Distinguishing cold and self-interacting dark matter through topological analysis
Alternative dark matter (DM) models have emerged to solve the challenges faced by the predictions of collisionless cold dark matter (CDM) on galactic scales ($\lesssim 1$ Mpc). However, disentangling alternative models from CDM is difficult on such small scales because of the degeneracy with baryonic physics. It is therefore necessary to use DM probes that are not affected by baryons, e.g. that stand on intermediate scales, larger than galactic while remaining smaller than the scale at which the models converge to CDM. For the first time, we distinguish self-interacting DM (SIDM) from CDM using the genus statistic, a metric that characterises the topology of the density field. We carried out the analysis on the Darkium DM-only cosmological simulations, using one CDM model and four SIDM models with cross-sections of various amplitudes and velocity dependencies. We computed the genus on selected 3-virial radius wide regions centred around halos, for few hundred halos with masses ranging from $10^{12}$ to $10^{14}$ M$_\odot/h$ over redshifts $z=0$ to $z=2$. We also explored a more observation-like configuration, where the DM density field is traced only from the halo distribution in thick 2D projection since in principle redshift errors hinder a 3D reconstruction of the density field. We find that the density field is systematically clumpier in CDM than in SIDM models up to $0.05~\mathrm{Mpc}/h$, for halos of masses larger than $10^{12}$ M$_\odot/h$ at $z=0$. These predictions show that the genus of the density field is sensitive to DM self-interactions, suggesting that topological analysis could provide a valuable probe for distinguishing SIDM from CDM in observed halo distributions.