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

We perform dark-matter-only simulations of a sample of 28 relaxed massive cluster-sized haloes in the Cold Dark Matter (CDM) and Self-Interacting Dark Matter (SIDM) models of structure formation, in order to study the structural differences across the models at large radii, in a regime that has been largely unexplored, and where the impact of baryonic physics is expected to be very limited. We find that the sample distributions for the radial profiles of the density, ellipsoidal axis ratios (halo shapes), and velocity anisotropies ($\beta$) of the haloes differ considerably between the models, even at $\gtrsim10\%$ of the virial radius, if the amplitude of the self-scattering cross section is $\sigma/m_\chi=1$ cm$^2$ gr$^{-1}$. For the density profiles and halo shapes, the separation is around the $1\sigma$ level, with the halo shapes showing the strongest deviations, whereas for $\beta$ we find a narrower distribution in SIDM by $\sim25\%$. This distribution is skewed towards isotropic orbits with no haloes in our SIDM sample having $\beta>0.2$ at $15\%$ of the virial radius, as opposed to 25$\%$ of the haloes for CDM. We estimate that an observational sample of $\sim60$ relaxed clusters of mass $\sim10^{15}$ M$_\odot$ would be needed to use $\beta$ as a diagnostic to put competitive constraints on SIDM. We also study the extent to which the memory of the assembly history of haloes is erased in SIDM clusters. For $\sigma/m_\chi=1$ cm$^2$ gr$^{-1}$, we find that this memory is erased only in the very central regions of the halo ($\sim1/4$ of the scale radius of the halo), and only for haloes that assembled their mass within this region earlier than a formation redshift $z_f\sim2$. When these conditions are not satisfied, the memory of assembly remains in SIDM and is reflected in similar ways, albeit with weaker trends, as it is in CDM.