The distribution and kinematics of early high-σ peaks in present-day haloes: Implications for rare objects and old stellar populations

We show that the hierarchical assembly of cold dark matter haloes preserves the memory of the initial conditions. Using N-body cosmological simulations, we demonstrate that the present-day spatial distribution and kinematics of objects that formed within early (z ≳ 10) protogalactic systems (old stars, satellite galaxies, globular clusters, massive black holes, etc.) depends mostly on the rarity of the peak of the primordial density field to which they originally belonged. Only for objects forming at lower redshifts does the exact formation site within the progenitor halo (e.g. whether near the centre or in an extended disc) become important. In present-day haloes, material from the rarer early peaks is more centrally concentrated and falls off more steeply with radius compared to the overall mass distribution, has a lower velocity dispersion, moves on more radial orbits, and has a more elongated shape. Population II stars that formed within protogalactic haloes collapsing from ≥2.5σ fluctuations would follow today an r-3.5 density profile with a half-light radius of 17 kpc and a velocity anisotropy that increases from isotropic in the inner regions to nearly radial at the halo edge. This agrees well with the radial velocity dispersion profile of Galaxy halo stars from the recent work of Battaglia et al. and with the anisotropic orbits of nearby halo stars.