Jeongin Moon, Eiichiro Komatsu, Robin Ciardullo, Olivia Curtis, Dustin Davis, Daniel J. Farrow, Karl Gebhardt, Caryl Gronwall, Laura Herold, Gary J. Hill, Donghui Jeong, Chenxu Liu, Maja Lujan Niemeyer, Erin Mentuch Cooper, Shiro Mukae, Shun Saito, Ariel G. Sánchez, Donald P. Schneider

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 $Λ$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.