We have employed the Giant Metre-wave Radio Telescope ( GMRT ) and the Very Large Array ( VLA ) to map the Lockman Hole .
At 610 and 1,400 MHz , we reach noise levels of 15 and 6 \mu Jy beam ^ { -1 } , respectively , with well-matched resolutions ( \sim 5 arcsec ) .
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 \sim 2 , we measure a mean radio spectral index of \alpha ^ { 1 , 400 } _ { 610 } = -0.75 \pm 0.06 ( where S _ { \nu } \propto \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 ( IC ) scattering off the cosmic microwave background ( CMB ) do not seem to affect their radio spectral energy distributions ( SEDs ) .
For those SMGs judged by Spitzer mid-infrared ( -IR ) 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 ^ { 1 , 400 } _ { 610 } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern% -6.0 pt \lower 1.72 pt \hbox { { $ \scriptstyle \sim$ } } } -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 .