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We use N-body simulations of galaxy cluster mergers to evaluate new and published statistical tests of substructure. These tests include 22 one-dimensional (normality) tests, four two-dimensional (spatial) tests, and five three-dimensional (velocity-spatial) tests. These tests are statistical in that they provide a significance level for the presence of substructure. All the tests are applied to the same data files so that their relative sensitivity can be compared. The data files contain positions and velocities of dark matter particles drawn randomly from the simulations. Three noncosmological simulations are run in which the subclusters begin as King spheres: a single isothermal cluster, a merger of a 1/6 mass subcluster, and a merger of a 1/3 mass subcluster. In this way, we examine the dependence of the tests on the subcluster's relative mass. We examine also the dependence on the total sample size, the epoch of merger (pre- and post-core-crossing), and the projection angle of the merger axis. The results allow a quantitative comparison of the effectiveness of each estimator under different observational scenarios. In general, the higher the dimensionality of the test, the more sensitive it is to substructure. The sensitivity of individual diagnostics depends on the line of sight relative to the merger axis. The three-dimensional tests are least sensitive to lines of sight perpendicular to the merger axis and are most sensitive to lines of sight 45%deg^-60ᵈeg^ from perpendicular. The two-dimensional tests are most sensitive to lines of sight perpendicular to the merger axis. The one-dimensional tests are the most sensitive to lines of sight parallel to the merger axis. No single substructure test is the most sensitive in all situations. Therefore, we recommend that a battery of tests be applied to each cluster. We provide a score for each test reflecting its relative sensitivity. We find that clusters with no merging components but a velocity dispersion gradient have an increased likelihood for a "false-positive" response from some three-dimensional tests. We examine also the signatures of merger and the detectability of mergers in redshift surveys. We find that cluster masses are overestimated by up to a factor of 2 for clusters undergoing mergers. We plot the dependence of mass estimators on projection angle and epoch of merger. We find that the detectability of postmerger states is hampered by small search radii (e. g. , <2. 0h₇5_^-1^ Mpc) in redshift surveys.
Pinkney et al. (Wed,) studied this question.