Deep multi-frequency radio imaging in the Lockman Hole - II. The spectral index of submillimetre galaxies

We have employed the Giant Metre-wave Radio Telescope and the Very Large Array to map the Lockman Hole. At 610 and 1400 MHz, we reach noise levels of 15 and 6 mu Jy beam-1, respectively, with well-matched resolutions (similar to 5 arcsec). At this depth, we obtained reliable detections for about half of the known sub-mm galaxies (SMGs) in the field. For radio-identified SMGs, which are typically at z similar to 2, we measure a mean radio spectral index of alpha 1400(610) = -0.75 +/- 0.06 (where S(nu) proportional to nu alpha) and standard deviation of 0.29, between approximate rest-frame frequencies of 1.8 and 4.2 GHz. The slope of their continuum emission is indistinguishable from that of local star-forming galaxies and suggests that extended optically thin synchrotron emission dominates the radio output of SMGs. Cooling effects by synchrotron emission and Inverse Compton scattering off the cosmic microwave background do not seem to affect their radio spectral energy distributions. For those SMGs judged by Spitzer mid-infrared colours and spectroscopy to host obscured active galactic nuclei (AGN), we find a clear deviation from the rest of the sample - they typically have steeper radio spectral indices, alpha 1400(610) less than or similar to -1.0. These findings suggest these mid-IR-/AGN-selected SMGs may have an intrinsically different injection mechanism for relativistic particles, or they might reside in denser environments. This work provides a reliable spectral template for the estimation of far-IR/radio photometric redshifts, and will enable accurate statistical K-corrections for the large samples of SMGs expected with SCUBA-2 and Herschel.