Extended H$\alpha$ over compact far-infrared continuum in dusty submillimeter galaxies -- Insights into dust distributions and star-formation rates at $z\sim2$

Using data from ALMA and near-infrared (NIR) integral field spectrographs including both SINFONI and KMOS on the VLT, we investigate the two-dimensional distributions of H$\alpha$ and rest-frame far-infrared (FIR) continuum in six submillimeter galaxies at $z\sim2$. At a similar spatial resolution ($\sim$0.5" FWHM; $\sim$4.5 kpc at $z=2$), we find that the half-light radius of H$\alpha$ is significantly larger than that of the FIR continuum in half of the sample, and on average H$\alpha$ is a median factor of $2.0\pm0.4$ larger. Having explored various ways to correct for the attenuation, we find that the attenuation-corrected H$\alpha$-based SFRs are systematically lower than the IR-based SFRs by at least a median factor of $3\pm1$, which cannot be explained by the difference in half-light radius alone. In addition, we find that in 40% of cases the total $V$-band attenuation ($A_V$) derived from energy balance modeling of the full ultraviolet(UV)-to-FIR spectral energy distributions (SEDs) is significantly higher than that derived from SED modeling using only the UV-to-NIR part of the SEDs, and the discrepancy appears to increase with increasing total infrared luminosity. Finally, considering all our findings along with the studies in the literature, we postulate that the dust distributions in SMGs, and possibly also in less IR luminous $z\sim2$ massive star-forming galaxies, can be decomposed into three main components; the diffuse dust heated by older stellar populations, the more obscured and extended young star-forming HII regions, and the heavily obscured central regions that have a low filling factor but dominate the infrared luminosity in which the majority of attenuation cannot be probed via UV-to-NIR emissions.