Eulerian BAO Reconstructions and N-Point Statistics

TL;DR

This work introduces several Eulerian BAO reconstruction schemes (EGS, EF2, and ERR) and connects them to standard Lagrangian reconstructions, showing that field-level, nondisplacing Eulerian methods can recover comparable BAO information. By expressing the reconstructed power spectrum as a sum of the unreconstructed spectrum plus targeted 2-, 3-, and 4-point statistics, the authors reveal that most gains arise from 3-point cross-spectra (notably the 13 term) while 4-point contributions are subdominant. In DM real space tests, Eulerian reconstructions achieve about 95% of the BAO signal-to-noise of the traditional LGS method up to k_max ≈ 0.4 h/Mpc, with LGS still offering the largest total gain. The results establish a physically transparent, model-lean path to enhanced BAO analyses and lay groundwork for extensions to galaxies and redshift space, where practical benefits could be substantial.

Abstract

As galaxy surveys begin to measure the imprint of baryonic acoustic oscillations (BAO) on large-scale structure at the sub-percent level, reconstruction techniques that reduce the contamination from nonlinear clustering become increasingly important. Inverting the nonlinear continuity equation, we propose an Eulerian growth-shift reconstruction algorithm that does not require the displacement of any objects, which is needed for the standard Lagrangian BAO reconstruction algorithm. In real-space DM-only simulations the algorithm yields 95% of the BAO signal-to-noise obtained from standard reconstruction. The reconstructed power spectrum is obtained by adding specific simple 3- and 4-point statistics to the pre-reconstruction power spectrum, making it very transparent how additional BAO information from higher-point statistics is included in the power spectrum through the reconstruction process. Analytical models of the reconstructed density for the two algorithms agree at second order. Based on similar modeling efforts, we introduce four additional reconstruction algorithms and discuss their performance.

Figures (12)

• Figure 1: Total DM power spectra before reconstruction (black squares), after standard Lagrangian growth-shift LGS reconstruction by particle displacements (circles), and after Eulerian growth-shift EGS reconstruction based on combining 2-, 3- and 4-point information (stars), for $1\%$ subsamples of simulations with BAO wiggles. Filled symbols show density auto-spectra, while open symbols show cross-spectra between the densities before and after reconstruction. Results are averaged over 3 realizations and error bars correspond to the standard error of the mean (they are smaller than the symbols except at very low $k$ where their size is similar to that of the symbols).
• Figure 2: Illustration of the BAO signal: Fractional difference of the power spectra in Fig. \ref{['fig:GSBroadbandSpectra']} between wiggle- and no-wiggle simulations. Again, error bars are smaller than the symbols.
• Figure 3: Signal-to-noise-squared for the BAO wiggles as a function of wavenumber $k$. The signal is given by the difference of the spectra specified in the legend between wiggle and nowiggle simulations, $S=P_\mathrm{wiggle}-P_\mathrm{nowiggle}$. The squared noise is approximated by Eq. (\ref{['eq:GaussianNoise']}). Error bars are not shown for clarity.
• Figure 4: Cumulative BAO signal-to-noise-squared as a function of $k_\mathrm{max}$ for EGS and LGS reconstruction.
• Figure 5: Illustration of 3- and 4-point contributions to reconstructed power spectra. The full reconstructed power spectra (circles and stars) can be obtained by adding the 3-point part (thin solid) and 4-point part (dash-dotted) to the pre-reconstruction power spectrum (black squares); see Section \ref{['se:3ptOr4pt']} for details. The curves show differences of the spectra specified in the legend between wiggle and nowiggle simulations, divided by the theoretical linear no-wiggle density power spectrum. At all $k$ error bars estimated from the scatter between the 3 realizations are roughly the same size as the thickness of the colored curves and smaller than the size of the circle, star and square symbols; they are not shown for clarity.