Correlations of λ_R, intr versus f_halo and f′_halo versus f_halo. Top row: Relationships between λ_R, intr and f_halo measured within R_e (first column), 3R_e (second column), and for all stars (third column). Fourth column: Relation between λ_R, intr(R_e) and f_halo(all). The solid red and blue lines, along with their corresponding dashed lines, represent the linear fits and 2σ confidence interval for the TNG50 and TNG100 datasets, respectively. Fit coefficients, σ values, and Pearson correlation coefficients (r_p) are provided in the top-right corner of each panel. Second row: Similar layout, but illustrating the relationship between f′_halo and f_halo. Here, the solid black and green lines, with accompanying dashed lines, indicate the linear fits and 2σ confidence interval for the TNG50 and TNG100 datasets, respectively.