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Evaluating the Calorimeter Model with Broadband, Continuous Spectra of Starburst Galaxies Observed with the Allen Telescope Array

Although the relationship between the far-infrared and cm-wave radio luminosities of normal galaxies is one of the most striking correlations in astronomy, a solid understanding of its physical basis is lacking. In one interpretation, the "calorimeter model," rapid synchrotron cooling of cosmic ray electrons is essential in reproducing the observed linear relationship. Observed radio spectra, however, are shallower than what is expected of cooled synchrotron emission. In Thompson et al. (2006), a simple parameterized model is presented to explain how relatively shallow observed spectra might arise even in the presence of rapid synchrotron cooling by accounting for ionization losses and other cooling mechanisms. During the commissioning of the 42-element Allen Telescope Array, we observed the starburst galaxies M82, NGC 253, and Arp 220 at frequencies ranging from 1 to 7 GHz, obtaining unprecedented broadband continuous radio spectra of these sources. We combine our observations with high-frequency data from the literature to separate the spectra into thermal and nonthermal components. The nonthermal components all steepen in the cm-wave regime and cannot be well-modeled as simple power laws. The model of Thompson et al. is consistent with our M82 results when plausible parameters are chosen, and our results in fact significantly shrink the space of allowed model parameters. The model is only marginally consistent with our NGC 253 data. Assuming the Thompson et al. model, a steep electron energy injection index of p = -2.5 is ruled out in M82 and NGC 253 to >99% confidence. We describe in detail the observing procedures, calibration methods, analysis, and consistency checks used for broadband spectral observations with the Allen Telescope Array.