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Our current understanding of ultraluminous infrared galaxies suggest thatthey are recent galaxy mergers in which much of the gas in the former spiraldisks, particularly that located at distances less than 5 kpc from each of thepre-merger nuclei, has fallen into a common center, triggering a huge starburstphenomenon. This large nuclear concentration of molecular gas has been detectedby many groups, and estimates of molecular mass and density have been made. Notsurprisingly, these estimates were found to be orders of magnitude larger thanthe corresponding values found in our Galaxy. In this paper, a self-consistentmodel of the high energy emission of the super-starburst galaxy Arp 220 ispresented. The model also provides an estimate of the radio emission from eachof the components of the central region of the galaxy (western and easternextreme starbursts, and molecular disk). The predicted radio spectrum is foundas a result of the synchrotron and free-free emission, and absorption, of theprimary and secondary steady population of electrons and positrons. The latteris output of charged pion decay and knock-on leptonic production, subject to afull set of losses in the interstellar medium. The resulting radio spectrum isin agreement with sub-arcsec radio observations, what allows to estimate themagnetic field. In addition, the FIR emission is modeled with dust emissivity,and the computed FIR photon density is used as a target for inverse Comptonprocess as well as to give account of losses in the $\gamma$-ray scape.Bremsstrahlung emission and neutral pion decay are also computed, and the$\gamma$-ray spectrum is finally predicted. Future possible observations withGLAST, and the ground based Cherenkov telescopes are discussed.Comment: 47 pages, 15 figures, 5 tables. A comment on pion cross section  parameterizations and gamma-ray yields at high energies, and 1 reference,  were added. For further details see appendix of astro-ph/0506240. Otherwise  replaced to match published article in Ap

Theoretical Modeling of the Diffuse Emission of Gamma Rays from Extreme Regions of Star Formation: The Case of ARP 220