The rotation of Io predicted by the Poincar\'e-Hough model

This note tackles the problem of the rotation of Io with the 4-degrees of freedom Poincar\'e-Hough model. Io is modeled as a 2-layer body, i.e. a triaxial fluid core and a rigid outer layer. We show that the longitudinal librations should have an amplitude of about 30 arcseconds, independent of the composition of the core. We also estimate the tidal instability of the core, and show that should be slowly unstable.