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The rest-frame $K$-band luminosity function of galaxies in clusters to $z=1.3$

We derive the rest-frame $K$-band luminosity function for galaxies in 32 clusters at $0.6 < z < 1.3$ using deep $3.6μ$m and $4.5μ$m imaging from the Spitzer Space Telescope InfraRed Array Camera (IRAC). The luminosity functions approximate the stellar mass function of the cluster galaxies. Their dependence on redshift indicates that massive cluster galaxies (to the characteristic luminosity $M^*_K$) are fully assembled at least at $z \sim 1.3$ and that little significant accretion takes place at later times. The existence of massive, highly evolved galaxies at these epochs is likely to represent a significant challenge to theories of hierarchical structure formation where such objects are formed by the late accretion of spheroidal systems at $z < 1$.