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.