MAMMOTH-MOSFIRE: Environmental Effects on Galaxy Interstellar Medium at $z\sim 2$

The MAMMOTH-MOSFIRE program is a deep Keck/MOSFIRE K-band spectroscopic follow-up of emission-line galaxies identified in the MAMMOTH-Grism HST/WFC3 G141 slitless spectroscopic survey, targeting the core regions of three most massive galaxy protoclusters at cosmic noon. To introduce this program, we present a comprehensive analysis of the $[\mathrm{N}\mathrm{I}\mathrm{I}]\lambda$6584, $[\mathrm{S}\mathrm{I}\mathrm{I}]\lambda \lambda$6717,6731, and $[\mathrm{O}\mathrm{I}]\lambda$6300 BPT diagnostics for a unique sample of 43 protocluster member galaxies at $z\sim 2$, investigating how the overdense environment influences their interstellar medium ionization conditions. We find that, similar to their field counterparts at $z\sim 2$, protocluster galaxies exhibit a systematic offset in the $[\mathrm{N}\mathrm{I}\mathrm{I}]$ BPT diagram relative to the local star-forming sequence, but no such offset in the $[\mathrm{S}\mathrm{I}\mathrm{I}]$ BPT diagram. Notably, we detect significantly elevated $[\mathrm{O}\mathrm{I}]$/$\mathrm{H}\alpha$ ratios, which can be well reproduced by photoionization models incorporating both $\mathrm{H}\mathrm{I}\mathrm{I}$ regions and low-velocity shocks ($v$ $\sim$ 200 km s${}^{-1}$). We caution that neglecting shock excitation can bias abundance measurements, leading to an overestimation of nitrogen enrichment. This provides a potential explanation for the long-standing puzzle of enhanced $[\mathrm{N}\mathrm{I}\mathrm{I}]$/$\mathrm{H}\alpha$ ratios observed in $z\sim 2$ galaxies. We further suggest that these shocks are likely environmentally driven, e.g., by ram-pressure stripping or tidal interactions, which requires future confirmation through direct observations of features such as stripped gas tails.