Probing the He II reionization ERa via Absorbing C IV Historical Yield (HIERACHY) III: The C IV absorber catalog and initial results on cosmic abundance evolution at $z\approx 3-5$

As part of the HIERACHY program, we collect the high-SN and high-spectral resolution optical spectra of 25 quasars at $z\approx4-5$ to constrain the C IV evolution at $z\approx 3-5$. In this paper, we report a catalog of 626 (1263) C IV absorption systems (components) at $z\approx3-5$ with a 50% completeness column density of log$(N_{\rm CIV}/\rm cm^{-2}) \approx 12.3$. The HIERACHY/MIKE C IV sample is one of the best C IV absorber samples optimized to study the IGM during the He II reionization epoch. Using 557 (1090) intervening absorption systems (components), we found the column density distribution function of C IV absorption systems with log$(N_{\rm CIV}/\rm cm^{-2})\gtrsim 12.3$ has a broken power-law shape, with the turn-over column density log$(N_{\rm crit}/\rm cm^{-2}) = 13.35^{+0.20}_{-0.19}$, which is close to or smaller than the detection limit of most literature samples. We also found that both comoving path length number density $dn/dX$ and cosmic abundance $\Omega$ for C IV absorption systems with log$(N_{\rm CIV}/\rm cm^{-2})> 13.2$ show an increase (at the 2.2$\sigma$ and 1.4$\sigma$ levels, respectively) from redshift $z\approx5$ to 3, while absorption systems with log$(N_{\rm CIV}/\rm cm^{-2})= 12.3-13.2$ exhibit a constant $dn/dX$ and $\Omega_{\rm CIV}$.