Title: The galaxy-galaxy strong lensing cross section and the internal distribution of matter in ΛCDM substructure

Abstract: Strong gravitational lensing offers a powerful probe of the detailed distribution of matter in lenses, while magnifying and bringing faint background sources into view. Observed strong lensing by massive galaxy clusters, which are often in complex dynamical states, has also been used to map their dark matter substructures on smaller scales. Deep high resolution imaging has revealed the presence of strong lensing events associated with these substructures, namely galaxy-scale sub-halos. However, an inventory of these observed galaxy-galaxy strong lensing (GGSL) events is noted to be discrepant with state-of-the-art {\Lambda}CDM simulations. Cluster sub-halos appear to be over-concentrated compared to their simulated counterparts yielding an order of magnitude higher value of GGSL. In this paper, we explore the possibility of resolving this observed discrepancy by redistributing the mass within observed cluster sub-halos in ways that are consistent within the {\Lambda}CDM paradigm of structure formation. Lensing mass reconstructions from data provide constraints on the mass enclosed within apertures and are agnostic to the detailed mass profile within them. Therefore, as the detailed density profile within cluster sub-halos currently remains unconstrained by data, we are afforded the freedom to redistribute the enclosed mass. We investigate if rearranging the mass to a more centrally concentrated density profile helps alleviate the GGSL discrepancy. We report that refitting cluster sub-halos to the ubiquitous {\Lambda}CDM-motivated Navarro-Frenk-White profile, and further modifying them to include significant baryonic components, does not resolve this tension. A resolution to this persisting GGSL discrepancy may require more careful exploration of alternative dark matter models.