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In preparation for the IGM tomography study by Subaru Prime FocusSpectrograph (PFS) survey and other large future telescopes such asTMT/ELT/GMT, we present the results of our pilot study on Ly$\alpha$ forest andIGM tomography statistics using the GADGET3-OSAKA cosmological smoothedparticle hydrodynamical simulation. Our simulation includes models for starformation and supernova feedback, which enables more realisticcross-correlation studies between galaxies, neutral hydrogen (HI) and metals incircumgalactic and intergalactic medium. We create a light-cone data set at$z=2-3$ from our simulations and generate mock Ly$\alpha$ forest data. As afirst step, in this paper, we focus on the distribution of HI and galaxies, andpresent statistical results on 1D flux PDF, 1D power spectrum, flux contrastvs. impact parameter, HI$-$galaxy cross-correlations. Our results show overallagreement with current observational data, with some interesting discrepancieson small scales that are due to either feedback effects or varyingobservational conditions. Our simulation shows stronger HI absorption withdecreasing transverse distance from galaxies. We find that the massive galaxieswith $M_\star \ge 10^{10}\,M_\odot$ contribute strongly to the flux contrastsignal, and that the lower-mass galaxies with $M_\star \sim10^8-10^{10}\,M_\odot$ tend to dilute the flux contrast signal from massivegalaxies. On large scales, the average flux contrast smoothly connects to theIGM level, supporting the concordance $\Lambda$ cold dark matter model. We alsofind an increase in the HI absorption toward the center of a protocluster.

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