OFFSETS BETWEEN THE X-RAY AND THE SUNYAEV-ZEL'DOVICH-EFFECT PEAKS IN MERGING GALAXY CLUSTERS AND THEIR COSMOLOGICAL IMPLICATIONS

Observations reveal that the peaks of the X-ray map and the Sunyaev-Zel'dovich (SZ) effect map of some galaxy clusters are offset from each other. In this paper, we perform a set of hydrodynamical simulations of mergers of two galaxy clusters to investigate the spatial offset between the maxima of the X-ray and the SZ surface brightness of the merging clusters. We find that significantly large SZ-X-ray offsets (>100 kpc) can be produced during the major mergers of galaxy clusters (with mass > 1 x 10(14) M-circle dot). The significantly large offsets are mainly caused by a "jump effect" that occurrs between the primary and secondary pericentric passages of the two merging clusters, during which the X-ray peak may jump to the densest gas region located near the center of the small cluster, but the SZ peak remains near the center of the large one. Our simulations show that merging systems with higher masses and larger initial relative velocities may result in larger offset sizes and longer offset time durations; and only nearly head-on mergers are likely to produce significantly large offsets. We further investigate the statistical distribution of the SZ-X-ray offset sizes and find that (1) the number distribution of the offset sizes is bimodal with one peak located at low offsets similar to 0 and the other at large offsets similar to 350-450 h(-1) kpc, but the objects with intermediate offsets are scarce; and (2) the probabilities of the clusters in the mass range higher than 2 x 10(14) h(-1)M(circle dot) that have offsets larger than 20, 50, 200, 300, and 500 h-1 kpc are 34.0%, 11.1%, 8.0%, 6.5%, and 2.0%, respectively, at z = 0.7. The probability is sensitive to the underlying pairwise velocity distribution and the merger rate of clusters. We suggest that the SZ-X-ray offsets provide a probe to the cosmic velocity fields on the cluster scale and the cluster merger rate, and future observations on the SZ-X-ray offsets for a large number of clusters may put strong constraints on them. Our simulation results suggest that the SZ-X-ray offset in the Bullet Cluster, together with the mass ratio of the two merging clusters, requires a relative velocity larger than 3000 km s(-1) at an initial separation 5 Mpc. The cosmic velocity distribution at the high-velocity end is expected to be crucial in determining whether there exists an incompatibility between the existence of the Bullet Cluster and the prediction of a ACDM model.