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Deep multi-frequency radio imaging in the Lockman Hole using the GMRT and VLA: II. The spectral index of submillimetre galaxies

We have employed the GMRT and the VLA to map the Lockman Hole. At 610 and 1,400 MHz, we reach noise levels of 15 and 6 uJy/beam, respectively, with well-matched resolutions (~5"). At this depth we obtained reliable detections for about half of the known submm galaxies (SMGs) in the field. For radio-identified SMGs, which are typically at z ~ 2, we measure a mean radio spectral index of alpha = -0.75 +/- 0.06 and standard deviation of 0.29, between rest-frame ~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 CMB do not seem to affect their radio SEDs. For those SMGs judged by Spitzer mid-IR colours and spectroscopy to host obscured AGN, we find a clear deviation from the rest of the sample - they typically have steeper radio spectral indices, alpha ~< -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.