The mass-metallicity relation at cosmic noon in overdense environments:
  first results from the MAMMOTH-Grism HST slitless spectroscopic survey
  The MAMMOTH-Grism slitless spectroscopic survey is a Hubble Space Telescope
(HST) cycle-28 medium program, which is obtaining 45 orbits of WFC3/IR grism
spectroscopy in the density peak regions of three massive galaxy protoclusters
at $z=2-3$ discovered using the MAMMOTH technique. We introduce this survey by
presenting the first measurement of the mass-metallicity relation (MZR) at high
redshift in overdense environments via grism spectroscopy. From the completed
MAMMOTH-Grism observations in the field of the BOSS1244 protocluster at
$z=2.24\pm0.02$, We secure a sample of 36 protocluster member galaxies at
$z\sim2.24$, showing strong nebular emission lines ([O III], H$\beta$ and [O
II]) in their G141 spectra. Using the multi-wavelength broad-band deep imaging
from HST and ground-based telescopes, we measure their stellar masses in the
range of $[10^{9},10^{10.4}]M_\odot$, instantaneous star formation rates (SFR)
from 10 to 240$M_\odot yr^{-1}$, and global gas-phase metallicities
[$\frac{1}{3}$,1] of solar. Compared with similarly selected field galaxy
sample at the same redshift, our galaxies show on average increased SFRs by
$\sim$0.06dex and $\sim$0.18dex at $\sim$10$^{10.1}M_\odot$ and
$\sim$10$^{9.8}M_\odot$, respectively. Using the stacked spectra of our sample
galaxies, we derive the MZR in the BOSS1244 protocluster core as $12+\log({\rm
O/H})=(0.136\pm0.018)\times\log(M_\ast/M_\odot)+(7.082\pm0.175)$, showing
significantly shallower slope than that in the field. This shallow MZR slope is
likely caused by the combined effects of efficient recycling of feedback-driven
winds and cold-mode gas accretion in protocluster environments. The former
effect helps low-mass galaxies residing in overdensities retain their metal
production, whereas the latter effect dilutes the metal content of high-mass
galaxies, making them more metal poor than their coeval field counterparts.
