Cosmological 3D HI Gas Map with HETDEX Ly$\alpha$ Emitters and eBOSS
  QSOs at $z=2$: IGM-Galaxy/QSO Connection and a $\sim$ 40-Mpc Scale Giant HII
  Bubble Candidate
  We present cosmological ($30-400$ Mpc) distributions of neutral hydrogen (HI)
in the inter-galactic medium (IGM) traced by Ly$\alpha$ Emitters (LAEs) and
QSOs at $z=2.1-2.5$, selected with the data of the on-going Hobby-Eberly
Telescope Dark Energy Experiment (HETDEX) and the eBOSS survey. We investigate
spatial correlations of LAEs and QSOs with HI tomography maps reconstructed
from HI Ly$\alpha$ forest absorption in the spectra of background galaxies and
QSOs obtained by the CLAMATO survey and this study, respectively. In the
cosmological volume far from QSOs, we find that LAEs reside in regions of
strong HI absorption, i.e. HI rich, which is consistent with results of
previous galaxy-background QSO pair studies. Moreover, there is an anisotropy
in the HI-distribution plot of transverse and line-of-sight distances; on
average the HI absorption peak is blueshifted by $\sim 200$ km s$^{-1}$ from
the LAE Ly$\alpha$ redshift, reproducing the known average velocity offset
between the Ly$\alpha$ emission redshift and the galaxy systemic redshift. We
have identified a $\sim$ 40-Mpc scale volume of HI underdensity that is a
candidate for a giant HII bubble, where six QSOs and an LAE overdensity exist
at $\left < z \right > =2.16$. The coincidence of the QSO and LAE overdensities
with the HI underdensity indicates that the ionizing photon radiation of the
QSOs has created a highly ionized volume of multiple proximity zones in a
matter overdensity. Our results suggest an evolutionary picture where HI gas in
an overdensity of galaxies becomes highly photoionized when QSOs emerge in the
galaxies.
