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We report the first time-series of broadband infrared (IR) color measurementsof Sgr A*, the variable emission source associated with the supermassive blackhole at the Galactic Center. Using the laser and natural guide star AO systemson the Keck II telescope, we imaged Sgr A* in multiple near-infrared broadbandfilters with a typical cycle time of ~3 min during 4 observing runs(2005-2006), two of which were simultaneous with Chandra X-ray measurements. Inspite of the large range of dereddened flux densities for Sgr A* (2-30 mJy),all of our near-IR measurements are consistent with a constant spectral indexof alpha = -0.6+-0.2. Furthermore, this value is consistent with the spectralindices observed at X-ray wavelengths during nearly all outbursts; which isconsistent with the synchrotron self-Compton model for the production of theX-ray emission. During the coordinated observations, one IR outburst occurs <36min after a possibly associated X-ray outburst, while several similar IRoutbursts show no elevated X-ray emission. A variable X-ray to IR ratio andconstant infrared spectral index challenge the notion that the IR and X-rayemission are connected to the same electrons. We, therefore, posit that thepopulation of electrons responsible for both the IR and X-ray emission aregenerated by an acceleration mechanism that leaves the bulk of the electronenergy distribution responsible for the IR emission unchanged, but has avariable high-energy cutoff. Occasionally a tail of electrons >1 GeV isgenerated, and it is this high-energy tail that gives rise to the X-rayoutbursts. One possible explanation for this type of variation is from theturbulence induced by a magnetorotational instability, in which the outer scalelength of the turbulence varies and changes the high-energy cutoff.

A Constant Spectral Index for Sagittarius A* During Infrared/X-ray Intensity Variations