The 3D Lyman-<i>α</i> forest power spectrum from eBOSS DR16

ABSTRACT We measure the three-dimensional power spectrum (P3D) of the transmitted flux in the Lyman-$\alpha$ (Ly $\alpha$) forest using the complete extended Baryon Oscillation Spectroscopic Survey data release 16 (eBOSS DR16). This sample consists of $\sim$205 000 quasar spectra in the redshift range $2\le z \le 4$ at an effective redshift $z=2.334$. We propose a pair-count spectral estimator in configuration space, weighting each pair by $\exp (i\mathbf {k}\cdot \mathbf {r})$, for wave vector $\mathbf {k}$ and pixel pair separation $\mathbf {r}$, effectively measuring the anisotropic power spectrum without the need for fast Fourier transforms. This accounts for the window matrix in a tractable way, avoiding artefacts found in Fourier-transform based power spectrum estimators due to the sparse sampling transverse to the line of sight of Ly $\alpha$ skewers. We extensively test our pipeline on two sets of mocks: (i) idealized Gaussian random fields with a sparse sampling of Ly $\alpha$ skewers, and (ii) log-normal LyaCoLoRe mocks including realistic noise levels, the eBOSS survey geometry and contaminants. On eBOSS DR16 data, the Kaiser formula with a non-linear correction term obtained from hydrodynamic simulations yields a good fit to the power spectrum data in the range $(0.02 \le k \le 0.35)\, h\, {\rm Mpc}^{-1}\,$ at the 1–2σ level with a covariance matrix derived from LyaCoLoRe mocks. We demonstrate a promising new approach for full-shape cosmological analyses of Ly $\alpha$ forest data from cosmological surveys such as eBOSS, the currently observing Dark Energy Spectroscopic Instrument and future surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.