Context: Recent observations with Spitzer and the Caltech Submillimeter Observatory have discovered the presence of a dust belt at about 3 AU, internal to the orbit of known exoplanet ∊ Eri b.
Aims: We investigate via numerical simulations the dynamical stability of a putative belt of minor bodies, as the collisional source of the observed dust ring. This belt must be located inside the orbit of the planet, since any external source would be ineffective in resupplying the inner dust band.
Methods: We explore the long-term behaviour of the minor bodies of the belt and how their lifetime depends on the orbital parameters of the planet, in particular for reaching a steady state.
Results: Our computations show that for an eccentricity of ∊ Eri b equal or higher than 0.15, the source belt is severely depleted of its original mass and substantially reduced in width. A “dynamical” limit of ≃0.10 comes out, which is inconsistent with the first estimate of the planet eccentricity (0.70±0.04), while the alternate value (0.23±0.2) can be consistent within the uncertainties.