Size difference between Halpha and cold dust in z~2 dusty star forming galaxies

Star-formation rates (SFRs) are among the most fundamental measurements to galaxy formation models, yet there is still a lack of agreement between measurements made using different methods, expecially when it comes to accounting for dust-obscured SFRs from nebular emission lines at z~1-3, the epoch when over 80% of the cosmic SFR density is obscured by dust. Part of the problem is hinged on a lack of knowledge with regard to the spatial distributions of dust relative to star-forming regions traced by optical emission lines, which requires both near-infrared IFU and sub-arcsecond far-infrared continuum observations that are only available recently. In this talk I will present results from our ongoing program to study dusty star-forming galaxies at z~2 that are detected in Halpha by the IFU from KMOS/SINFONI, as well as in far-infrared continuum by ALMA with a matched spatial resolution. I will present the relative spatial distributions of these two tracers of SFRs and their sizes. I will discuss the impact of our findings on galaxy formation models in general, as well as on the planning of future IFU observations by JWST and ELT.