Strong Lensing Arcs

Strong gravitational lensing by galaxy clusters produces spectacular arc-like images of background galaxies near the cluster critical curves. The statistics of strong lensing arcs — their number counts, length distributions, redshift distributions, and morphologies — encode the cluster mass distribution, concentration, substructure, and the source galaxy population. Large surveys of cluster arc statistics have found persistent tensions with ΛCDM predictions: the observed number of long arcs is higher than CDM simulations with standard NFW concentration parameters predict (the arc statistics problem); arcs are found around clusters at higher redshifts than expected from the growth of structure; and the cross-section for giant arc formation in observed clusters exceeds simulation predictions by factors of several at the highest mass thresholds. These excesses compound the smaller-scale concentration excess and suggest that cluster inner mass profiles are systematically more concentrated or more substructured than CDM models produce.

Successive Collision Theory resolves the strong lensing arc statistics problem through the gravitational superposition mechanism and the angular momentum-enhanced concentration. In SCT, the effective projected mass density within each cluster's Einstein radius is boosted above the standard NFW prediction by the superposition contribution from overlapping nested frames, which adds a smooth but significant mass component concentrated within the cluster's virial radius. This superposition mass effectively increases the Einstein radius and critical curve area, enlarging the strong lensing cross-section beyond what the cluster's observed baryonic and halo mass alone would produce. The factor-of-several excess in arc abundance at high mass thresholds corresponds directly to the ratio of the total effective lensing mass (including superposition) to the discrete lensing mass measured in standard analyses, and this ratio increases with the depth of the cluster's frame hierarchy embedding.

The high-redshift excess in strong lensing arc occurrence follows from the pre-existing mass concentrations from the colliding pockets. In ΛCDM, very massive clusters at z > 0.5 are exponentially rare because hierarchical assembly from a random initial power spectrum does not produce enough extreme mass concentrations in the available time. In SCT, the pre-existing massive structures from the colliding pockets — proto-clusters and proto-groups that were already partially assembled before the collision — seed the most massive lensing-efficient structures at high redshift, making them more abundant than the post-collision hierarchical assembly timeline predicts. These pre-existing mass concentrations, thermalized and incorporated into the post-collision debris, form the cores of the most extreme strong lensing clusters, explaining both the arc excess at high cluster masses and at high redshifts within a single consistent framework.