The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Effect of smoothing of density field on reconstruction and anisotropic BAO analysis

TL;DR

The paper investigates how the Gaussian smoothing scale in density-field reconstruction affects anisotropic BAO measurements and the fidelity of the reconstructed displacement (velocity) field. Using QPM sky mocks and RunPB simulations, it shows that a smoothing length around $R o 5~h^{-1}{ m Mpc}$ optimizes the precision and minimizes bias in the anisotropic BAO parameters, while larger scales degrade the quadrupole and shift the BAO features. It also analyzes covariance-noise effects and compares reconstruction implementations, finding consistent results for the dilation parameters but differing quadrupole amplitudes. The findings guide optimal reconstruction choices for current and future surveys, with implications for $D_A(z)$ and $H(z)$ constraints and velocity-field applications.

Abstract

The reconstruction algorithm introduced by \cite{Eis07}, which is widely used in clustering analysis, is based on the inference of the first order Lagrangian displacement field from the Gaussian smoothed galaxy density field in redshift space. The \modif2{smoothing scale} applied to the density field affects the inferred displacement field that is used to move {the galaxies}, and partially \modif2{erases} the nonlinear evolution {of the density field}. In this article, we explore this crucial step \modif2{in} the reconstruction algorithm. We study the performance of the reconstruction technique using two metrics: first, we study the performance using the anisotropic clustering, extending previous studies focused on isotropic clustering; second, we study its effect on the displacement field. We find that smoothing has a strong effect in the quadrupole of the correlation function and affects the accuracy and precision \modif2{with} which we can measure $D_A (z)$ and $H(z)$. We find that the optimal smoothing scale to use in the reconstruction algorithm applied to BOSS-CMASS is between 5-10 $h^{-1}$Mpc. Varying from the "usual" 15$h^{-1}$Mpc to $5 h^{-1}$Mpc \modif2{shows} $\sim$ 0.3\% variations in $D_A(z)$ and $\sim$ 0.4\% $H(z)$ and uncertainties are also reduced by 40\% and 30\% respectively. We also find that the accuracy of velocity field reconstruction depends strongly on the smoothing scale used for the density field. We measure the bias and uncertainties associated with different choices of smoothing length.

Figures (20)

• Figure 1: Performance of reconstruction tested in different kinds of sky-type mock catalogues. We show the mean of monopole [top panel], quadrupole [bottom panel] from 100 mocks pre-reconstruction and post-reconstruction. The different colours are different kinds of mock catalogues: darker shades are pre-reconstruction and lighter shades are post-reconstruction catalogues. In blue are the PTHALOS man13. In green are the Quick Particle Mesh QPM . In red are the PATCHY (Kitaura et al 2015; companion paper). For the monopole we get pretty similar results in the BAO fitting range. However, in all cases the post-reconstruction quadrupole is not exactly zero; there is an extra correlation (negative or positive). The purpose of this work is to disentangle the relation of this residual with the smoothing length and check the effect of the smoothing length on the BAO anisotropic post-reconstruction results.
• Figure 2: Mean of $200$ QPM mocks NGC reconstructed with different smoothing scale $5 h^{-1}$Mpc [green], $10 h^{-1}$Mpc [cyan], $15 h^{-1}$Mpc [magenta] and $40 h^{-1}$Mpc [blue]. The smoothing scale is correlated with the negative correlation observed in the quadrupole; a smaller smoothing scale decreases the correlation observed; a $5 h^{-1}$Mpc smoothing scale erases the quadrupole almost completely. Right panel: Zoom to the monopole [top panel] and quadrupole [bottom panel] in the BAO range.
• Figure 3: Dispersion plots of $\alpha_{15}$ vs $\alpha_{5,10,40}$. The legend includes the values of the correlation coefficient in the three cases. The large values of the correlation coefficient just shows that we are effectively using the same set of mocks for the test and that changing the smoothing scale of reconstruction affects the correlation between the results slightly, but remains large.
• Figure 4: Mean of best fits for $\alpha$ and $\epsilon$ for $200$ QPM mocks NGC analysed with different smoothing scales. The error bars are given by the standard deviation from $200$ realisations. For $\alpha$, the smaller dispersion is for 10-15 $h^{-1}$Mpc; however, the 15 $Mpc/h$ is significantly biased (5.3 $\sigma$). The best is 5 $h^{-1}$Mpc, which has less significant bias with small dispersion (0.8$\sigma$). For $\epsilon$, the less significant bias ($b_\epsilon/\sigma_\epsilon$ lower) is for the 5 $h^{-1}$Mpc smoothing scale given their small bias and dispersion.
• Figure 5: Mean of best fits for $\beta$ and $\chi^2/d.o.f.$ for $200$ QPM mocks analysed with different smoothing scales. The error bars are given by the standard deviation from $200$ realisations. The 5,10 $h^{-1}$ Mpc smoothing scale gives similar RMS and bias for linear redshift distortion parameter $\beta$ but slightly more bias for larger smoothing. Even though $\beta$ is a nuisance parameter in BAO analysis, it is interesting to observe the value fitted, as it indicates the level at which the redshift corrections are using the right value of the velocity field. The $\chi^2/d.o.f$ values are very similar between the different smoothing scales explored.