  We report the first time-series of broadband infrared (IR) color measurements
of Sgr A*, the variable emission source associated with the supermassive black
hole at the Galactic Center. Using the laser and natural guide star AO systems
on the Keck II telescope, we imaged Sgr A* in multiple near-infrared broadband
filters with a typical cycle time of ~3 min during 4 observing runs
(2005-2006), two of which were simultaneous with Chandra X-ray measurements. In
spite 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 index
of alpha = -0.6+-0.2. Furthermore, this value is consistent with the spectral
indices observed at X-ray wavelengths during nearly all outbursts; which is
consistent with the synchrotron self-Compton model for the production of the
X-ray emission. During the coordinated observations, one IR outburst occurs <36
min after a possibly associated X-ray outburst, while several similar IR
outbursts show no elevated X-ray emission. A variable X-ray to IR ratio and
constant infrared spectral index challenge the notion that the IR and X-ray
emission are connected to the same electrons. We, therefore, posit that the
population of electrons responsible for both the IR and X-ray emission are
generated by an acceleration mechanism that leaves the bulk of the electron
energy distribution responsible for the IR emission unchanged, but has a
variable high-energy cutoff. Occasionally a tail of electrons >1 GeV is
generated, and it is this high-energy tail that gives rise to the X-ray
outbursts. One possible explanation for this type of variation is from the
turbulence induced by a magnetorotational instability, in which the outer scale
length of the turbulence varies and changes the high-energy cutoff.
