Several lines of evidence suggest that as dark matter haloes grow their scale radius increases, and that the density in their central region drops. Major mergers seem an obvious mechanism to explain both these phenomena, and the resulting patterns in the concentration-mass-redshift relation. To test this possibility, we have simulated equal-mass mergers between haloes with a variety of cosmological density profiles, placed on various different orbits. The remnants typically have higher densities than the initial conditions, but differ only slightly from self-similar scaling predictions. They are reasonably well fit by Einasto profiles, but have parameters distinct from those of the initial conditions. The net internal energy available to the merger remnant, relative to the internal energy of the initial conditions, κ, has the greatest influence on the properties of the final mass distribution. As expected, energetic encounters produce more extended remnants while mergers of strongly bound systems produce compact remnants. Surprisingly, however, the scale radius of the density profile shows the opposite trend, increasing in the remnants of low-energy encounters relative to energetic ones. Also even in the most energetic encounters, the density within the scale radius decreases only slightly (by 10-20%), while for very low-energy systems it increases significantly after the merger. We conclude that while major mergers can produce remnants that are more diffuse at large radii, they are relatively ineffective at changing the central densities of haloes, and seem unlikely to explain the mean trends in the concentration-mass-redshift relation.

The structural properties of individual dark matter haloes, including shape, spin, concentration, and substructure, are linked to the halo's growth history, but the exact connection between the two is unclear. One open question, in particular, is the effect of major mergers on halo structure. We have performed a large set of simulations of binary equal-mass mergers between isolated haloes with various density profiles, to map out the relationship between the initial conditions and merger parameters and the structure of the final remnant. In this paper we describe our initial set-up and analysis methods, and report on the results for the size, shape, and spin of the merger remnant. The outcomes of mergers are most easily understood in terms of a scaled dimensionless energy parameter κ and an angular momentum (or spin) parameter λ. We find that the axis ratio c/a scales roughly linearly with energy κ while the axis ratio c/b scales linearly with spin λ. Qualitatively, mergers on radial orbits produce prolate remnants, while mergers on tangential orbits produce oblate remnants. The spin of the remnant can be predicted from angular momentum conservation, while the overall size changes as ∼ κ −5 , as expected from self-similar scaling at constant mean density. We discuss potential cosmological applications for these simple patterns.

The abundance of galaxy clusters in the low-redshift universe provides an important cosmological test, constraining a product of the initial amplitude of fluctuations and the amount by which they have grown since early times. The degeneracy of the test with respect to these two factors remains a limitation of abundance studies. Clusters will have different mean assembly times, however, depending on the relative importance of initial fluctuation amplitude and subsequent growth. Thus, structural probes of cluster age such as concentration, shape or substructure may provide a new cosmological test that breaks the main degeneracy in number counts. We review analytic predictions for how mean assembly time should depend on cosmological parameters, and test these predictions using cosmological simulations. Given the overall sensitivity expected, we estimate the cosmological parameter constraints that could be derived from the cluster catalogues of forthcoming surveys such as Euclid, the Nancy Grace Roman Space Telescope, eROSITA, or CMB-S4. We show that by considering the structural properties of their cluster samples, such surveys could easily achieve errors of Δσ8 = 0.01 or better.