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, $r\equiv
(\rho_X/\rho_m)\propto a^{\xi}$. 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
$\Omega_{m0}=0.27_{-0.02}^{+0.02}(1\sigma)_{-0.03}^{+0.04}(2\sigma)$,
$\xi=3.15_{-0.50}^{+0.48}(1\sigma)_{-0.71}^{+0.72}(2\sigma)$, and
$w_X=-1.05_{-0.14}^{+0.15}(1\sigma)_{-0.21}^{+0.21}(2\sigma)$, which are more
stringent than previous results. These results show that the standard
$\Lambda$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.
