THE POWER RATIO METHOD

Different statistics have been suggested to quantify substructures, the approach used here is based on the so-called power ratios ( _m). It amounts to a multipole expansion accounting for the angle dependence of cluster X-ray surface brightness, limited to the first few multipoles and at a fixed scale (~ Mpc). The main points are:

Fig.1: A random subset of the one-million  particle distribution in a cosmological simulation of a CDM universe with  m=1 and an Hubble constant of 50 Km/sec/Mpc. The size of the box is 400Mpc =  1.3 109 light-years. ( Click on the image for a large view) Fig. 2: X-ray emissivity maps of 4 simulated clusters at z = 0 in a CDM universe with  m= 1 and h = 0.5. ( Click on the image for a large view)

Three spatially flat cosmological models have been considered: CDM,  CDM with a cosmological constant accounting for 70% of the critical density, and CHDM with 1 massive neutrino with mass m = 4.65 eV, yielding a HDM density parameter  h = 0.20 .  For CDM and CHDM h =0.5,  and h=0.7 for  CDM; for all models the primeval spectral index n=1 and the baryon density parameter is selected to give  b h2 = 0.015. All models were normalized in order to reproduce the present observed cluster abundance. In order to achieve a safe statistical basis for each cosmological model the 40 most massive clusters have been selected from an N-body P3M simulation. ( see Fig.1 )  For each of them  a hydrodynamical TREESPH simulation is run staring from the initial redshift. Details about the simulations are widely discussed in [2].   Clusters are distributed in redshift so to reproduce the same redshfit distribution of the observed cluster sample. The observed data set includes nearby (z < 0.2) clusters observed with ROSAT PSPC instrument.The resulting sample is partially incomplete, but, clusters were not selected for reasons related to their morphology and the missing clusters are expected to have a distribution of power ratios similar to the observed one.  For simulated clusters, power ratios  (m) have been computed from the gas distribution ( see Fig.2 ).In this way one can perform a statistical comparison of the global morphology of clusters, expected in each cosmological model, with ROSAT data, using the Student t-test, the F-test and the Kolmogorov-Smirnov test.   Quite in general we conclude [1] that while CDM and CHDM are marginally consistent with data,  CDM is far below them. Such results seem to exclude that  CDM can be considered a reasonable approximation to data. The best score belongs to CDM , but also CHDM is not fully excluded. An inspection of the model clusters actually shows that the  CDM A possible interpretation of such output is that the actual amount of substructures is  governed by  0 rather than by the shape of power spectra.   According to the same tests, if cosmological models are compared with data on the basis of DM  (m) , values are shifted, indicating an increase in the amount of substructures for DM with respect to the gas.This is to be ascribed to the smoothing effects of the interactions among gas particles, which erase anisotropies and structures. Hence, using DM  (m)  leads to biased scores: CDM and CHDM models keep too many substructures and are no longer consistent with data; on the contrary, the increase of substructures pushes  CDM to agree with ROSAT sample outputs.