Star formation traced by optical and millimeter hydrogen recombination
  lines and free-free emissions in the dusty merging galaxy NGC 3256 --
  MUSE/VLT and ALMA synergy
  A galaxy-galaxy merger and the subsequent triggering of starburst activity
are fundamental processes linked to the morphological transformation of
galaxies and the evolution of star formation across the history of the
Universe. Both nuclear and disk-wide starbursts are assumed to occur during the
merger process. However, quantifying both nuclear and disk-wide star formation
activity is non-trivial because the nuclear starburst is dusty in the most
active merging starburst galaxies. This paper presents a new approach to this
problem: combining hydrogen recombination lines in optical, millimeter, and
free-free emission. Using NGC~3256 as a case study, H$\beta$, H40$\alpha$, and
free-free emissions are investigated using the Multi Unit Spectroscopic
Explorer at the Very Large Telescope of the European Southern Observatory
(MUSE/VLT) and the Atacama Large Millimeter/submillimeter Array (ALMA). The
H$\beta$ image obtained by MUSE identifies star-forming regions outside the
nuclear regions, suggesting a disk-wide starburst. In contrast, the H40$\alpha$
image obtained by ALMA identifies a nuclear starburst where optical lines are
undetected due to dust extinction ($A_{\rm V}\sim25$). Combining both MUSE and
ALMA observations, we conclude that the total SFR is
$49\pm2~M_{\odot}$~yr$^{-1}$ and the contributions from nuclear and disk-wide
starbursts are $\sim34~\%$ and $\sim66~\%$, respectively. This suggests the
dominance of disk-wide star formation in NGC~3256. In addition, pixel-by-pixel
analyses for disk-wide star-forming regions suggest that shock gas tracers
(e.g., CH$_3$OH) are enhanced where gas depletion time ($\tau_{\rm
gas}$=$M_{\rm gas}/SFR$) is long. This possibly means that merger-induced
shocks regulate disk-wide star formation activities.
