A Quantitative Study of Interacting Dark Matter in Halos

TL;DR

The paper addresses the central cusp problem in dark matter halos by testing self-interacting dark matter (SIDM) using N-body simulations with a Monte Carlo scattering prescription. It introduces a dimensionless cross section $\hat{\sigma}_{DM}$ and analyzes a one-parameter SIDM family across Hernquist halos, revealing rapid formation of a constant-density core ($\sim 0.4a$) followed by non-diffusive core collapse, with the timing strongly dependent on $\hat{\sigma}_{DM}$ through $t_{rc}=1.7 t_{dyn}/\hat{\sigma}_{DM}$. Adiabatic contraction by cooling baryons steepens central cusps to roughly $\rho\propto 1/r^2$ and greatly accelerates collapse, undermining the core-preserving aim of SIDM. Spherical-collapse tests show higher central densities can be achieved, but end states resemble collisionless profiles, leading to the conclusion that SIDM likely exacerbates rather than resolves the cusp problem; thus cross sections must be sufficiently small to avoid significant scattering over cosmic time. This work constrains SIDM viability and highlights the significant interplay between baryons and DM self-interactions in shaping halo cores.

Abstract

We study the evolution of Hernquist profile ``galaxies'' in the presence of self-interacting dark matter (SIDM), where the properties of the dark matter can be parameterized by one number, sigma-hat = sigma M/a^2 for a halo of mass M and break radius a. While the halos form constant density cores of size a/2 on the core radius relaxation time scale core collapse begins shortly thereafter and a steeper 1/r^2 central density cusp starts forming faster than predicted by 2-body relaxation. The formation of the steeper central cusp is accelerated if the cooling baryons adiabatically compress the dark matter. The natural consequence of SIDM is to exacerbate rather than to mitigate astrophysical problems created by dark matter density cusps.

Figures (3)

• Figure 1: (Top) The halo density profiles at $t\simeq t_{\rm dyn}$ for models with $\hat{\sigma}_{DM}=0$, $0.3$, $1.0$, $3.0$ and $10.0$. The dotted line shows the initial Hernquist profile. Note that after only one dynamical time the $\hat{\sigma}_{DM}=3$ and $10$ cases have started to core collapse. The force softening is indicated by $h$.
• Figure 2: (Top) Core radius evolution as a function of dynamical time. The solid lines show the evolution of the core radius (temporally smoothed) for dimensionless cross sections of $\hat{\sigma}_{DM}=0$, $0.3$, $1.0$, $3.0$ and $10.0$. Note that the standard ($10^5$ particles) and "Large-N" ($8\times 10^5$ particles) simulations for $\hat{\sigma}_{DM}=1$ show identical evolution. (Middle) Central density evolution as a function of relaxation time $t_{rc}=1.7t_{\rm dyn}/\hat{\sigma}_{DM}$. As expected, the minimum core density occurs at $t_{rc}\simeq 1$. (Bottom) Recollapse. The recollapse of the core after reaching maximum expansion near $t/t_{rc}=1$ is self-similar for a time scale of $t_{rc}\hat{\sigma}_{DM}^{1/2}$.
• Figure 3: The combined effects of SIDM and adiabatic compression. The SIDM cross section is $\hat{\sigma}=0$ (solid) or $1$ (dashed) and the adiabatically compressed curves include the baryonic contribution (Eq. \ref{['eqn:baryons']}). Curves of increasing central density are just before the compression ($t=t_{\rm dyn}$), just after the compression ($t=3t_{\rm dyn}$) and some time after compression ($t=4.0t_{\rm dyn}$). The force smoothing scale is $0.01a$.