Combining conservation of energy throughout nearly-spherical collapse of galaxy clusters with the virial theorem, we derive the mass-temperature relation for X-ray clusters of galaxies T=CM2/3. The normalization factor C and the scatter of the relation are determined. We are also able to reproduce the recently observed break in the M-T relation at T \~ 3 keV, based on the scatter in the underlying density field for a low density \ΛCDM cosmology. Finally, by combining observational data of high redshift clusters with our theoretical formalism, we find a semi-empirical temperature-mass relation which is expected to hold at redshifts up to unity with less than 5% systematic error.
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Afshordi et al. (2002) studied this question.
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