The dust-continuum size of TNG50 galaxies at $z=1-5$: a comparison with the distribution of stellar light, stars, dust and H$_2$.

We present predictions for the extent of the dust-continuum emission of thousands of main-sequence galaxies drawn from the TNG50 simulation between $z=1-5$. To this aim, we couple the radiative transfer code SKIRT to the output of the TNG50 simulation and measure the dust-continuum half-light radius of the modeled galaxies, assuming a Milky Way dust type and a metallicity dependent dust-to-metal ratio. The dust-continuum half-light radius at observed-frame 850 $\mu$m is up to $\sim$75 per cent larger than the stellar half-mass radius, but significantly more compact than the observed-frame 1.6 $\mu$m (roughly corresponding to H-band) half-light radius, particularly towards high redshifts: the compactness compared to the 1.6 $\mu$m emission increases with redshift. This is driven by obscuration of stellar light from the galaxy centres, which increases the apparent extent of 1.6 $\mu$m disk sizes relative to that at 850 $\mu$m. The difference in relative extents increases with redshift because the observed-frame 1.6 $\mu$m emission stems from ever shorter wavelength stellar emission. These results suggest that the compact dust-continuum emission observed in $z>1$ galaxies is not (necessarily) evidence of the buildup of a dense central stellar component. We also find that the dust-continuum half-light radius very closely follows the radius containing half the star formation in galaxies, indicating that single band dust-continuum emission is a good tracer of the location of (obscured) star formation. The dust-continuum emission is more compact than the H2 mass (for galaxies at $z\geq 2$) and the underlying dust mass. The dust emission strongly correlates with locations with the highest dust temperatures, which do not need to be the locations where most H$_2$ and/or dust is located. The presented results are a common feature of main-sequence galaxies.