Probing the He II re-Ionization ERa via Absorbing C IV Historical Yield (HIERACHY) II: Project Design, Current Status, and Examples of Initial Data Products

The He II reionization epoch is expected to take place at $z\sim3-5$. In this stage, the helium and metals in the inter-galactic medium (IGM) are further ionized with additional contributions from harder non-stellar sources, and some large-scale gravitationally bound systems approach virialization. The "Probing the He II re-Ionization ERa via Absorbing C IV Historical Yield (HIERACHY)" program utilizes high- and medium-resolution spectra of bright background quasars at $z\approx3.9-5.2$ to investigate Ly$\alpha$, C IV, and other metal absorption lines during this epoch. Additionally, we employ narrow-band imaging to search for Ly$\alpha$ emitters associated with C IV absorbers, alongside multi-wavelength observations to identify and study particularly intriguing cases. In this paper, we present the design of the HIERACHY program, its current status, major scientific goals, and examples of initial data products from completed Magellan/MIKE, MagE spectroscopy, and MDM imaging observations. We also provide a brief outlook on future multi-wavelength observations that may significantly impact the related science.