HETDEX [OII] galaxies at $z \le 0.48$: Volume-limited samples and their power spectra
The catalog from the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Public Data Release 1 (PDR1) contains half a million emission-line-selected [OII] galaxies spread across $540~\mathrm{deg}^2$ at $z \le 0.48$ from HETDEX's unprecedented untargeted spectroscopic survey. In this paper, we construct volume-limited samples from PDR1 in three luminosity bins across the two main fields: "Spring'' and "Fall''. The numbers of galaxies in the bins range from 11,354 to 64,794 and number densities, $\bar{n}\simeq (2-5)\times10^{-3}~h^3~\mathrm{Mpc}^{-3}$, are higher than those of typical cosmological spectroscopic surveys of emission-line galaxies by a factor of five to ten. The monopole and quadrupole power spectra derived from these samples are in excellent agreement with the mock power spectra from the Uchuu simulation based on a flat $\Lambda$CDM model and the cosmological parameters from the Planck cosmic microwave background data, at all wavenumbers used for the measurement ($0.01<k<0.7~h~\mathrm{Mpc}^{-1}$). We find that the power spectrum amplitudes are consistent with a characteristic dark matter halo mass of $\log(M_0~[h^{-1}M_{\odot}])\simeq 11.9$-$12.3$, with the halo mass showing a weak dependence on [OII] luminosity, $M_0\propto L^a$, increasing with a slope of $a = 0.37\pm0.10$. The best-fit mock suggests that approximately 13 percent of the [OII] galaxies in our sample reside in subhalos. The new, high-density tracers of the underlying matter distribution presented in this paper provide precise measurements of clustering in a low-redshift regime sensitive to the late-time growth of structures. These samples will form the basis for forthcoming analyses of the redshift-space distortion effect, galaxy-halo connection, and cross-correlations with external low-redshift probes.