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The origin of the recently reported systematic bias in the spectroscopictemperature of galaxy clusters is investigated using cosmologicalhydrodynamical simulations. We find that the local inhomogeneities of the gastemperature and density, after corrected for the global radial profiles, havenearly a universal distribution that resembles the log-normal function. Basedon this log-normal approximation for the fluctuations in the intra-clustermedium, we develop an analytical model that explains the bias in thespectroscopic temperature discovered recently. We conclude that the multi-phasenature of the intra-cluster medium not only from the radial profiles but alsofrom the local inhomogeneities plays an essential role in producing thesystematic bias.Comment: 17 pages,10 figures, accepted to ApJ, Minor change

Radial Profile and Lognormal Fluctuations of the Intracluster Medium as the Origin of Systematic Bias in Spectroscopic Temperature