Mass function, velocity dispersion and temperature function of clusters in the Cold + Hot dark matter model

Astronomy and Astrophysics – Astronomy

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Scientific paper

Using a set of P(3) M simulation which accurately treats the density evolution of two components of dark matter, we study the evolution of clusters in the Cold + Hot dark matter (CHDM) model. The mass function, the velocity dispersion function and the temperature function of clusters are calculated for four different epochs of z<= 0.5. We also use the simulation data to test the Press-Schechter expression of the halo abundance as a function of the velocity dispersion sigma_v . The model predictions are in good agreement with the observational data of local cluster abundances (z=0). We also tentatively compare the model with the Gunn and his collaborators' observation of rich clusters at z~ 0.8 and with the x-ray luminous clusters at z~ 0.5 of the Einstein Extended Medium Sensitivity Survey. The important feature of the model is the rapid formation of clusters in the near past: the abundances of clusters of sigma_v >= 700kms(-1) and of sigma_v >= 1200kms(-1) at z=0.5 are only 1/4 and 1/10 respectively of the present values (z=0). Ongoing ROSAT and AXAF surveys of distant clusters will provide sensitive tests to the model. The abundance of clusters at z~ 0.5 would also be a good discriminator between the CHDM model and a low-density flat CDM model both of which show very similar clustering properties at z=0.

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