The role of prompt cusps in driving the core collapse of SIDM halos

Abstract

Prompt cusps (PCs) form from the direct collapse of overdensities in the early Universe, reside at the center of every dark matter halo, and have density profiles steeper than $r^{-1}$ NFW cusps. Using a suite of high-resolution N-body simulations, we study the evolution of isolated halos in self-interacting dark matter (SIDM) with massive PCs embedded at their centers, a scenario that could be realized in certain SIDM models with light mediators that predict a small-scale suppression of the linear matter power spectrum. We track the evolution of three equally concentrated $10^7\,{\rm{M}}_\odot$ halos, hosting PCs of various total masses, and quantify how the presence of a PC affects the processes of core formation and collapse. Early in the core-formation phase, halos with more prominent PCs exhibit a delayed evolution by a factor of $\sim 2$ due to smaller velocity dispersion gradients in the inner region. During most of the core-collapse phase, the halo evolution becomes closely aligned in physical time, with appropriate rescaling of densities, radii, and velocity dispersions. The scale densities and radii preserve the virial mass of the original halos, but with increased concentration. Deviations occur at the late phase of core-collapse at the level of $\sim 5\%$ relative to the reference collapse track of an NFW halo. These deviations depend non-trivially on both the increased concentration incurred by the PCs, as well as the velocity dispersion (temperature) of the outer halo regions, which can inhibit or enhance the heat transfer process. Our simulations illustrate the complex interplay between the inner and outer halo profiles in determining the onset of core collapse and motivate future studies in the full cosmological context.

Figures (11)

• Figure 1: The density profiles (top), logarithmic density profile slopes (middle), and one-dimensional velocity dispersion profiles (bottom) for the four halos described in Section \ref{['ssec:modelsetup']}. The reference NFW profile is shown in dashed cyan, while the low-cusp, high-cusp, and extreme-cusp configurations are shown in blue, orange, and red, respectively. The vertical dashed lines represent $r_{-2}$, the radius at which the logarithmic slope reaches the value of $-2$, which coincides with the scale radius $r_{\rm{s}}$ of the reference NFW profile.
• Figure 2: The fractional differences in the initial density profiles $\rho(r)$ (top), enclosed mass profiles $M(r)$ (middle), and one-dimensional velocity dispersion $\sigma_{\rm{1D}} (r)$ (bottom) of the four halos relative to the reference NFW halo (SIDM-control). $r_{-2}$ and $r_{200}$ are indicated by vertical dashed lines. As a result of the functional form of the parametric model and the exponential cut-off model beyond $r_{200}$, the halos differ not only in the prompt cusp–dominated region but also across the entire halo, particularly in the outer regions. These differences may influence the subsequent time evolution of the halo core during the core-collapse phase.
• Figure 3: The evolution of the density (top) and velocity dispersion (bottom) profiles of the high-cusp (solid) and control NFW (dashed) halos during the core-formation phase. Several snapshots are chosen, spanning from the earliest epoch, approximately $0.1\%$ of the collapse timescale, to $T \sim 6\,{\rm Gyr}$, which marks the transition into the core-collapse phase. Overall, the high-cusp halo evolves significantly slower than the NFW reference until the onset of core collapse, at which point the two halos begin to exhibit similar internal structures.
• Figure 4: Evolutions of the core density $\rho_{\rm{c}}$ (top), core half-density radius $r_{\rho/2}$ (middle), and core one-dimensional velocity dispersion $\sigma_{\rm{1D,c}}$ (bottom) of the four halos in runs with the VICS per particle mass of $\sigma / m = 83.86\,{\rm cm}^2\,{\rm g}^{-1}$. As a result of their initially denser cusps, the prompt-cusp halos reach higher minimum core densities and smaller half-density radii compared to the NFW reference.
• Figure 5: Scaled evolutions of the core density $\rho_{\rm{c}}$ (top), core half-density radius $r_{\rho/2}$ (middle), and core one-dimensional velocity dispersion $\sigma_{\rm{1D,c}}$ (bottom) for the four halos in VDCS (left) and VICS (right) models. The sub-panels show the zoomed-in scaled core density evolution during the core-formation phase. The effective scale density $\bar{\rho}_{\rm{s}}$, effective scale radius $\bar{r}_{\rm{s}}$, and effective scale velocity $\sigma_{\rm{s}}$ are taken as shown in Table \ref{['tab:collapse_params']}. Generally, the evolutionary trajectories of the different halos appear broadly overlapping, with the exception of the extreme-cusp halo. The prompt-cusp halos are also observed to form cores more gradually while undergoing core collapse at accelerated rates.