The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey:
  N-body Mock Challenge for the Quasar Sample
  The growth rate and expansion history of the Universe can be measured from
large galaxy redshift surveys using the Alcock-Paczynski effect. We validate
the Redshift Space Distortion models used in the final analysis of the Sloan
Digital Sky Survey (SDSS) extended Baryon Oscillation Spectroscopic Survey
(eBOSS) Data Release 16 quasar clustering sample, in configuration and Fourier
space, using a series of HOD mock catalogues generated using the OuterRim
N-body simulation. We test three models on a series of non-blind mocks, in the
OuterRim cosmology, and blind mocks, which have been rescaled to new
cosmologies, and investigate the effects of redshift smearing and catastrophic
redshifts. We find that for the non-blind mocks, the models are able to recover
$f\sigma_8$ to within 3% and $\alpha_\parallel$ and $\alpha_\bot$ to within 1%.
The scatter in the measurements is larger for the blind mocks, due to the
assumption of an incorrect fiducial cosmology. From this mock challenge, we
find that all three models perform well, with similar systematic errors on
$f\sigma_8$, $\alpha_\parallel$ and $\alpha_\bot$ at the level of
$\sigma_{f\sigma_8}=0.013$, $\sigma_{\alpha_\parallel}=0.012$ and
$\sigma_{\alpha_\bot}=0.008$. The systematic error on the combined consensus is
$\sigma_{f\sigma_8}=0.011$, $\sigma_{\alpha_\parallel}=0.008$ and
$\sigma_{\alpha_\bot}=0.005$, which is used in the final DR16 analysis. For BAO
fits in configuration and Fourier space, we take conservative systematic errors
of $\sigma_{\alpha_\parallel}=0.010$ and $\sigma_{\alpha_\bot}=0.007$.
