An ALMA survey of submillimetre galaxies in the Extended Chandra Deep Field South: radio properties and the far-infrared/radio correlation

We present a study of the radio properties of 870$\mu$m-selected submillimetre galaxies (SMGs), observed at high resolution with ALMA in the Extended Chandra Deep Field South. From our initial sample of 76 ALMA SMGs, we detect 52 SMGs at $>3\sigma$ significance in VLA 1400MHz imaging, of which 35 are also detected at $>3\sigma$ in new 610MHz GMRT imaging. Within this sample of radio-detected SMGs, we measure a median radio spectral index $\alpha_{610}^{1400} = -0.79 \pm 0.06$, (with inter-quartile range $\alpha=[-1.16,-0.56]$) and investigate the far-infrared/radio correlation via the parameter $q_{\rm IR}$, the logarithmic ratio of the rest-frame 8-1000$\mu$m flux and monochromatic radio flux. Our median $q_{\rm IR} = 2.56 \pm 0.05$ (inter-quartile range $q_{\rm IR}=[2.42,2.78]$) is higher than that typically seen in single-dish 870$\mu$m-selected sources ($q_{\rm IR} \sim 2.4$), which may reflect the fact that our ALMA-based study is not biased to radio-bright counterparts, as previous samples were. Finally, we search for evidence that $q_{\rm IR}$ and $\alpha$ evolve with age in a co-dependent manner, as predicted by starburst models: the data populate the predicted region of parameter space, with the stellar mass tending to increase along tracks of $q_{\rm IR}$ versus $\alpha$ in the direction expected, providing the first observational evidence in support of these models.