Enhanced Microlensing by Stars around the Black Hole in the Galactic Center

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Abstract
The effect of stars on the lensing properties of the supermassive black hole in the Galactic center is similar to the effect of planets on microlensing by a star. We show that the dense stellar cluster around Sgr A* increases by factors of a few the probability of high-magnification lensing events of a distant background source by the black hole. Conversely, the gravitational shear of the black hole changes and enhances the microlensing properties of the individual stars. The effect is largest when the source image lies near the Einstein radius of the black hole (175 ± 020 for a source at infinity). We estimate that the probability of observing at least one distant background star, which is magnified by a factor greater than 5 in any infrared snapshot of the inner ~2'' of the Galactic center, is ~1% with a K-band detection threshold of 20 mag. The largest source of uncertainty in this estimate is the luminosity function of the background stars. The gravitational shear of the black hole lengthens the duration of high-magnification events near the Einstein radius up to a few months and introduces a large variety of light-curve shapes that are different from those of isolated microlenses. Identification of such events by image subtraction can be used to probe the mass function, density, and velocity distributions of faint stars near the black hole, which are not detectable otherwise.