Misalignment angle between the major axis of the BCG (estimated using the inner 50% of the star particles) and of its host DM halo (estimated from the total mass within R₂₀₀), shown as a function of half stellar mass of the BCG. Symbol size and color are proportional to the ratio between the central galaxy and host halo sizes for the CDM runs. A dashed gray band encloses 50% of the data points. Black, blue, green, and purple lines show the running median for the CDM, SIDM1, vSIDM, and WDM3 cases, respectively. Horizontal lines on the right indicate the median value, over all half stellar mass values, for the corresponding DM model.