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Simulation studies of dark energy clustering induced by the formation of dark matter halos

In this paper, we present a simulation method within the two-component spherical collapse model to investigate dark energy perturbations associated with the formation of dark matter halos. The realistic mass accretion history of a dark matter halo taking into account its fast and slow growth is considered by imposing suitable initial conditions and isotropized virializations for the spherical collapse process. The dark energy component is treated as a perfect fluid described by two important parameters, the equation of state parameter $w$ and the sound speed $c_s$. Quintessence models with $w>-1$ are analyzed. We adopt the Newtonian gauge to describe the spacetime which is perturbed mainly by the formation of a dark matter halo. It is found that the dark energy density perturbation $δ_{DE}$ depends on $w$ and $c_s$, and its behavior follows closely the gravitational potential $Φ$ of the dark matter halo with $δ_{DE}\approx -(1+w)Φ/c_s^2$. For $w>-1$, the dark energy perturbation presents a clustering behavior with $δ_{DE}>0$ during the entire formation of the dark matter halo, from linear to nonlinear and virialized stages. The value of $δ_{DE}$ increases with the increase of the halo mass. For a cluster of mass $M\sim 10^{15} M_{\odot}$, $δ_{DE}\sim 10^{-5}$ within the virialized region for $c_s^2 \in [0.5, 1]$, and it can reach $δ_{DE}=O(1)$ with $c_s^2=0.00001$. For a scalar-field dark energy model, we find that with suitably modeled $w$ and $c_s$, its perturbation behavior associated with the nonlinear formation of dark matter halos can well be analyzed using the fluid approach, demonstrating the validity of the fluid description for dark energy even considering its perturbation in the stage of nonlinear dark matter structure formation.