a, Absolute V-band magnitude of the Haumea system as a function of time. Diamonds represent observations and lines are models. The cyan curve represents a model without a ring, the black curve is a model with a 70-km-wide ring and with a reflectivity of I/F = 0.09, similar to that of Chariklo’s main ring. The ring in this model contributes approximately 2.5% of the total flux of Haumea plus Hi’iaka in 2017. The dark blue curve corresponds to a model with a wider (140 km) and brighter (I/F = 0.36) ring, which contributes 20% of the total brightness in 2017. This model can be discarded because it would produce a change in the amplitude of the light curve that is too rapid to be compatible with the observations (see b). b, Amplitude of the rotational light curve determined from the ground for the same three models as in a (using the same colour coding). The diamonds represent observations from the literature^1,17 and from this work (for 2017). See Methods for further explanations. Error bars show the errors of the measurements from refs 1 and 17 and from the determination in 2017 from this work, shown in Extended Data Fig. 6.