Universal Properties of Dark Matter Halos

We discuss the universal relation between density and size of observed dark matter halos that was recently shown to hold on a wide range of scales, from dwarf galaxies to galaxy clusters. Predictions of cold dark matter ($\Lambda \mathrm{CDM}$) $N$-body simulations are consistent with this relation. We demonstrate that this property of $\Lambda \mathrm{CDM}$ can be understood analytically in the secondary infall model. Qualitative understanding given by this model provides a new way to predict which deviations from $\Lambda \mathrm{CDM}$ or large-scale modifications of gravity can affect universal behavior and, therefore, to constrain them observationally.

Figure 1

Column density $\mathcal{S}$ as a function of halo mass $M_{200}$. The gray solid line is the relation (2), coinciding with predictions of $N$-body simulations [13], using the WMAP5 [2] cosmological parameters. The shaded region shows the $3\sigma$ scatter in the simulation data. The vertical lines indicate the mass range probed by simulations. The gray dashed line shows the results from the Aquarius simulation [23] for satellite haloes. The black dashed-dotted line follows from the infall model.