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We characterize the luminosity functions of galaxies residing in $z\sim0$groups and clusters over the broadest ranges of luminosity and mass reachableby the Sloan Digital Sky Survey. Our measurements cover four orders ofmagnitude in luminosity, down to about $M_r=-12$ mag or $L=10^7\,L_\odot$, andthree orders of magnitude in halo mass, from $10^{12}$ to $10^{15} \, {\rmM}_\odot$. We find a characteristic scale, $M_r\sim-18$ mag or $L\sim10^9\,L_\odot$, below which the slope of the luminosity function becomessystematically steeper. This trend is present for all halo masses andoriginates mostly from red satellites. This ubiquitous faint-end upturnsuggests 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 simplemanner by a double Schechter function with amplitudes scaling with halo massover the entire range of observables. Combining these conditional luminosityfunctions with the dark matter halo mass function, we accurately recover theentire field luminosity function over 10 visual magnitudes and reveal thatsatellite galaxies dominate the field luminosity function at magnitudes fainterthan $-17$. We find that the luminosity functions of blue and red satellitegalaxies show distinct shapes and we present estimates of the stellar massfraction as a function of halo mass and galaxy type. Finally, using a simplemodel, we demonstrate that the abundances and the faint-end slopes of blue andred satellite galaxies can be interpreted in terms of their formation history,with two distinct modes separated by some characteristic time.

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