High resolution spectral imaging of CO(7–6), [CI](2–1), and continuum of three high-z lensed dusty star-forming galaxies using ALMA

High-redshift dusty star-forming galaxies with very high star formation rates (500 -- 3000 M$_{\odot}$ yr$^{-1}$) are key to understanding the formation of the most extreme galaxies in the early Universe. Characterising the gas reservoir of these systems can reveal the driving factor behind the high star formation. Using molecular gas tracers like high-J CO lines, neutral carbon lines and the dust continuum, we can estimate the gas density and radiation field intensity in their interstellar media. In this paper, we present high resolution ($\sim$0.4$^{\prime\prime}$) observations of CO(7-6), [CI](2-1) and dust continuum of 3 lensed galaxies from the SPT-SMG sample at $z\sim$ 3 with the Atacama Large Millimeter/submillimeter Array. Our sources have high intrinsic star-formation rates ($>$850 M$_{\odot}$yr$^{-1}$) and rather short depletion timescales ($
29 pages, 26 figures, Accepted for publication in A&A. Figure 16 and the related conclusions have been revised