Testing cold dark matter with the hierarchical build-up of stellar light

The hierarchical growth of mass in the Universe is a pillar of all cold dark matter (CDM) models. In this paper we demonstrate that this principle leads to a robust, falsifiable prediction of the stellar content of groups and clusters, which is testable with current observations and is relatively insensitive to the details of baryonic physics or cosmological parameters. Since it is difficult to preferentially remove stars from dark matter dominated systems, when these systems merge the fraction of total mass in stars can only increase ( via star formation) or remain constant, relative to the fraction in the combined systems prior to the merger. Therefore, hierarchical models can put strong constraints on the observed correlation between stellar fraction, f(*), and total system mass, M-500. In particular, if this relation is fixed and does not evolve with redshift, CDM models predict b = d log f(*)/d logM(500) greater than or similar to -0.3. This constraint can be weakened if the f(*) - M-500 relation evolves strongly, but this implies more stars must be formed in situ in groups at low redshift. Conservatively requiring that at least half the stars in groups were formed by z = 1, the constraint from evolution models is b greater than or similar to - 0.35. Since the most massive clusters ( M similar to 10(15)M(circle dot)) are observed to have f(*) similar to 0.01, this means that groups with M = 5 x 10(13)M(circle dot) must have f(*) <= 0.03. Recent observations by Gonzalez, Zaritsky & Zabludoff indicate a much steeper relation, with f(*) > 0.04 in groups leading to b approximate to -0.64. If confirmed, this would rule out hierarchical structure formation models: today's clusters could not have been built from today's groups, or even from the higher redshift progenitors of those groups. We perform a careful analysis of these and other data to identify the most important systematic uncertainties in their measurements. Although correlated uncertainties on stellar and total masses might explain the steep observed relation, the data are only consistent with theory if the observed group masses are systematically underestimated.