source. We consider sources with a half-light radius of 0.1–1.0 arcsec and peak surface brightness of 0.05 – 4.0 mJy beam$^{-1}$. Finally, we bin the mock visibilities in the $uv$-plane using exactly the same procedure as applied to real data in Section \[subsec:uv-plane\].

Figure \[fig:mock\_radius\_1comp\] shows the inferred radius as a function of the surface brightness maximum alongside the 1$\sigma$ uncertainty from the $uv$-plane fitting. The measured \[\] and 160-$\mu$m continuum sizes in ALESS 49.1 and 57.1 are all smaller than sizes inferred for input sources with $R_{1/2}\geq0.2$ arcsec in the relevant peak surface brightness range. In other words, given the observed peak surface brightness, $R_{1/2}^\mathrm{[CII]}>$0.2 arcsec source sizes would be recovered within 10% uncertainty for both ALESS 49.1 and 57.1. For comparison, the CO(3–2) half-light radii in ALESS 49.1 and 57.1 are $R_{1/2}^\mathrm{CO}$=0.33$\pm$0.06 and 0.39$\pm$0.06 arcsec, respectively.

Therefore, we consider it unlikely that the \[\]/160-$\mu$m continuum follow a single-Gaussian surface brightness distribution with the same size as CO(3–2) emission (0.33$\pm$0.05 and 0.39$\pm$0.06 arcsec for ALESS 49.1 and 57.1, respectively). However, we can not exclude a combination of a bright compact and faint extended \[\] and continuum components. In the following analysis, we will focus on the center of the 