The Three-Dimensional Shapes of Galaxy Clusters
  While clusters of galaxies are considered one of the most important
cosmological probes, the standard spherical modelling of the dark matter and
the intracluster medium is only a rough approximation. Indeed, it is well
established both theoretically and observationally that galaxy clusters are
much better approximated as triaxial objects. However, investigating the
asphericity of galaxy clusters is still in its infancy. We review here this
topic which is currently gathering a growing interest from the cluster
community. We begin by introducing the triaxial geometry. Then we discuss the
topic of deprojection and demonstrate the need for combining different probes
of the cluster's potential. We discuss the different works that have been
addressing these issues. We present a general parametric framework intended to
simultaneously fit complementary data sets (X-ray, Sunyaev Zel'dovich and
lensing data). We discuss in details the case of Abell 1689 to show how
different models/data sets lead to different haloe parameters. We present the
results obtained from fitting a 3D NFW model to X-ray, SZ, and lensing data for
4 strong lensing clusters. We argue that a triaxial model generally allows to
lower the inferred value of the concentration parameter compared to a spherical
analysis. This may alleviate tensions regarding, e.g. the over-concentration
problem. However, we stress that predictions from numerical simulations rely on
a spherical analysis of triaxial halos. Given that triaxial analysis will have
a growing importance in the observational side, we advocate the need for
simulations to be analysed in the very same way, allowing reliable and
meaningful comparisons. Besides, methods intended to derive the three
dimensional shape of galaxy clusters should be extensively tested on simulated
multi-wavelength observations.
