  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.

Cosmology and Nongalactic Astrophysics;Instrumentation and Methods for Astrophysics