Sub-arcsecond-resolution LOFAR observations of bright sub-millimetre galaxies in the North Ecliptic Pole field

Bright SMGs contribute significantly to the star formation rate (SFR) density (20-50\%) and stellar mass density ($\sim$ 30-50\%) at $z=$ 2-4 with SFRs$\ge 1000$ M$_\odot$,yr$^{-1}$ and stellar masses of $\sim 10^{11}$-$10^{12}$ M$_\odot$. The number of bright SMGs with such high SFRs is hard to reconcile with the standard models of galaxy formation and evolution. In this paper we provide evidence that, in a small sample of 12 bright SMGs, the SFRs derived from spectral energy distribution (SED) fitting are significantly higher than those obtained using low-frequency radio emission as a proxy for star formation. Using the International LOFAR Telescope (ILT), which allows imaging at 144 MHz with sub-arcsecond angular resolution, we have produced deep images of a small sample of bright SMGs in the North Ecliptic Pole (NEP) field extracted from the NEPSC2 survey. For all 12 SMGs, we find radio-emitting mid-infrared galaxies at distances from a few arcseconds down to sub-arcsecond scales from the SMG and/or the presence of a radio-emitting AGN. The SFRs derived from the radio emission of the SMG, disentangled from the AGN-related radio emission, are systematically lower by a factor of $\sim 5$ (median value) than those derived from the multi-band SED fitting. We discuss whether our assumptions might be, at least in part, responsible for the observed discrepancy. We argue that the radio-derived SFRs are not systematically underestimated but can be affected by a significant dispersion ($0.3-0.5$ dex). Considering these new SFR estimates, the offset of the specific SFR of the 12 bright SMGs from the star-forming galaxy main sequence ($\Delta\mathrm{(SSFR)}$) is significantly reduced, with all 12 bright SMGs which are only a factor of 2 more star-forming than the main sequence galaxies.