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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 |$\rm {\mathit{ w}_p}\left(\mathit{ r}_p\right)$| and the redshift-space multipole ξ(ℓ = 0, 2, 4)(s) correlation functions down to |$0.1\, h^{-1}{\rm Mpc}$|⁠ , regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales |$s\gtrsim 20\, h^{-1}{\rm Mpc}$| for ξℓ, 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 |$\sim 0.1\, h^{-1}{\rm Mpc}$| 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. [ABSTRACT FROM AUTHOR]

We examine recent high-precision measurements of small-scale quasar clustering (at z ∼ 0.5–2 on scales of |${\sim }25~\mathrm{kpc}\, h^{-1}$|⁠) from the SDSS in the context of the MassiveBlack II (MBII) cosmological hydrodynamic simulation and conditional luminosity function (CLF) modelling. At these high luminosities (g < 20.85 quasars), the MBII simulation volume (⁠|$100~\mathrm{cMpc}\, h^{-1}$| comoving boxsize) has only three quasar pairs at distances of 1–4 Mpc. The black hole masses for the pairs range between |$M_{\rm bh}\sim 1{\, \rm and\, }3\times 10^{9}~\mathrm{M}_{\odot }\, h^{-1}$| and the quasar hosts are haloes of |$M_{\rm h}\sim 1\hbox{--}3\times 10^{14}~\mathrm{M}_{\odot }\, h^{-1}$|⁠. Such pairs show signs of recent major mergers in the MBII simulation. By modelling the central and satellite AGN CLFs as lognormal and Schechter distributions, respectively (as seen in MBII AGNs), we arrive at CLF models which fit the simulation predictions and observed luminosity function and the small-scale clustering measured for the SDSS sample. The small-scale clustering of our mock quasars is well-explained by central--satellite quasar pairs that reside in |$M_{\rm h}\gt 10^{14}~\mathrm{M}_{\odot }\, h^{-1}$| dark matter haloes. For these pairs, satellite quasar luminosity is similar to that of central quasars. Our CLF models imply a relatively steep increase in the maximum satellite luminosity, |$L^*_{\mathrm{sat}}$|⁠, in haloes of |$M_{\rm h}\gt 10^{14}~\mathrm{M}_{\odot }\, h^{-1}$| with associated larger values of |$L^*_{\mathrm{sat}}$| at higher redshift. This leads to increase in the satellite fraction that manifests itself in an enhanced clustering signal at ≲1 Mpc  h −1. For the ongoing eBOSS-CORE sample, we predict ∼200–500 quasar pairs at z ∼ 1.5 (with |$M_{\rm h} \gtrsim 10^{13}~\mathrm{M}_{\odot }\, h^{-1}$| and |$M_{\rm bh} \gtrsim 10^{8}~\mathrm{M}_{\odot }\, h^{-1}$|⁠) at ∼25 kpc scales. Such a sample would be ≳ 10 times larger than current pair samples. [ABSTRACT FROM AUTHOR]

We measure the two-point clustering of spectroscopically confirmed quasars from the final sample of the Baryon Oscillation Spectroscopic Survey (BOSS) on comoving scales of 4 ≤ s ≤ 22h-1Mpc. The sample covers 6950deg² [ ~ 19(h-1Gpc)³] and, over the redshift range 2.2 ≤ z ≤ 2.8, contains 55 826 homogeneously selected quasars, which is twice as many as in any similar work. We deduce bQ = 3.54 ± 0.10; the most precise measurement of quasar bias to date at these redshifts. This corresponds to a host halo mass of ~2 × 1012h-1M⊙ with an implied quasar duty cycle of ~1 per cent. The real-space projected correlation function is well fitted by a power law of index 2 and correlation length r0 = (8.12 ± 0.22)h-1 Mpc over scales of 4 ≲ rp ≲ 25h-1 Mpc. To better study the evolution of quasar clustering at moderate redshift, we extend the redshift range of our study to z ~ 3.4 and measure the bias and correlation length of three subsamples over 2.2 ≤ z ≤ 3.4. We find no significant evolution of r0 or bias over this range, implying that the host halo mass of quasars decreases somewhat with increasing redshift. We find quasar clustering remains similar over a decade in luminosity, contradicting a scenario in which quasar luminosity is monotonically related to halo mass at z ≈ 2.5. Our results are broadly consistent with previous BOSS measurements, but they yield more precise constraints based upon a larger and more uniform data set. [ABSTRACT FROM AUTHOR]