A Multi-Wavelength Study of Sgr A*: The Role of Near-IR Flares in Production of X-ray, Soft $\gamma$-ray and Sub-millimeter Emission

41 pages, 12 figures, submitted to ApJAlthough Sgr A* is known to be variable in radio, millimeter, near-IR and X-rays, the correlation of the variability across its spectrum has not been fully studied. Here we describe highlights of the results of two observing campaigns in 2004 to investigate the correlation of flare activity in different wavelength regimes, using a total of nine ground and space-based telescopes. We report the detection of several new near-IR flares during the campaign based on {\it HST} observations. The level of near-IR flare activity based on {\it HST} data can be as low as $\sim0.15$ mJy at 1.6 $\mu$m and continuous up to $\sim$40% of the total observing time, thus placing better limits than ground-based near-IR observations. We also show the detection of a simultaneous bright X-ray and near-IR flare in which we observe for the first time correlated substructures as well as a submillimeter and near-IR flare using the NICMOS instrument on the {\it HST}, the {\it XMM-Newton} and {\it Caltech Submillimeter} observatories. X-ray emission as arising from the population of near-IR-synchrotron-emitting relativistic particles, which scatter submillimeter seed photons within the inner 10 Schwarzschild radii (R$_{sch}$) of Sgr A* up to X-ray energies. In addition, using the inverse Compton scattering picture, we explain the high energy 20-120 keV emission from the direction toward Sgr A*, and the lack of one-to-one X-ray counterparts to near-IR flares, by the variation of the magnetic field and the spectral index distributions of this population of nonthermal particles. In this picture, the evidence for the variability of submillimeter emission during a near-IR flare is accounted for by the low-energy component of the population of particles emitting synchrotron near-IR emission