The synchronous rotations of Eris/Dysnomia and Orcus/Vanth binary systems

We have measured the rotation periods of the Eris/Dysnomia and Orcus/Vanth binary systems using long-term observations obtained with the SMARTS 1.3m telescope at Cerro Tololo, combined with incidental observations obtained by the La Silla - QUEST survey on the ESO 1.0-m Schmidt at La Silla, and using historical observations of Eris published by others. We find that both binary systems are synchronous, with the dominant periodicity in their light curves matching their mutual orbit periods (9.54 and 15.774 days, respectively). For Orcus/Vanth, the reflected light from both bodies contributes to the signal. The measured periodicity could be due to the rotation of Orcus or Vanth separately, but it is most likely the system is doubly synchronous. For Eris/Dysnomia, only Eris is bright enough to contribute significantly to the observations. The conclusion is therefore unambiguous that Eris is synchronously rotating with the orbit of Dysnomia. This is surprising given that Eris is 500 times brighter than Dysnomia, and likely to be 100 to 10000 times more massive (assuming an albedo > 5% for Dysnomia). If Dysnomia has migrated outward from Eris owing to long-term tidal interactions, the time for Eris to slow from an initially fast rotation (period < 1 day) to a synchronous one is longer than the age of the solar system. We discuss the constraints these observations place on the relative albedos, masses, and internal composition of the two binary systems.