On the shape of dark matter halos from MultiDark Planck simulations
  The halo shape plays a central role in determining important observational
properties of the haloes such as mass, concentration and lensing
cross-sections. The triaxiality of lensing galaxy clusters has a substantial
impact on the distribution of the largest Einstein radii, while weak lensing
techniques are sensitive to the intrinsic halo ellipticity. In this work, we
provide scaling relations for the shapes of dark matter haloes as a function of
mass (peak height) and redshift over more than four orders of magnitude in halo
masses, namely from $10^{11.5}$ to $10^{15.8}~h^{-1}~$M$_\odot$. We have
analysed four dark matter only simulations from the MultiDark cosmological
simulation suite with more than 56 billion particles within boxes of 4.0, 2.5,
1.0 and 0.4 $h^{-1}$Gpc size assuming \textit{Planck} cosmology. The dark
matter haloes have been identified in the simulations using the {\sc rockstar}
halo finder, which also determines the axis ratios in terms of the
diagonalization of the inertia tensor. In order to infer the shape for a
hypothetical halo of a given mass at a given redshift, we provide fitting
functions to the minor-to-major and intermediate-to-major axis ratios as a
function of the peak height.
