Probing Feedback via IGM tomography and Ly$\alpha$ forest with Subaru PFS, TMT/ELT, & JWST.

In preparation for the IGM tomography study by Subaru Prime Focus Spectrograph (PFS) survey and other large future telescopes such as TMT/ELT/GMT, we present the results of our pilot study on Lyman-$\alpha$ forest and IGM tomography statistics using the GADGET3-Osaka cosmological smoothed particle hydrodynamical simulation. Our simulation includes models for star formation and supernova feedback, which enables more realistic cross-correlation studies between galaxies, neutral hydrogen (HI) and metals in circumgalactic and intergalactic medium. We create light-cone data set at $z=2-3$ from our simulations and generate mock Ly$\alpha$ forest data. As a first step, in this paper, we focus on the distribution of HI and galaxies, and present statistical results on 1-D flux PDF, 1-D power spectrum, flux contrast vs. impact parameter, HI$-$galaxy cross-correlations. Our results show overall agreement with current observational data, with some interesting discrepancies on small scales which are due to either feedback effects or varying observational conditions. Our simulation shows stronger HI absorption with decreasing transverse distance from galaxies. Comparison with observations shows that the current observed data points include important contributions from lower mass galaxies of $M_\star \sim 10^8-10^{10}\,{\rm M}_\odot$ rather than just from massive galaxies of $M_\star \ge 10^{10}\,{\rm M}_\odot$, which dilutes the stronger signal of flux contrast around massive galaxies. On large scales, the average absorption decrement smoothly connects to the IGM level, supporting the concordance $\Lambda$ cold dark matter model. We also find an increase in the HI absorption towards the center of proto-cluster.