Universality of dark matter haloes shape over six decades in mass:
  Insights from the Millennium XXL and SBARBINE simulations
  For the last 30 years many observational and theoretical evidences have shown
that galaxy clusters are not spherical objects, and that their shape is much
better described by a triaxial geometry. With the advent of multi-wavelength
data of increasing quality, triaxial investigations of galaxy clusters is
gathering a growing interest from the community, especially in the time of
"precision cosmology". In this work, we aim to provide the first statistically
significant predictions in the unexplored mass range above 3x10^14 Mo/h, using
haloes from two redshifts (z=0 and z=1) of the Millennium XXL simulation. The
size of this cosmological dark matter only simulation (4.1 Gpc) allows the
formation of a statistically significant number of massive cluster scale haloes
(about 500 with M>2x10^15 Mo/h and 780000 with M>10^14 Mo/h). Besides, we aim
to extend this investigation to lower masses in order to look for universal
predictions across nearly six orders of magnitude in mass, from 10^10 to almost
10^16 Mo/h. For this purpose we use the SBARBINE simulations, allowing to model
haloes of masses starting from 10^10 Mo/h. We use an elliptical overdensity
method to select haloes and compute the shapes of the unimodal ones
(approximately 50%), while we discard the unrelaxed. The minor to major and
intermediate to major axis ratio are found to be well described by simple
functional forms. For a given mass we can fully characterize the shape of a
halo and give predictions about the distribution of axis ratios for a given
cosmology and redshift. Moreover, these results are in some disagreement with
the findings of Jing & Suto (2002) which are widely used in the community even
though they have to be extrapolated far beyond their original mass range. This
"recipe" is made available to the community in this paper and in a dedicated
web page.
