The Hubble constant estimated from the combined analysis of the Sunyaev-Zel'dovich effect and X-ray observations of galaxy clusters is systematically lower than estimates from other methods by 10%-15%. We examine the origin of the systematic underestimate using an analytic model of the intracluster medium (ICM), and compare the prediction with idealistic triaxial models and with clusters extracted from cosmological hydrodynamic simulations. We identify three important sources for the systematic errors; density and temperature inhomogeneities in the ICM, departures from isothermality, and asphericity. In particular, the combination of the first two leads to the systematic underestimate of the ICM spectroscopic temperature relative to its emission-weighted one. We find that these three systematics reproduce well both the observed bias and the intrinsic dispersions of the Hubble constant estimated from the Sunyaev-Zel'dovich effect.
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