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We report the first detection at multiple radio wavelengths (13, 6 and 3.6cm) of the compact sources within both nuclei of the Ultra Luminous Infra-RedGalaxy Arp 220. We present the radio spectra of the 18 detected sources. Injust over half of the sources we find that these spectra and other propertiesare consistent with the standard model of powerful Type IIn supernovaeinteracting with their pre-explosion stellar wind. The rate of appearance ofnew radio sources identified with these supernova events suggests that anunusually large fraction of core collapse supernovae in Arp 220 are highlyluminous; possibly implying a radically different stellar initial mass functionor stellar evolution compared to galactic disks. Another possible explanationinvokes very short (~3 x 10^5 year) intense (~10^3 M_Sol year^-1) starformation episodes with a duty cycle of ~10%. A second group of our detectedsources, consisting of the brightest and longest monitored sources at 18 cm donot easily fit the radio supernova model. These sources show a range ofspectral indexes from -0.2 to -1.9. We propose that these are young supernovaremnants which have just begun interacting with a surrounding ISM with adensity between 10^4 and 10^5 cm^-3. One of these sources is probably resolvedat 3.6 cm wavelength with a diameter 0.9 pc. In the western nucleus we estimatethat the ionized component of the ISM gives rise to foreground free-freeabsorption with opacity at 18 cm of <0.6 along the majority of lines of sight.Other sources may be affected by absorption with opacity in the range 1 to 2.These values are consistent with previous models as fitted to the radiorecombination lines and the continuum spectrum.Comment: 44 pages, 9 figures, 2 tables. Accepted for publication in Ap

The Radio Spectra of the Compact Sources in Arp 220: A Mixed Population of Supernovae and Supernova Remnants