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.
