The slope of the mass-luminosity relation, κ (Eq. (1)), for the models listed in Table 1. The observational constraints with confidence intervals are depicted as hatched regions (1, 2, and 3σ region). Satellites with a larger dark-matter mass are on average more luminous such that the mass-luminosity relation has κ > 0. However, the observational constraints lie in the region κ ≈ 0 (see Table 1). The hypothesis that the data are consistent with any one of the models can be discarded with very high (at least 3σ, or more than 99.7 per cent) confidence.