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.
