Dynamical evolutin of quintessence dark energy in collapsing dark matter
  halos
  In this paper, we analyze the dynamical evolution of quintessence dark energy
induced by the collapse of dark matter halos. Different from other previous
studies, we develop a numerical strategy which allows us to calculate the dark
energy evolution for the entire history of the spherical collapse of dark
matter halos, without the need of separate treatments for linear, quasi-linear
and nonlinear stages of the halo formation. It is found that the dark energy
perturbations evolve with redshifts, and their specific behaviors depend on the
quintessence potential as well as the collapsing process. The overall energy
density perturbation is at the level of $10^{-6}$ for cluster-sized halos. The
perturbation amplitude decreases with the decrease of the halo mass. At a given
redshift, the dark energy perturbation changes with the radius to the halo
center, and can be either positive or negative depending on the contrast of
$\partial_t \phi$, $\partial_r \phi$ and $\phi$ with respect to the background,
where $\phi$ is the quintessence field. For shells where the contrast of
$\partial_r \phi$ is dominant, the dark energy perturbation is positive and can
be as high as about $10^{-5}$.
