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

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)