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

The reconstruction algorithm introduced by \cite{Eis07}, which is widely used in clustering analysis, is based on the inference of the displacement field using the Zeldovich approximation from the Gaussian-smoothed density field in redshift space. The smoothing-scale applied to the density field affects the inferred displacement field that is used to move the particles, and partially erase their nonlinear evolution. In this article we explore this crucial step on the reconstruction algorithm. We study the performance of the reconstruction technique from two different aspects: the first one, the anisotropic clustering going beyond previous studies, which focus on isotropic clustering, the second is its effect on displacement field. We find that smoothing has a strong effect in the quadrupole of the correlation function and affects the accuracy and precision at which we can measure $D_A (z)$ and $H(z)$. We find that the best smoothing scale for BOSS-CMASS galaxies is between 5-10 $h^{-1}$Mpc. Varying from the "usual" 15$h^{-1}$Mpc to $5 h^{-1}$Mpc show $\sim$ 0.5\% variations in $D_A(z)$ and $H(z)$ and uncertainties are 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.