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

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.