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 tackles the systematic bias introduced by fibre collisions in SDSS-IV eBOSS clustering measurements. It develops and validates a pairwise-inverse-probability (PIP) weighting scheme, augmented by angular up-weighting, to recover unbiased two-point statistics down to very small scales. Tests with EZmocks show that PIP alone fixes large-scale clustering but misses the very small-scale 1-halo regime, while the combined PIP+ANG approach yields unbiased results for $w_p(r_p)$ and the redshift-space multipoles $ξ^{(ℓ)}$ across all tracers, enabling access to the 1-halo term at $~0.1\,h^{-1}{\rm Mpc}$ and strengthening constraints on halo occupation and growth-rate measurements. The methods are applied to the final DR16 catalogues, demonstrating robustness and comparability with standard CP corrections on large scales, while providing superior accuracy on small scales. Overall, the work provides a reliable framework for exploiting small-scale clustering in large spectroscopic surveys to improve cosmological and galaxy-halo modeling.

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 $ξ^l$ 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 $ξ^l$, 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.

Figures (5)

• Figure 1: Sky coverage of the eBOSS DR16 QSO catalogue. Blue dots are targets included in the LSS catalogue used for the cosmological analyses. Red dots represent targets not included in the LSS catalogues due to a number of issues such as redshift failure, fibre collisions, veto masks, low survey completeness. Black thick (thin) ellipses show the positions of eBOSS (SEQUELS) plates tiled for subsequent observation. Solid ellipses show tiles that were observed, and dashed ellipses those that were not observed. eBOSS LRGs have the same large-scale window function as the quasars and hence are not shown.
• Figure 2: Same as in Fig. \ref{['fig:tiling_qso']} but here for the sample of ELGs.
• Figure 3: The distribution of the fraction of targets that get a fibre among 1860 fibre assignment runs on the LRG DR16 catalogue. The vertical red dashed line shows the mean of the distribution while the vertical shaded band represents the standard deviation. The vertical blue line shows the fraction of targets that received a fibre for the actual eBOSS observation.
• Figure 4: As in Fig. \ref{['fig:tiling_stat_lrg']}, here for the catalogue of quasars.
• Figure 5: As in Fig. \ref{['fig:tiling_stat_lrg']}, here for the catalogue of emission-line galaxies.