ABSTRACT We use the Atacama Large sub/Millimetre Array (ALMA) to efficiently observe spectral lines across Bands 3, 4, 5, 6, 7, and 8 at high-resolution (0.5–0.1 arcsec) for 16 bright southern Herschel sources at $1.5 \lt z \lt 4.2$. With only six and a half hours of observations, we reveal 66 spectral lines in 17 galaxies. These observations detect emission from CO (3−2) to CO(18−17), as well as atomic ([C i](1−0), (2−1), [O i] 145 $\mu$m and [N ii] 205 $\mu$m) lines. Additional molecular lines are seen in emission (${\rm H_2O}$ and ${\rm H_2O^+}$) and absorption (OH$^+$ and CH$^+$). The morphologies based on dust continuum ranges from extended sources to strong lensed galaxies with magnifications between 2 and 30. CO line transitions indicate a diverse set of excitation conditions with a fraction of the sources ($\sim 35$ per cent) showcasing dense, warm gas. The resolved gas to star formation surface densities vary strongly per source, and suggest that the observed diversity of dusty star-forming galaxies could be a combination of lensed, compact dusty starbursts and extended, potentially merging galaxies. The predicted gas depletion time-scales are consistent with 100 Myr to 1 Gyr, but require efficient fuelling from the extended gas reservoirs onto the more central starbursts, in line with the Doppler-shifted absorption lines that indicate inflowing gas for two out of six sources. This pilot paper explores a successful new method of observing spectral lines in large samples of galaxies, supports future studies of larger samples, and finds that the efficiency of this new observational method will be further improved with the planned ALMA Wideband Sensitivity Upgrade.
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