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 mea surement of the Sunyaev-Zeldovich (SZ) effect in clusters of galaxies are systematically lower than those derived by other methods (e.g., Ce pheid variable stars or the Tully-Fisher relation). We investigate the possibility that systematic errors may be introduced into the analysi s by the generally adopted assumptions that observed clusters are in h ydrostatic equilibrium, are spherically symmetric, and are isothermal. We construct self-consistent theoretical models of merging clusters o f 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 applyi ng each of the standard assumptions used in the interpretation of obse rvations. Our results indicate that the assumption of isothermality in the evolving clusters can result in H-0 being underestimated by 10%-3 0%, depending upon both epoch and projection angle. Moreover, use of t he projected, emission-weighted temperature profile under the assumpti on of spherical symmetry does not significantly improve the situation except in the case of more extreme mergers (i.e., those involving rela tively 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 ne arly on-axis, mergers) and viewed along its major axis, H-0 will be sy stematically underestimated. More extreme off-axis mergers may result in oblate merger remnants, which, when viewed nearly face-on, may resu lt in an overestimation of H-0. A similar effect is noted when viewing a prolate distribution along a line of sight that is nearly perpendic ular to its major axis. In both cases the potential overestimation occ urs only when the remnant is viewed within 15 degrees-30 degrees of fa ce-on. Bulk gas motions and the kinematic SZ effect do not appear to b e significant except for a brief period during the very early stages o f a merger. Our study shows that the most meaningful SZ measurement wi ll be accompanied by high-resolution temperature data and a detailed d ynamical modeling of the observed system. In lieu of this, a large sam ple selected to avoid dynamically evolving systems is preferred.