Core collapse in resonant self-interacting dark matter across two decades in halo mass

TL;DR

This work shows that resonant self-interacting dark matter can drive non-self-similar core formation and collapse in low-mass halos due to velocity-dependent enhancements in the scattering cross section. By comparing single- and multi-peak resonance models across $M_{200}=10^7$–$10^9\,M_\odot$ with high-resolution N-body simulations, the authors find that adaptive-time scaling reveals near-universal core-formation behavior, while core-collapse exhibits model-dependent deviations, especially for single-peak resonances. The study demonstrates that resonant features can produce a wide range of rotation curves, contributing to the observed diversity of dwarf-galaxy kinematics, and highlights the importance of halo velocity structure relative to resonant velocities. These results extend previous single-resonance work to multi-peak resonances and set the stage for cosmological, baryon-inclusive investigations of SIDM with resonances.

Abstract

Core collapse, a process associated with self-interacting dark matter (SIDM) models, can increase the central density of halos by orders of magnitude with observable consequences for dwarf galaxy properties and gravitational lensing. Resonances in the self-interaction cross section, features of hidden-sector models with light mediators and attractive potentials, can boost the strength of self-interactions near specific relative velocities, accelerating collapse in halos with central velocity dispersions near the resonance. To explore this phenomenon, we present a suite of idealized N-body simulations of isolated halos with masses $10^7$-$10^9 \ \rm{M_\odot}$ evolved under two resonant cross section (RCS) models with localized enhancement to the cross section on scales $v \sim 5$-$50 \ \rm{km} \ \rm{s^{-1}}$. We show that the change in halo internal structure depends on how the velocity distribution of bound particles moves across resonances in the cross section during core formation and collapse. The interplay between the velocity distribution of bound particles and localized features of the cross section causes deviations from self-similar evolution, a characteristic of velocity-independent cross sections, at the level of up to $20\%$. Depending on the alignment with resonant features, halos of different masses reach different evolutionary stages after a fixed physical time and develop diverse density profiles and rotation curves.

Figures (8)

• Figure 1: The single- (top) and multi-peak (bottom) cross sections per unit of mass ($\sigma/m$, solid lines) versus the relative velocity of DM particles and halo mass, which are matched based on the most probable relative velocity magnitude $v_{\rm{rel},\kappa}^{\rm{max}}$ of the heat conductivity-weighted MB distribution for each halo (Equation \ref{['eqn:p_kappa']}). The dashed lines show the heat conductivity-averaged cross sections $\sigma_\kappa/m$, and the shaded regions show the FWHM of the heat conductivity-weighted MB distributions for the halos of mass $10^7, 10^8$, and $10^9{\,\rm M_\odot}$. Although the resonant features of the multi-peak RCS model are more complicated, in the relevant scales, $\sigma_\kappa/m$ appears flatter than that in the single-peak model.
• Figure 2: The collision rate-weighted MB distributions calculated using the single-peak (red) and multi-peak (orange) RCSs, $p_{\Gamma,{\rm{s}}} (v_{\rm{rel}})$ and $p_{\Gamma,{\rm{m}}} (v_{\rm{rel}})$, respectively, following Equation \ref{['eqn:p_Gamma']} with $\sigma_{\rm{1D}} = 1.10 \sigma_{\rm{s}}$ for the halos of mass $10^7$ (top), $10^8$ (middle), and $10^9{\,\rm M_\odot}$ (bottom). The cross section profiles (shaded fills) are also shown as references. As the halo mass changes, the principle resonant features governing the particle collisions shift. These features deviate significantly from the regions most relevant to the heat conductivity-weighted MB distributions and corresponding timescale, which is as expected from the constructions of the two distributions.
• Figure 3: Evolution of the core one-dimensional velocity dispersion $\sigma_{\rm{1D,c}}$ (top), core density $\rho_{\rm{c}}$ (middle), and core half-density radius $r_{\rho/2}$ (bottom) of three halos in the single-peak (left) and multi-peak (right) RCS models in terms of the heat conductivity-averaged adaptive $\tilde{t}_\kappa$ (solid) and linear $t = T/\tau_\kappa$ (dashed) scaled times. The shaded regions surrounding the solid lines represent the measured uncertainties of the different parameters. The cyan-shaded region shows the $\pm 1\sigma$ variation in the universal self-similar, halo mass-independent core-collapse track in VICS models. The vertical dashed lines and the shaded gray regions indicate roughly when maximum core sizes are reached and the uncertainties. In terms of $\tilde{t}_\kappa$, the core-formation durations in different halos remain consistent with the universal evolution track. In this phase, the evolutions of the core one-dimensional velocity dispersion follow closely those in halos evolved under VICSs. In the core-collapse phase, halos evolved under the single-peak RCS model exhibit deviations of the order of $\sim 10 \text{--} 20\%$ from the universal self-similar core-collapse track, most clearly in the minimum core densities, maximum core radii, and the core-collapse times. On the other hand, halos evolved under the multi-peak RCS model follow the self-similar track closely, with deviations appearing only later in the core-collapse phase.
• Figure 4: The dependency of the core half-density radius $r_{\rho/2}^{*}$ on core density $\rho_{\rm{c}}^{*}$ at the epoch of maximum core half-density radius in the single-peak (red) and multi-peak (orange) RCS models. The value achieved in a halo evolved under a VICS (cyan) is shown as a reference. As expected from core temperatures reaching similar (scaled) values across models, $r_{\rho/2}^{*}$ and $\rho_{\rm{c}}^{*}$ appear to be correlated following $\left(\rho_{\rm{c}}^{*}/\rho_{\rm{s}}\right) (r_{\rho/2}^{*}/r_{\rm{s}})^2 \sim \left(\sigma_{\rm{1D,c}}^{*}/\sigma_{\rm{s}}\right)^2 \simeq \text{const}$. The black line and gray-shaded region display such a relation and its corresponding uncertainty.
• Figure 5: The minimum core density $\rho_{\rm{c}}^{*}$ (top) and core collapse time $t_{\rm{gc}}$ (bottom) (relative to their expected values in the VICS models) as a function of $\eta$ (Equation \ref{['eqn:eta']}). Results in the single- and multi-peak RCS models are shown in red and orange. Regarding $\rho_{\rm{c}}^{*}$, a positive correlation with $\eta$ is observed, suggesting that halos with greater variations in the effective cross section during evolution deviate more significantly from self-similarity. However, the core collapse time displays no clear correlation with $\eta$.