Spherical Collapse Models with Clustered Dark Energy

TL;DR

This paper models galaxy cluster formation considering dark energy clustering, introducing a parameter to quantify clustering, and finds that the collapse process is largely unaffected by early-time DE perturbations.

Contribution

It presents a novel spherical collapse model incorporating a clustering parameter for dark energy, providing a simple yet effective way to analyze cluster formation with clustered DE.

Findings

Estimated virialized overdensities suggest 0.5 < r < 0.8 for clustered DE with w < -0.9.

Collapse process is largely independent of initial DE perturbations.

Method aligns with linear perturbation theory results at early times.

Abstract

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.