Illustration of the constraining power of imaging data on a cored mass component (Eq. (35)). Shown are the parameter inference of the power-law profile mock quadruply lensed quasar of Fig. A.2 when including a marginalization of an additional cored power law profile (Eq. (38)). Orange lines indicate the input truth of the model without a cored component. λ_c is the scaled core model parameter (Eq. (35)) resembling the pure MST for large core radii (λ_c ≈ λ_int) (https://github.com/TDCOSMO/hierarchy_analysis_2020_public/blob/6c293af582c398a5c9de60a51cb0c44432a3c598/MST_impact/MST_pl_cored.ipynb).