An ALMA survey of submillimetre galaxies in the COSMOS field: The extent of the radio-emitting region revealed by 3 GHz imaging with the Very Large Array

We determine the radio size distribution of a large sample of 152 SMGs in COSMOS that were detected with ALMA at 1.3 mm. For this purpose, we used the observations taken by the VLA-COSMOS 3 GHz Large Project. One hundred and fifteen of the 152 target SMGs were found to have a 3 GHz counterpart. The median value of the major axis FWHM at 3 GHz is derived to be $4.6\pm0.4$ kpc. The radio sizes show no evolutionary trend with redshift, or difference between different galaxy morphologies. We also derived the spectral indices between 1.4 and 3 GHz, and 3 GHz brightness temperatures for the sources, and the median values were found to be $\alpha=-0.67$ and $T_{\rm B}=12.6\pm2$ K. Three of the target SMGs, which are also detected with the VLBA, show clearly higher brightness temperatures than the typical values. Although the observed radio emission appears to be predominantly powered by star formation and supernova activity, our results provide a strong indication of the presence of an AGN in the VLBA and X-ray-detected SMG AzTEC/C61. The median radio-emitting size we have derived is 1.5-3 times larger than the typical FIR dust-emitting sizes of SMGs, but similar to that of the SMGs' molecular gas component traced through mid-$J$ line emission of CO. The physical conditions of SMGs probably render the diffusion of cosmic-ray electrons inefficient, and hence an unlikely process to lead to the observed extended radio sizes. Instead, our results point towards a scenario where SMGs are driven by galaxy interactions and mergers. Besides triggering vigorous starbursts, galaxy collisions can also pull out the magnetised fluids from the interacting disks, and give rise to a taffy-like synchrotron-emitting bridge. This provides an explanation for the spatially extended radio emission of SMGs, and can also cause a deviation from the well-known IR-radio correlation.