The high energy activity in the inner few degrees of the Galactic center is traced by diffuse radio, X-ray and gamma-ray emission. The physical relationship between different components of diffuse gas emitting at multiple wavelengths is a focus of this work. We first present radio continuum observations using Green Bank Telescope and model the nonthermal spectrum in terms of a broken power-law distribution of GeV electrons emitting synchrotron radiation. We show that the emission detected by Fermi is primarily due to nonthermal bremsstrahlung produced by the population of synchrotron emitting electrons in the GeV energy range interacting with neutral gas. The extrapolation of the electron population measured from radio data to low and high energies can also explain the origin of FeI 6.4 keV line and diffuse TeV emission, as observed with Suzaku, XMM-Newton, Chandra and the H.E.S.S. observatories. The inferred physical quantities from modeling multi-wavelength emission in the context of bremsstrahlung emission from the inner 300x120 parsecs of the Galactic center are constrained to have the cosmic ray ionization rate 1-10x10^{-15} s^-1, molecular gas heating rate elevating the gas temperature to 75-200K, fractional ionization of molecular gas 10^{-6} to 10^{-5}, large scale magnetic field 10-20 micro Gauss, the density of diffuse and dense molecular gas 100 and 10^3 cm^{-3} over 300pc and 50pc pathlengths, and the variability of FeI Kalpha 6.4 keV line emission on yearly time scales. Important implications of our study are that GeV electrons emitting in radio can explain the GeV gamma-rays detected by Fermi and that the cosmic ray irradiation model, like the model of the X-ray irradiation triggered by past activity of Sgr A*, can also explain the origin of the variable 6.4 keV emission from Galactic center molecular clouds.
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