Radio Spectra and Sizes of Atacama Large Millimeter/submillimeter Array-identified Submillimeter Galaxies: Evidence of Age-related Spectral Curvature and Cosmic-Ray Diffusion?

We analyze the multifrequency radio spectral properties of 41 6 GHz-detected Atacama Large Millimeter/submillimeter Array (ALMA)-identified, submillimeter galaxies (SMGs), observed at 610 MHz, 1.4 GHz, and 6 GHz with the Giant Metrewave Radio Telescope and the Very Large Array. Combining high-resolution (∼0.″5) 6 GHz radio and ALMA 870 μm imaging (tracing rest frame ∼20 GHz, and ∼250 μm dust continuum), we study the far-infrared/radio correlation via the logarithmic flux ratio qIR, measuring for our sample. We show that the high-frequency radio sizes of SMGs are ∼1.9 ± 0.4× (∼2–3 kpc) larger than those of the cool dust emission, and find evidence for a subset of our sources being extended on ∼10 kpc scales at 1.4 GHz. By combining radio flux densities measured at three frequencies, we can move beyond simple linear fits to the radio spectra of high-redshift star-forming galaxies, and search for spectral curvature, which has been observed in local starburst galaxies. At least a quarter (10/41) of our sample shows evidence of a spectral break, with a median , but —a high-frequency flux deficit relative to simple extrapolations from the low-frequency data. We explore this result within this subset of sources in the context of age-related synchrotron losses, showing that a combination of weak magnetic fields (B ∼ 35 μG) and young ages (tSB ∼ 40–80 Myr) for the central starburst can reproduce the observed spectral break. Assuming these represent evolved (but ongoing) starbursts, and we are observing these systems roughly halfway through their current episode of star formation, this implies starburst durations of ≲100 Myr, in reasonable agreement with estimates derived via gas depletion timescales.