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Testing the phenomenological interacting dark energy with observational $H(z)$ data

In order to test the possible interaction between dark energy and dark matter, we investigate observational constraints on a phenomenological scenario, in which the ratio between the dark energy and matter densities is proportional to the power law case of the scale factor, $r\equiv (ρ_X/ρ_m)\propto a^ξ$. By using the Markov chain Monte Carlo method, we constrain the phenomenological interacting dark energy model with the newly revised $H(z)$ data, as well as the cosmic microwave background (CMB) observation from the 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) results, the baryonic acoustic oscillation (BAO) observation from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 (DR7) galaxy sample and the type Ia supernovae (SNe Ia) from Union2 set. The best-fit values of the model parameters are $Ω_{m0}=0.27_{-0.02}^{+0.02}(1σ)_{-0.03}^{+0.04}(2σ)$, $ξ=3.15_{-0.50}^{+0.48}(1σ)_{-0.71}^{+0.72}(2σ)$, and $w_X=-1.05_{-0.14}^{+0.15}(1σ)_{-0.21}^{+0.21}(2σ)$, which are more stringent than previous results. These results show that the standard $Λ$CDM model without any interaction remains a good fit to the recent observational data; however, the interaction that the energy transferring from dark matter to dark energy is slightly favored over the interaction from dark energy to dark matter. It is also shown that the $H(z)$ data can give more stringent constraints on the phenomenological interacting scenario when combined to CMB and BAO observations, and the confidence regions of $H(z)$+BAO+CMB, SNe+BAO+CMB, and $H(z)$+SNe+BAO+CMB combinations are consistent with each other.