Giant Arc Angular Size
Giant gravitational arcs — highly elongated images of background galaxies formed by strong lensing near the critical curves of massive galaxy clusters — provide a direct probe of the projected mass distribution in cluster cores. The observed angular sizes and length-to-width ratios of giant arcs in cluster samples have been found to be systematically larger and more elongated than predicted by ΛCDM cluster models calibrated on CDM N-body simulations with typical NFW concentration parameters. The abundance of very long arcs (length-to-width ratio > 10) in observed cluster samples exceeds simulation predictions by factors of three to ten in various analyses, a discrepancy that has been attributed to either higher central mass concentrations than CDM predicts, triaxial halo projections, substructure along the line of sight, or systematic errors in arc detection algorithms.
Successive Collision Theory resolves the giant arc excess through the gravitational superposition mechanism combined with the angular momentum-enhanced central concentration. In SCT, the effective central mass density of each cluster is boosted above the pure NFW profile by two contributions: the gravitational superposition from overlapping nested frames, which adds a smooth effective mass concentrated toward the cluster center where frame overlap is deepest, and the centrifugal barrier from the inherited angular momentum, which is weakest in the cluster core (where angular momentum support is minimal) and allows matter to pile up at smaller radii than CDM halos predict. Both effects increase the projected mass density within the Einstein radius, enlarging the critical curve and producing longer arcs at fixed cluster mass compared to standard CDM profiles.
The SCT prediction for the giant arc distribution is that the arc excess should be most pronounced for clusters in the richest large-scale environments — supercluster nodes and massive filament intersections — where the frame superposition is deepest and the effective central concentration is highest. Isolated clusters with shallow frame hierarchy depth should show arc length distributions closer to CDM predictions, while clusters embedded in the densest environments should show the strongest excess. This environmental dependence of the arc excess provides a clean test of the superposition mechanism: if the excess correlates with cluster environment rather than being uniformly distributed across all cluster masses, it strongly favors the SCT explanation over simple concentration-boost models that would apply uniformly to all clusters of a given mass.