A theoretical study of the mass-temperature relation for clusters of galaxies

I derive the mass-temperature relation and its time evolution for clusters of galaxies in different cosmologies by means of two different models. The first one is a modification and improvement of a model by Del Popolo & Gambera, namely based upon a modification of the top-hat model in order to take account of angular momentum acquisition by protostructures and of an external pressure term in the virial theorem. The second one is based on the merging-halo formalism of Lacey & Cole, accounting for the fact that massive clusters accrete matter quasi-continuously, and is an improvement of a model proposed by Voit, again to take account of angular momentum acquisition by protostructures. The final result is that, in both models, the M-T relation shows a break at T similar to 3-4 keV. The behaviour of the M-T relation is as usual, M proportional to T-3/2, at the high-mass end, and M proportional to T-gamma, with a value of gamma > 3/2 depending on the chosen cosmology. Larger values of gamma are related to open cosmologies, while Lambda-cold dark matter (LambdaCDM) cosmologies give results of the slope intermediate between the flat case and the open case. The evolution of the M-T relation, for a given M-vir, is more modest both in flat and open universes in comparison with previous estimates found in the literature, even more modest than what found by Voit. Moreover, the time evolution is more rapid in models with L = 0 than in models in which the angular momentum acquisition by protostructures is taken into account (L not equal 0). The effect of a non-zero cosmological constant is that of slightly increasing the evolution of the M-T relation with respect to open models with L not equal 0. The evolution is more rapid for larger values (in absolute value) of the spectral index, n.