The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Pairwise-Inverse-Probability and Angular Correction for Fibre Collisions in Clustering Measurements

TL;DR

This paper introduces new correction techniques for fibre collision effects in galaxy clustering measurements, enabling more accurate small-scale analyses in large spectroscopic surveys like SDSS-IV eBOSS.

Contribution

It presents the pairwise-inverse-probability and angular up-weighting methods to correct for fibre collisions, improving the accuracy of clustering measurements down to 0.1 Mpc/h.

Findings

Unbiased measurements of $w_p$ and $\xi^l$ down to 0.1 Mpc/h.

Corrected small-scale clustering enables better cosmological constraints.

Approximate methods suffice for large-scale measurements, but new methods access small scales.

Abstract

The completed eBOSS catalogues contain redshifts of 344080 QSOs over 0.8<z<2.2 covering 4808 deg$^2$, 174816 LRGs over 0.6<z<1.0 covering 4242 deg$^2$ and 173736 ELGs over 0.6<z<1.1 covering 1170 deg$^2$ in order to constrain the expansion history of the Universe and the growth rate of structure through clustering measurements. Mechanical limitations of the fibre-fed spectrograph on the Sloan telescope prevent two fibres being placed closer than 62", the fibre-collision scale, in a single pass of the instrument on the sky. These `fibre collisions' strongly correlate with the intrinsic clustering of targets and can bias measurements of the two-point correlation function resulting in a systematic error on the inferred values of the cosmological parameters. We combine the new techniques of pairwise-inverse-probability weighting and the angular up-weighting to correct the clustering measurements for the effect of fibre collisions. Using mock catalogues we show that our corrections provide unbiased measurements, within data precision, of both the projected correlation function $w_p$ and the multipoles $\xi^l$ of the redshift-space correlation functions down to 0.1Mpc/h, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales greater than s~20Mpc/h for $\xi^l$, as used to make BAO and large-scale RSD measurements, approximate methods such as Nearest-Neighbour up-weighting are sufficiently accurate given the statistical errors of the data. Using the PIP method, for the first time for a spectroscopic program of the Sloan Digital Sky Survey we are able to successfully access the 1-halo term in the 3D clustering measurements down to ~0.1Mpc/h scales. Our results will therefore allow studies that use the small-scale clustering measurements to strengthen the constraints on both cosmological parameters and the halo-occupation distribution models.