At a fixed halo mass, galaxy clusters with higher magnitude gaps have larger brightest central galaxy (BCG) stellar masses. Recent studies have shown that by including the magnitude gap ($rm m_{gap}$) as a latent parameter in the stellar mass - halo mass (SMHM) relation, we can make more precise measurements on the amplitude, slope, and intrinsic scatter. Using galaxy clusters from the Sloan Digital Sky Survey, we measure the SMHM-$rm m_{gap}$ relation and its evolution out to $z=0.3$. Using a fixed comoving aperture of 100kpc to define the central galaxys stellar mass, we report statistically significant negative evolution in the slope of the SMHM relation to $z = 0.3$ ($> 3.5sigma$). The steepening of the slope over the last 3.5 Gyrs can be explained by late-time merger activity at the cores of galaxy clusters. We also find that the inferred slope depends on the aperture used to define the radial extent of the central galaxy. At small radii (20kpc), the slope of the SMHM relation is shallow, indicating that the core of the central galaxy is less related to the growth of the underlying host halo. By including all of the central galaxys light within 100kpc, the slope reaches an asymptote at a value consistent with recent high resolution hydrodynamical cosmology simulations.
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