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We measure the clustering of quasars of the final data release (DR16) ofeBOSS. The sample contains $343\,708$ quasars between redshifts $0.8\leqz\leq2.2$ over $4699\,\mathrm{deg}^2$. We calculate the Legendre multipoles(0,2,4) of the anisotropic power spectrum and perform a BAO and a Full-Shape(FS) analysis at the effective redshift $z{\rm eff}=1.480$. The errors includesystematic errors that amount to 1/3 of the statistical error. The systematicerrors comprise a modelling part studied using a blind N-Body mock challengeand observational effects studied with approximate mocks to account for varioustypes of redshift smearing and fibre collisions. For the BAO analysis, wemeasure the transverse comoving distance $D_{\rm M}(z_{\rm eff})/r_{\rmdrag}=30.60\pm{0.90}$ and the Hubble distance $D_{\rm H}(z_{\rm eff})/r_{\rmdrag}=13.34\pm{0.60}$. This agrees with the configuration space analysis, andthe consensus yields: $D_{\rm M}(z_{\rm eff})/r_{\rm drag}=30.69\pm{0.80}$ and$D_{\rm H}(z_{\rm eff})/r_{\rm drag}=13.26\pm{0.55}$. In the FS analysis, wefit the power spectrum using a model based on Regularised Perturbation Theory,which includes Redshift Space Distortions and the Alcock-Paczynski effect. Theresults are $D_{\rm M}(z_{\rm eff})/r_{\rm drag}=30.68\pm{0.90}$ and $D_{\rmH}(z_{\rm eff})/r_{\rm drag}=13.52\pm{0.51}$ and we constrain the linear growthrate of structure $f(z_{\rm eff})\sigma_8(z_{\rm eff})=0.476\pm{0.047}$. Ourresults agree with the configuration space analysis. The consensus analysis ofthe eBOSS quasar sample yields: $D_{\rm M}(z_{\rm eff})/r_{\rmdrag}=30.21\pm{0.79}$, $D_{\rm H}(z_{\rm eff})/r_{\rm drag}=3.23\pm{0.47}$ and$f(z_{\rm eff})\sigma_8(z_{\rm eff})=0.462\pm{0.045}$ and is consistent with aflat $\Lambda {\rm CDM}$ cosmological model using Planck results.

monthly notices of the royal astronomical society

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey:  BAO and RSD measurements from the anisotropic power spectrum of the Quasar  sample between redshift 0.8 and 2.2