Equation of state for an interacting holographic dark energy model

We investigate a model of the interacting holographic dark energy with cold dark matter (CDM). In the case that the holographic energy density whose infrared cutoff is given by the future event horizon decays into CDM, we find two types of equation of state. For a constant ratio of two energy densities, their effective equations of state are given by the same negative constant. Actually, the cosmic anti-friction arisen from the vacuum decay process induces acceleration. For a variable ratio, their effective equations of state are dynamical but they approach the same negative constant in the far future. Furthermore, we find that such an interacting holographic energy model cannot accommodate a transition from the dark energy with $\omega^{\rm eff}_{\rm \Lambda}\ge-1$ to phantom regime with $\omega^{\rm eff}_{\rm \Lambda}<-1$.