We present an analysis of 1524 spectra of Vega spanning 10 years, in which we search for periodic radial velocity variations. A signal with a periodicity of 0.676 days and a semi-amplitude of ~10 m/s is consistent with the rotation period measured over much shorter time spans by previous spectroscopic and spectropolarimetric studies, confirming the presence of surface features on this A0 star. The timescale of evolution of these features can provide insight into the mechanism that sustains the weak magnetic fields in normal A type stars. Modeling the radial velocities with a Gaussian process using a quasi-periodic kernel suggests that the characteristic spot evolution timescale is ~180 days, though we cannot exclude the possibility that it is much longer. Such long timescales may indicate the presence of failed fossil magnetic fields on Vega. TESS data reveal Vegas photometric rotational modulation for the first time, with a total amplitude of only 10 ppm, and a comparison of the spectroscopic and photometric amplitudes suggest the surface features may be dominated by bright plages rather than dark spots. For the shortest orbital periods, transit and radial velocity injection recovery tests exclude the presence of transiting planets larger than 2 Earth radii and most non-transiting giant planets. At long periods, we combine our radial velocities with direct imaging from the literature to produce detection limits for Vegan planets and brown dwarfs out to distances of 15 au. Finally, we detect a candidate radial velocity signal with a period of 2.43 days and a semi-amplitude of 6 m/s. If caused by an orbiting companion, its minimum mass would be ~20 Earth masses; because of Vegas pole-on orientation, this would correspond to a Jovian planet if the orbit is aligned with the stellar spin. We discuss the prospects for confirmation of this candidate planet.
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