Cosmological Simulations with Self-Interacting Dark Matter I: Constant Density Cores and Substructure

TL;DR

This work tests velocity-independent SIDM using cosmological N-body simulations with cross sections $\sigma/m = 1$ and $0.1\ \mathrm{cm}^2/\mathrm{g}$, introducing a Boltzmann-based scattering algorithm implemented in GADGET-2. It finds that SIDM produces constant-density cores whose sizes scale with the CDM halo scale radius, while leaving large-scale clustering and halo abundances effectively unchanged, and only modestly reducing subhalo counts in the inner regions. The authors develop scaling relations and an analytic model to explain core formation and connect core properties to halo mass, showing a strong core–CDM scale-radius correlation. Observational comparisons favor $\sigma/m \approx 0.1\ \mathrm{cm}^2/\mathrm{g}$ across clusters to dwarfs, with velocity-independent SIDM offering a good fit without requiring velocity dependence, and with large-scale CDM successes retained.

Abstract

We use cosmological simulations to study the effects of self-interacting dark matter (SIDM) on the density profiles and substructure counts of dark matter halos from the scales of spiral galaxies to galaxy clusters, focusing explicitly on models with cross sections over dark matter particle mass σ/m = 1 and 0.1 cm^2/g. Our simulations rely on a new SIDM N-body algorithm that is derived self-consistently from the Boltzmann equation and that reproduces analytic expectations in controlled numerical experiments. We find that well-resolved SIDM halos have constant-density cores, with significantly lower central densities than their CDM counterparts. In contrast, the subhalo content of SIDM halos is only modestly reduced compared to CDM, with the suppression greatest for large hosts and small halo-centric distances. Moreover, the large-scale clustering and halo circular velocity functions in SIDM are effectively identical to CDM, meaning that all of the large-scale successes of CDM are equally well matched by SIDM. From our largest cross section runs we are able to extract scaling relations for core sizes and central densities over a range of halo sizes and find a strong correlation between the core radius of an SIDM halo and the NFW scale radius of its CDM counterpart. We construct a simple analytic model, based on CDM scaling relations, that captures all aspects of the scaling relations for SIDM halos. Our results show that halo core densities in σ/m = 1 cm^2/g models are too low to match observations of galaxy clusters, low surface brightness spirals (LSBs), and dwarf spheroidal galaxies. However, SIDM with σ/m ~ 0.1 cm^2/g appears capable of reproducing reported core sizes and central densities of dwarfs, LSBs, and galaxy clusters without the need for velocity dependence. (abridged)

Figures (16)

• Figure 1: Fraction of the expected total number of interactions that are computed in our test simulation as a function of the self-interaction smoothing length. The self-interaction cross section for each run is shown in units of cm$^2$/g in the legend. The code converges to the expected number of interactions when the smoothing length approaches the background inter-particle separation, i.e. when $h_\mathrm{si} (\rho_\mathrm{bg}/m_\mathrm{p})^{1/3} \gtrsim 0.2$.
• Figure 2: Top: Large scale structure in CDM (left) and SIDM$_1$ (right) shown as a $50\times50 \, h^{-1} \, {\mathrm{Mpc}}$ slice with $10 \, h^{-1} \, {\mathrm{Mpc}}$ thickness through our cosmological simulations. Particles are colored according to their local phase-space density. There are no visible differences between the two cases. Bottom: Small scale structure in a Milky Way mass halo (Z12) simulated with CDM (left) and SIDM$_1$ (right), including all particles within $200 h^{-1} \, {\mathrm{kpc}}$ of the halo centers. The magnitude of the central phase-space density is lower in SIDM because the physical density is lower and the velocity dispersion is higher. The core of the SIDM halo is also slightly rounder. Note that substructure content is quite similar except in the central regions
• Figure 3: Large-scale characteristics Left: Dark matter two-point correlation functions from our CDM-50 (CDM-25) and SIDM$_1$-50 (SIDM$_1$-25) simulations in black (grey) and blue (cyan) colors respectively. There are no noticeable difference between the CDM and SIDM$_1$ dark matter clustering over the scales plotted. Right: Cumulative number density of dark matter halos as a function of their maximum circular velocity ($V_{\mathrm{max}}$) at different redshifts for our CDM-50 (solid) and SIDM$_1$-50 (dashed) simulations. There are no significant differences in the $V_{\mathrm{max}}$ functions of CDM and SIDM$_1$ at any redshift.
• Figure 4: Density profiles for our six example halos from our SIDM$_1$ (blue stars) and SIDM$_{0.1}$ (green triangles) simulations and their CDM counterparts. With self-interactions turned on, halo central densities decrease, forming cored density profiles. Solid lines are for the best NFW (black) and Burkert (blue) fits, with the points representing the density at each radial bin found by AHF. The arrow indicates the location of the Burkert core radius $r_\mathrm{b}$. $r_\mathrm{s}$ is the NFW scale radius of the corresponding CDM halo density profile (black solid line). Burkert profiles provide a reasonable fit to our SIDM$_1$ halos only because $r_\mathrm{b} \approx r_\mathrm{s}$ for $\sigma/m=1 \, {{\rm cm}^2/{\rm g}}$, so a cored profile with a single scale radius works. As discussed in § \ref{['analytic.sec']} this is not the case for $\sigma/m=0.1 \, {{\rm cm}^2/{\rm g}}$ and thus Burkert profiles are not a good fit to our SIDM$_{0.1}$ halos.
• Figure 5: Circular velocity profiles for our example selection of six well resolved halos from our CDM, SIDM$_1$ and SIDM$_{0.1}$ simulations. The magnitude of the circular velocity at small radii $r \lesssim r_\mathrm{s}$ is lowered for all halos when self-interactions are turned on. $r_\mathrm{s}$ is the NFW scale radius of the corresponding CDM halo density profile.