The Compressed 3D Lyman-Alpha Forest Bispectrum

TL;DR

This work develops a comprehensive EFT-based framework for the 3D Ly-$ ext{a}$ forest bispectrum in redshift space, introducing a 2nd-order Ly-$ ext{a}$ flux bias expansion under $SO(2)$ symmetry and constructing 26 skew-spectrum operators to efficiently capture higher-order information. It extends the skew-spectrum methodology to the Ly-$ ext{a}$ forest, including shifted skew spectra to probe non-squeezed bispectrum shapes and a forward-modeling approach to the survey window suitable for DESI. The authors validate the theory with 2SPT field realizations and AbacusSummit mocks, showing 1–2$\sigma$ level agreement up to $k o 0.17~h ext{ Mpc}^{-1}$ (and similar behavior with LOS smoothing for observational data up to $k o 0.34~h ext{ Mpc}^{-1}$ in certain configurations). They also provide practical guidance for incorporating observational windows via pair-count estimators and outline how the shifted skew spectra can be extended to more general survey geometries and primordial-non-Gaussianity templates. Overall, this work lays the groundwork for leveraging higher-order Ly-$ ext{a}$ statistics in DESI-era analyses to break degeneracies and extract cosmological information from the high-redshift Ly-$ ext{a}$ forest.

Abstract

Cosmological studies of the Lyman-Alpha (Lya) forest typically constrain parameters using two-point statistics. However, higher-order statistics, such as the three-point function (or its Fourier counterpart, the bispectrum) offer additional information and help break the degeneracy between the mean flux and power spectrum amplitude, albeit at a significant computational cost. To address this, we extend an existing highly informative compression of the bispectrum, the skew spectra, to the Lya forest. We derive the tree-level bispectrum of Lya forest fluctuations in the framework of effective field theory (EFT) directly in redshift space and validate our methodology on synthetic Lya forest data. We measure the anisotropic cross-spectra between the transmitted flux fraction and all quadratic operators arising in the bispectrum, yielding a set of 26 skew spectra. Using idealized 3D Gaussian smoothing (R=10 Mpc/h), we find good agreement (1-2 sigma level based on the statistical errors of the mocks) with the theoretical tree-level bispectrum prediction for monopole and quadrupole up to k <= 0.17 h/Mpc. To enable the cosmological analysis of Lya forest data from the currently observing Dark Energy Spectroscopic Instrument (DESI), where we cannot do 3D smoothing, we use a line-of-sight smoothing and introduce a new statistic, the shifted skew spectra. These probe non-squeezed bispectrum triangles and avoid locally applying quadratic operators to the field by displacing one copy of the field in the radial direction. Using a fixed displacement of 40 Mpc/h (and line-of-sight smoothing of 10 Mpc/h) yields a similar agreement with the theory prediction. For the special case of correlating the squared (and displaced) field with the original one, we analytically forward model the window function making this approach readily applicable to DESI data.

Figures (9)

• Figure 1: Squared isotropic smoothing kernel $W(k; R)=\exp{-\left(\frac{1}{2} k^2R^2\right)}$ for wavenumber $k$ and smoothing radii $R=20\,h^{-1}\, {\rm Mpc}\xspace$ shown as a dashed, $R=10\,h^{-1}\, {\rm Mpc}\xspace$ as a solid and $R=5\,h^{-1}\, {\rm Mpc}\xspace$ as a dotted black line. The vertical gray lines indicate the scales where power is suppressed by a factor of 20.
• Figure 2: Consistency test of the skew spectrum monopole methodology and pipeline, comparing the 26 theory Ly-$\alpha$ forest skew spectra (black solid line) to averages over 12 realizations of the synthetic three-dimensional Ly-$\alpha$ fields using perturbation theory up to second order (2SPT; blue triangles) and average over 12 realizations of the AbacusSummit Ly-$\alpha$ forest mock (red dots) for model III. The skew spectra are presented in units of volume, specifically $P_{\mathcal{S}^{\ell}_{i}}(k)$ in $[h^3 \, \mathrm{Mpc}^{-3}]$ for index $i$. For the theory and 2SPT fields we use the bias parameters given in Table \ref{['tab:abacus_models']} which are obtained by fitting the one-loop EFT Ly-$\alpha$ power spectrum to the AbacusSummit simulations. We apply a Gaussian smoothing kernel to fields entering the quadratic operators with $R=10\,h^{-1}\, {\rm Mpc}\xspace$, corresponding to truncation of skew spectra (or bispectrum information) above $k \hbox{$\; \buildrel > \over \sim \;$} 0.17 \,h\, {\rm Mpc}^{-1}\xspace$. The error bars are the root mean square between the realizations. Following baseline expectation, we find excellent agreement between the theory predictions and the 2SPT fields and agreement at the $\sim 2\sigma$ level with the AbacusSummit data points given the different sensitivity to bias parameters.
• Figure 3: Same as Fig. \ref{['fig:comparison_2SPT_abacus_model3_ell0']} for the quadrupole: comparison of 26 theory Ly-$\alpha$ forest skew spectra (black solid line) to averages over 12 realizations of the synthetic three-dimensional Ly-$\alpha$ fields using perturbation theory up to second order (2SPT; gray triangles) and average over 12 realizations of the AbacusSummit Ly-$\alpha$ forest mock (green squares) for model III. The error bars are the root mean square between the realizations.
• Figure 4: Same as Fig. \ref{['fig:comparison_2SPT_abacus_model3_ell0']} for the monopole of the shifted skew spectra $\mathcal{S}_{n,\, \alpha}$, given in Eq. \ref{['eqn:shifted_kernel']}, using $\alpha=20 \,h^{-1}\, {\rm Mpc}\xspace$ and only applying line-of-sight smoothing with $R_\parallel=10 \,h^{-1}\, {\rm Mpc}\xspace$.
• Figure 5: Same as Fig. \ref{['fig:comparison_2SPT_abacus_model3_ell0_shifted']} for the quadrupole of the shifted skew spectra using $\alpha=20 \,h^{-1}\, {\rm Mpc}\xspace$ and only applying line-of-sight smoothing with $R_\parallel=10 \,h^{-1}\, {\rm Mpc}\xspace$.