MAMMOTH: Confirmation of Two Massive Galaxy Overdensities at $z=2.24$ with H$\alpha$ Emitters

Massive galaxy overdensities at the peak epoch of cosmic star formation provide ideal testbeds for the formation theories of galaxies and large-scale structure. We report the confirmation of two massive galaxy overdensities at $z=2.24$, BOSS1244 and BOSS1542, selected from the MAMMOTH project using Ly$\alpha$ absorption from the intergalactic medium over the scales of 15$-$30 $h^{-1}$ Mpc imprinted on the quasar spectra. We use H$\alpha$ emitters (HAEs) as the density tracer and identify them using deep narrowband $H_2S1$ and broadband $K_{\rm s}$ imaging data obtained with CFHT/WIRCam. In total, 244 and 223 line emitters are detected in these two fields, and $196\pm 2$ and $175\pm 2$ are expected to be HAEs with an H$\alpha$ flux of $> 2.5\times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$ (corresponding to an SFR of $>$5 M$_\odot$ yr$^{-1}$). The detection rate of HAE candidates suggests an overdensity factor of $\delta_{\rm gal}=5.6\pm0.3$ and $4.9\pm0.3$ over the volume of $54\times32\times32$ cMpc$^3$. The overdensity factor increases $2-3$ times when focusing on the high-density regions of scales $10-15$ cMpc. Interestingly, the HAE density maps reveal that BOSS1244 contains a dominant structure, while BOSS1542 manifests as a giant filamentary structure. We measure the H$\alpha$ luminosity functions (HLF), finding that BOSS1244's HLF is nearly identical to that of the general field at the same epoch, while BOSS1542 shows an excess of HAEs with high H$\alpha$ luminosity, indicating the presence of enhanced star formation or AGN activity. We conclude that the two massive MAMMOTH overdensities are undergoing a rapid galaxy mass assembly.