# The structure and assembly history of cluster-size haloes in Self-Interacting Dark Matter

## TL;DR

This study compares the structural properties of cluster-sized haloes in Cold Dark Matter and Self-Interacting Dark Matter models through simulations, revealing significant differences at large radii and potential observational constraints on SIDM.

## Contribution

It provides the first detailed comparison of halo structures in CDM and SIDM at large radii, highlighting observable differences and implications for dark matter physics.

## Key findings

- SIDM haloes show more isotropic orbits than CDM.
- Density profiles disfavor SIDM with cross section 1 cm²/g at large radii.
- Halo assembly memory is suppressed only in central regions for SIDM.

## Abstract

We perform dark-matter-only simulations of 28 relaxed massive cluster-sized haloes for Cold Dark Matter (CDM) and Self-Interacting Dark Matter (SIDM) models, to study structural differences between the models at large radii, where the impact of baryonic physics is expected to be very limited. We find that the distributions for the radial profiles of the density, ellipsoidal axis ratios, and velocity anisotropies ($\beta$) of the haloes differ considerably between the models (at the $\sim1\sigma$ level), even at $\gtrsim10\%$ of the virial radius, if the self-scattering cross section is $\sigma/m_\chi=1$ cm$^2$ gr$^{-1}$. Direct comparison with observationally inferred density profiles disfavours SIDM for $\sigma/m_\chi=1$ cm$^2$ gr$^{-1}$, but in an intermediate radial range ($\sim3\%$ of the virial radius), where the impact of baryonic physics is uncertain. At this level of the cross section, we find a narrower $\beta$ distribution in SIDM, clearly skewed towards isotropic orbits, with no SIDM (90\% of CDM) haloes having $\beta>0.12$ at $7\%$ of the virial radius. We estimate that with an observational sample of $\sim30$ ($\sim10^{15}$ M$_\odot$) relaxed clusters, $\beta$ can potentially be used to put competitive constraints on SIDM, once observational uncertainties improve by a factor of a few. We study the suppression of the memory of halo assembly history in SIDM clusters. For $\sigma/m_\chi=1$ cm$^2$ gr$^{-1}$, we find that this happens only in the central halo regions ($\sim1/4$ of the scale radius of the halo), and only for haloes that assembled their mass within this region earlier than a formation redshift $z_f\sim2$. Otherwise, the memory of assembly remains and is reflected in ways similar to CDM, albeit with weaker trends.