Mass‐Temperature Relation of Galaxy Clusters: A Theoretical Study

Combining conservation of energy throughout nearly-spherical collapse ofgalaxy clusters with the virial theorem, we derive the mass-temperaturerelation for X-ray clusters of galaxies $T=CM^{2/3}$. The normalization factor$C$ and the scatter of the relation are determined from first principles withthe additional assumption of initial Gaussian random field. We are also able toreproduce the recently observed break in the M-T relation at $T \sim 3 \keV$,based on the scatter in the underlying density field for a low density$\Lambda$CDM cosmology. Finally, by combining observational data of highredshift clusters with our theoretical formalism, we find a semi-empiricaltemperature-mass relation which is expected to hold at redshifts up to unitywith less than 20% error.Comment: 43 pages, 13 figures, One figure is added and minor changes are made. Accepted for Publication in Ap