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#### The completed SDSS-IV extended baryon oscillation spectroscopic survey: pairwise-inverse probability and angular correction for fibre collisions in clustering measurements

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##### Citation

Mohammad, F. G., Percival, W. J., Seo, H.-J., Chapman, M. J., Bianchi, D., Ross, A. J., et al. (2020).
The completed SDSS-IV extended baryon oscillation spectroscopic survey: pairwise-inverse probability and angular correction
for fibre collisions in clustering measurements.* Monthly Notices of the Royal Astronomical Society,*
*498*(1), 128-143. doi:10.1093/mnras/staa2344.

Cite as: http://hdl.handle.net/21.11116/0000-0007-F747-3

##### Abstract

The completed extended Baryon Oscillation Spectroscopic Survey (eBOSS) catalogues contain redshifts of 344 080 quasars at 0.8 < z < 2.2, 174 816 luminous red galaxies between 0.6 < z < 1.0, and 173 736 emission-line galaxies over 0.6 < z < 1.1 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 arcsec in a single pass of the instrument. 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 and the angular upweighting (PIP+ANG) 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 w

_{p}(r_{p}) and the redshift-space multipole ξ^{(ℓ = 0, 2, 4)}(s) correlation functions down to 0.1h^{−1}Mpc, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales s≳20h^{−1}Mpc for ξ^{ℓ}, as used to make baryon acoustic oscillation and large-scale redshift-space distortion measurements, approximate methods such as nearest-neighbour upweighting 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 one-halo term in the clustering measurements down to ∼0.1h^{−1}Mpc scales. Our results will therefore allow studies that use the small-scale clustering to strengthen the constraints on both cosmological parameters and the halo occupation distribution models.