The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey:
  N-body Mock Challenge for the eBOSS Emission Line Galaxy Sample
  Cosmological growth can be measured in the redshift space clustering of
galaxies targeted by spectroscopic surveys. Accurate prediction of clustering
of galaxies will require understanding galaxy physics which is a very hard and
highly non-linear problem. Approximate models of redshift space distortion
(RSD) take a perturbative approach to solve the evolution of dark matter and
galaxies in the universe.
  In this paper we focus on eBOSS emission line galaxies (ELGs) which live in
intermediate mass haloes. We create a series of mock catalogues using haloes
from the Multidark and {\sc Outer Rim} dark matter only N-body simulations. Our
mock catalogues include various effects inspired by baryonic physics such as
assembly bias and the characteristics of satellite galaxies kinematics,
dynamics and statistics deviating from dark matter particles.
  We analyse these mocks using the TNS RSD model in Fourier space and the CLPT
in configuration space. We conclude that these two RSD models provide an
unbiased measurement of redshift space distortion within the statistical error
of our mocks. We obtain the conservative theoretical systematic uncertainty of
$3.3\%$, $1.8\%$ and $1.5\%$ in $f\sigma_8$, $\alpha_{\parallel}$ and
$\alpha_{\bot}$ respectively for the TNS and CLPT models. We note that the
estimated theoretical systematic error is an order of magnitude smaller than
the statistical error of the eBOSS ELG sample and hence are negligible for the
purpose of the current eBOSS ELG analysis.
