Observational constraint on the interacting dark energy models including
  the Sandage-Loeb test
  Two types of interacting dark energy models are investigated using the type
Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave
background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We
find that the inclusion of SL test can obviously provide more stringent
constraint on the parameters in both models. For the constant coupling model,
the interaction term including the SL test is estimated at $\delta=-0.01 \pm
0.01 (1\sigma) \pm 0.02 (2\sigma)$, which has been improved to be only a half
of original scale on corresponding errors. Comparing with the combination of
SNIa and OHD, we find that the inclusion of SL test directly reduces the
best-fit of interaction from 0.39 to 0.10, which indicates that the
higher-redshift observation including the SL test is necessary to track the
evolution of interaction. For the varying coupling model, we reconstruct the
interaction $\delta (z)$, and find that the interaction is also negative
similar as the constant coupling model. However, for high redshift, the
interaction generally vanishes at infinity. The constraint result also shows
that the $\Lambda$CDM model still behaves a good fit to the observational data,
and the coincidence problem is still quite severe. However, the phantom-like
dark energy with $w_X<-1$ is slightly favored over the $\Lambda$CDM model.
