We present an analysis of the 4-2600 $mu$m spectral energy distributions (SEDs) of the west and east nuclei and the diffuse infrared (IR) region of the merger-driven starburst Arp 220. We examine several possible source morphologies and dust temperature distributions using a mixture of silicate and carbonaceous grains. From fits to the SEDs we derive dust masses, temperatures, luminosities, and dust inferred gas masses. We show that the west and east nuclei are powered by central sources deeply enshrouded behind $sim 10^{26}$ cm$^{-2}$ column densities of hydrogen with an exponential density distribution, and that the west and east nuclei are optically thick out to wavelengths of $sim 1900$ and $sim 770$ $mu$m, respectively. The nature of the central sources cannot be determined from our analysis. We derive star formation rates or black hole masses needed to power the IR emission, and show that the [C II] 158$mu$m line cannot be used as a tracer of the star formation rate in heavily obscured systems. Dust inferred gas masses are larger than those inferred from CO observations, suggesting either larger dust-to-H mass ratios, or the presence of hidden atomic H that cannot be inferred from CO observations. The luminosities per unit mass in the nuclei are $sim 450$, in solar units, smaller that the Eddington limit of $sim 1000 - 3000$ for an optically thick star forming region, suggesting that the observed gas outflows are primarily driven by stellar winds and supernova shock waves instead of radiation pressure on the dust.
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