A New Method to Correct for Fiber Collisions in Galaxy Two-Point Statistics

TL;DR

This paper tackles fiber-collision biases in galaxy clustering by exploiting tile overlap regions to correct missed close pairs. It partitions targets into Population 1 (decollided) and Population 2 (potentially collided) and uses the resolved Population 2 galaxies to reconstruct full two-point statistics via a decomposition that accounts for angular completeness. Tests on 40 LasDamas CMASS-like mocks show the method accurately recovers the projected and redshift-space two-point correlation functions on scales across and below the fiber-collision scale, outperforming nearest-neighbor and angular corrections. The stated statistical error scales approximately as $1/\sqrt{V}$, and systematic errors are bounded around $\lesssim5\%$, making this method practical for current and upcoming fiber-fed surveys to measure full 3D galaxy clustering on all scales.

Abstract

In fiber-fed galaxy redshift surveys, the finite size of the fiber plugs prevents two fibers from being placed too close to one another, limiting the ability of studying galaxy clustering on all scales. We present a new method for correcting such fiber collision effects in galaxy clustering statistics based on spectroscopic observations. Our method makes use of observations in tile overlap regions to measure the contributions from the collided population, and to therefore recover the full clustering statistics. The method is rooted in solid theoretical ground and is tested extensively on mock galaxy catalogs. We demonstrate that our method can well recover the projected and the full three-dimensional redshift-space two-point correlation functions on scales both below and above the fiber collision scale, superior to the commonly used nearest neighbor and angular correction methods. We discuss potential systematic effects in our method. The statistical correction accuracy of our method is only limited by sample variance, which scales down with (the square root of) the volume probed. For a sample similar to the final SDSS-III BOSS galaxy sample, the statistical correction error is expected to be at the level of 1% on scales 0.1--30Mpc/h for the two-point correlation functions. The systematic error only occurs on small scales, caused by non-perfect correction of collision multiplets, and its magnitude is expected to be smaller than 5%. Our correction method, which can be generalized to other clustering statistics as well, enables more accurate measurements of full three-dimensional galaxy clustering on all scales with galaxy redshift surveys. (abridged)

Figures (8)

• Figure 1: The full pair counts $N_{DD}$ (solid lines) for $\xi(s)$ and $\xi(r_p,\pi)$ in the simplified case. For the latter, we only show the example of $\pi=2\,h^{-1}{\rm {Mpc}}$. The solid and dotted curves are the corrected pair counts averaged over the 40 mocks, obtained from the spectroscopic galaxies, while the squares show the actual pair counts. The shaded areas are the $1\sigma$ error distribution of the corrected $N_{DD}$. The corrected pair counts are further decomposed as the contribution from the different populations, $N_{D_1D_1}$, $N_{D_1D_2}$, and $N_{D_2D_2}$, shown as the dotted lines, labeled here simply as $11$, $12$, and $22$. The vertical dashed lines denote the physical fiber collision scale corresponding to the fiber collision angular constraint, determined by the highest redshifts in the mocks.
• Figure 2: An example of the galaxy distribution in one of our mocks. Large circles are the placed plug-plate tiles. The open symbols are decollided $D_1$ galaxies. The blue squares denote the $D_2'$ galaxies (i.e., resolved $D2$ galaxies, with fibers assigned), while the red squares are those $D_2$ galaxies without any fiber assigned. We also mark the different $N_{\rm tile}$ regions in the figure.
• Figure 3: Tests of different fiber-collision correction methods for the projected correlation function, $w_p(r_p)$, and the redshift-space correlation function, $\xi(s)$, for the simplified case. Top panels show the results for $r_p\times w_p(r_p)$ (left) and $s\times\xi(s)$ (right) while the ratios of the estimates to the full measurements, without any missing fiber-collided galaxies, are shown on the bottom. Solid lines correspond to the different correction methods, filled black squares are the true full measurements, and open magenta squares are the results without any fiber-collision correction applied. Error bars reflect the $1\sigma$ variation among the 40 LasDamas mock catalogs. (In top panels, for clarify, error bars are only shown for the true case and for our correction.) We plot as well the individual components of the 2PCF decomposition in the true case (black dotted lines; Eq. \ref{['eqn:xid']}) and for our correction (blue dashed lines; Eq. \ref{["eqn:xid'"]}). The vertical dotted lines denote the physical fiber collision scale corresponding to the fiber collision angular constraint, determined by the highest redshifts in the mocks.
• Figure 4: The same as Figure \ref{['fig:wp']} but now for the tiled mocks.
• Figure 5: The quadrupole $\xi_2(s)$ (left panel) and the hexadecapole $\xi_4(s)$ (right panel) from different correction methods. The lines and symbols are similar to Figure \ref{['fig:wptile']}.