  We investigate the potential to improve optical tracers of cluster mass by
exploiting measurements of the magnitude gap, m12, defined as the difference
between the r-band absolute magnitude of the two brightest cluster members. We
find that in a mock sample of galaxy groups and clusters constructed from the
Bolshoi simulation, the scatter about the mass-richness relation decreases by
15-20% when magnitude gap information is included. A similar trend is evident
in a volume-limited, spectroscopic sample of galaxy groups observed in the
Sloan Digital Sky Survey (SDSS). We find that SDSS groups with small magnitude
gaps are richer than large-gap groups at fixed values of the one-dimensional
velocity dispersion among group members sigma_v, which we use as a mass proxy.
We demonstrate explicitly that m12 contains information about cluster mass that
supplements the information provided by group richness and the luminosity of
the brightest cluster galaxy, L_bcg. In so doing, we show that the luminosities
of the members of a group with richness N are inconsistent with the
distribution of luminosities that results from N random draws from the global
galaxy luminosity function. As the cosmological constraining power of galaxy
clusters is limited by the precision in cluster mass determination, our
findings suggest a new way to improve the cosmological constraints derived from
galaxy clusters.
