Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data

In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on Markov chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from \textit{Planck}, baryon acoustic oscillation, and type Ia supernovae; the dynamic measurement is $f\sigma_8(z)$ data points which is obtained from the growth rate via redshift-space distortion, and $\sigma_8(z)$ is the root-mean-square amplitude of the density contrast $\delta$ at the comoving $8h^{-1}$ Mpc scale. The jointed constraint shows that $\alpha$ = $ 0.000662_{- 0.000662}^{+ 0.000173}$ and $\sigma_8$ = $ 0.824_{- 0.0166}^{+ 0.0128}$. The CMB and matter power spectra are both similar for the case of $\alpha=$ mean value and that of $\alpha=0$. However, the evolutionary curves of $f\sigma_8(z)$ are different. This means that, to some extent, the data points of the growth rate could break the degeneracy of the dark energy models.