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The galaxy luminosity function in groups and clusters: the faint-end upturn and the connection to the field luminosity function

We characterize the luminosity functions of galaxies residing in $z\sim0$ groups and clusters over the broadest ranges of luminosity and mass reachable by the Sloan Digital Sky Survey. Our measurements cover four orders of magnitude in luminosity, down to about $M_r=-12$ mag or $L=10^7\,L_\odot$, and three orders of magnitude in halo mass, from $10^{12}$ to $10^{15} \, {\rm M}_\odot$. We find a characteristic scale, $M_r\sim-18$ mag or $L\sim10^9\, L_\odot$, below which the slope of the luminosity function becomes systematically steeper. This trend is present for all halo masses and originates mostly from red satellites. This ubiquitous faint-end upturn suggests that it is formation, rather than halo-specific environmental effect, that plays a major role in regulating the stellar masses of faint satellites. We show that the satellite luminosity functions can be described in a simple manner by a double Schechter function with amplitudes scaling with halo mass over the entire range of observables. Combining these conditional luminosity functions with the dark matter halo mass function, we accurately recover the entire field luminosity function over 10 visual magnitudes and reveal that satellite galaxies dominate the field luminosity function at magnitudes fainter than $-17$. We find that the luminosity functions of blue and red satellite galaxies show distinct shapes and we present estimates of the stellar mass fraction as a function of halo mass and galaxy type. Finally, using a simple model, we demonstrate that the abundances and the faint-end slopes of blue and red satellite galaxies can be interpreted in terms of their formation history, with two distinct modes separated by some characteristic time.