(Proposal ID) S17B-129 (PI) Mukae, Shiro (Proposal Title) IGM Tomography of the Extremely Extended and Luminous Ly\alpha Nebulae (Abstract) We propose deep LRIS spectroscopy for background galaxies in remarkable giant Ly alpha nebulae of MAMMOTH-1 and Slug Nebula at z ~ 2.3, whose Ly alpha emission extends over 400 pkpc beyond the virial diameter. We will take spectra of the bright background galaxies at z_{photo} ~ 2.3-2.7 with MOS masks. The background galaxy spectra will provide IGM HI Ly alpha absorptions in the giant Ly alpha nebulae, and a tomographic reconstruction map of the IGM HI gas beyond the size of the giant Ly alpha nebulae. We combine the study of giant Ly alpha nebulae with IGM tomography, for the first time. Our goals are to test whether the Ly alpha emission mechanism scenarios of giant Ly alpha nebulae is i) the recombination radiation from HI gas that has been photoionized by the quasar or ii) the resonant scattering of Ly alpha produced in the quasar broad line region, and to investigate the HI extension of giant Ly alpha Nebula in the cosmic web, for understanding connection between giant Ly alpha nebulae and galaxy formation in large-scale structure. This is a pathfinder study for the planned Subaru/PFS survey being discussed by the PFS group, and an early completion of our spectroscopy is important for the PFS survey planning that is finished in about one year.