From adaptive optics observations with the Palomar 5 m telescope we place upper limits on the masses of any planetary companions located between ~30 and 230 AU away from Vega, where our data are sensitive to depths ranging from H = 12.5-19.0 mag fainter than Vega itself. Our observations cover a plus-shaped area with two 25'' × 57'' elements, excluding 7'' × 7'' centered on the star. We have identified two double and four single point sources. These projected companions are 14.9-18.9 mag fainter than Vega and, if physically associated, would have masses ranging from 4 to 35 MJ and orbital radii of 170-260?AU. Recent simulations of dusty rings around Vega predict the presence of a perturbing body with a mass of less than 2-3 MJ and an orbital radius of ~40-100?AU, and more massive (10 MJ) planets cannot be excluded. None of the detected objects are this predicted planet. Based on a color-magnitude, spectroscopic, and proper motion analysis, all objects are consistent with being background sources. Given the glare of Vega, a 2 MJ object near the expected orbital radii would not have been visible at the 5 σ level in our data, though any brown dwarf with mass greater than 10 MJ could have been seen at a separation greater than 80 AU.
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