Spherical Collapse Models with Clustered Dark Energy
  We investigate the clustering effect of dark energy (DE) in the formation of
galaxy clusters using the spherical collapse model. Assuming a fully clustered
DE component, the spherical overdense region is treated as an isolated system
which conserves the energy separately for both matter and DE inside the
spherical region. Then, by introducing a parameter $r$ to characterize the
degree of DE clustering, which is defined by the nonlinear density contrast
ratio of matter to DE at turnaround in the recollapsing process, i.e. $r\equiv
\nld_{\de,\ta}/\nld_{\m,\ta}$, we are able to uniquely determine the spherical
collapsing process and hence obtain the virialized overdensity $\Dvir$ through
a proper virialization scheme. Estimation of the virialized overdensities from
current observation on galaxy clusters suggests that $0.5 < r < 0.8$ at
$1\sigma$ level for the clustered DE with $w < -0.9$. Also, we compare our
method to the linear perturbation theory that deals with the growth of DE
perturbation at early times. While both results are consistent with each other,
our method is practically simple and it shows that the collapse process is
rather independent of initial DE perturbation and its evolution at early times.
