We study predictions for galaxy cluster observables that can test the statistics of dark matter halo shapes expected in a flat \Lambda CDM universe .
We present a simple analytical model for the prediction of cluster–scale X-ray observations , approximating clusters as isothermal systems in hydrostatic equilibrium , and dark matter haloes as ellipsoids with uniform axial ratios ( homeoidal ellipsoids ) .
We test the model against high–resolution , hydrodynamic cluster simulations to gauge its reliability .
We find that this simple prescription does a good job of predicting cluster X-ray ellipticities compared to the simulations as long as one focuses on cluster regions that are less sensitive to recent mergers .
Based on this simple model , the distribution of cluster–size halo shapes expected in the concordance \Lambda CDM cosmology implies an X-ray ellipticity distribution with a mean \langle \epsilon _ { X } \rangle = 0.32 \pm 0.01 , and a scatter \sigma _ { \epsilon } = 0.14 \pm 0.01 for the mass range ( 1 - 4 ) \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } .
We find it important to include the mass dependence of halo shape when making comparisons to observational samples that contain many , very massive clusters .
We analyse the systematics of four observational samples of cluster ellipticities and find that our results are statistically compatible with observations .
In particular , we find remarkably good agreement between two recent ROSAT samples and \Lambda CDM predictions that do not include gas cooling .
We also test how well our analytical model can predict Sunyaev–Zel ’ dovich decrement maps and find that it is less successful although still useful ; the model does not perform as well as a function of flux level in this case because of the changing triaxiality of dark matter haloes as a function of radial distance .
Both this effect and the changing alignment of isodensity shells of dark matter haloes leave an imprint on cluster gas that appears to be seen in observational data .
Thus , dark matter haloes can not be accurately characterized as homeoidal ellipsoids for all comparisons .