from the lens itself.