Systematic errors in the Hubble constant based upon measurement of the Sunyaev-Zeldovich effect

Values of the Hubble constant reported to date that are based upon measurement of the Sunyaev-Zeldovich (SZ) effect in clusters of galaxies are systematically lower than those derived by other methods (e.g., Cepheid variable stars or the Tully-Fisher relation). We investigate the possibility that systematic errors may be introduced into the analysis by the generally adopted assumptions that observed clusters are in hydrostatic equilibrium, are spherically symmetric, and are isothermal. We construct self-consistent theoretical models of merging clusters of galaxies, using hydrodynamic/N-body simulations. We then compute the magnitude of H-0 derived from the SZ effect at different times and at different projection angles, both from first principles and by applying each of the standard assumptions used in the interpretation of observations. Our results indicate that the assumption of isothermality in the evolving clusters can result in H-0 being underestimated by 10%-30%, depending upon both epoch and projection angle. Moreover, use of the projected, emission-weighted temperature profile under the assumption of spherical symmetry does not significantly improve the situation except in the case of more extreme mergers (i.e., those involving relatively gas-rich subclusters). Although less significant, we find that asphericity in the gas density can also result in a 15% error in H-0. If the cluster is prolate (as is generally the case for on-axis, or nearly on-axis, mergers) and viewed along its major axis, H-0 will be systematically underestimated. More extreme off-axis mergers may result in oblate merger remnants, which, when viewed nearly face-on, may result in an overestimation of H-0. A similar effect is noted when viewing a prolate distribution along a line of sight that is nearly perpendicular to its major axis. In both cases the potential overestimation occurs only when the remnant is viewed within 15 degrees-30 degrees of face-on. Bulk gas motions and the kinematic SZ effect do not appear to be significant except for a brief period during the very early stages of a merger. Our study shows that the most meaningful SZ measurement will be accompanied by high-resolution temperature data and a detailed dynamical modeling of the observed system. In lieu of this, a large sample selected to avoid dynamically evolving systems is preferred.