  The near-IR and X-ray flares in Sagittarius A* are believed to be produced by
relativistic electrons via synchrotron and synchrotron self-Comptonization,
respectively. These electrons are likely energized by turbulent plasma waves
through second-order Fermi acceleration that, in combination with the radiative
cooling processes, produces a relativistic Maxwellian distribution in the
steady state. This model has four principal parameters, namely the magnetic
field B, the electron density n and temperature \gamma_c mec2, and the size of
the flare region R. In the context of stochastic acceleration, the quantities
Rn^1/2B and \gamma_cRn should remain nearly constant in time. Therefore,
simultaneous spectroscopic observations in the NIR and X-ray bands can readily
test the model, which, if proven to be valid, may be used to determine the
evolution of the plasma properties during an eruptive event with spectroscopic
observations in either band or simultaneous flux density measurements in both
bands. The formulae can be applied to other isolated or confined systems, where
electrons are accelerated to relativistic energies by plasma wave turbulence
and produce most of the emission via synchrotron processes.
