The near-IR and X-ray flares in Sagittarius A* are believed to be produced by relativistic electrons via synchrotron and synchrotron self-Comptonization (SSC), 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, their ``temperature'' gamma c me c2, and the size of the flare region R. In the context of stochastic acceleration by plasma waves, the quantities R n1/2 B and gamma c R n 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 formulation we develop here may also be applicable to other sources radiating via thermal synchrotron and SSC processes.
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