How well does the \[\] emission trace the molecular gas reservoir in SMGs?

Compared to the high-redshift, high-resolution \[\]-only studies (e.g.,@Gullberg2018 [@Zanella2018]), resolved emission line maps of two different species (C$^+$ and $^{12}$CO) allow us to study the relation between \[\] emission and the colder molecular gas.

This paper is structured as follows: in Section \[sec:observations\], we give the details of ALMA observations. Section \[sec:Results\] details the processing of the data in both the image- and $uv$-plane, the assessment of the systematic errors and kinematic modelling. Section \[sec:discussion\] presents the spatial and kinematic comparison of the interpretation of the \[\]/CO(3–2)/FIR observations, results of PDR modelling and a discussion of the physical processes driving the \[\]/FIR deficit. Finally, Section \[sec:conclusions\] summarizes the conclusions of this paper.

Throughout this paper we use a flat $\Lambda$CDM cosmology from @Planck2015. We adopt the CO(3–2) spectroscopic redshifts from @CR18: $z$=2.943$\pm$0.001 and $z$=2.943$\pm$0.002 for ALESS 49.1 and 57.1. Consequently, 1 arcsec corresponds to 7.9 kpc for both ALESS 49.1 and ALESS 57.1; the luminosity distance to both sources is 25445 Mpc [@Wright2006].

Observations and data reduction {#sec:observations}
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Sample selection
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The two galaxies analyzed in this paper were identified by @Hodge2013 as a part of 