MAMMOTH-MOSFIRE: Environmental Effects on Galaxy Interstellar Medium at $z\sim2$

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 $\rm [N\,II]\lambda$6584, $\rm [S\,II]\lambda\lambda$6717,6731, and $\rm [O\,I]\lambda$6300 BPT diagnostics for a unique sample of 43 protocluster member galaxies at $z\sim2$, investigating how the overdense environment influences their interstellar medium ionization conditions. We find that, similar to their field counterparts at $z\sim2$, protocluster galaxies exhibit a systematic offset in the $\rm [N\,II]$ BPT diagram relative to the local star-forming sequence, but no such offset in the $\rm [S\,II]$ BPT diagram. Notably, we detect significantly elevated $\rm [O\,I]$/$\rm H \alpha$ ratios, which can be well reproduced by photoionization models incorporating both $\rm H II$ 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 $\rm [N\,II]$/$\rm H \alpha$ ratios observed in $z\sim2$ 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.