Dark halo mergers and the formation of a universal profile

We argue that a universal density profile for dark matter haloes arises as a natural consequence of hierarchical structure formation: it is a fixed point in the process of repeated mergers. We present analytic and numerical arguments for the emergence of a particular form of the central cusp profile. At small radii, the density should vary as r ^−α, with α determined by the way in which the characteristic density of haloes scales with their mass. If small haloes are dense, then α is large. The mass–density relation can be related to the power spectrum of initial fluctuations, P ( k ), through 'formation time' arguments. Early structure formation leads to steep cusps. For P ( k ) ∼  k ⁿ we find α ≃ 3(3 +  n )/(5 +  n ). The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.     

Density cusps: restrictions on non-axisymmetric models

Galactic nuclei are now generally thought to have density cusps in their centres, and the evidence is mounting that as a consequence they are unlikely to be triaxial. Self-consistent stellar dynamical models of non-axisymmetric cusps would be an interesting counter-argument to this conclusion. We consider 2D analogues of triaxial cusps: a sequence of non-axisymmetric, cuspy discs first described by Sridhar & Touma. Scale-free models with potential Φ ∝  r ^α are examined in detail. It is shown analytically for 0 < α ≲ 0.43 that self-consistent models with positive phase-space density do not exist. Numerical solutions of the combined Vlasov and Poisson equations suggest that the whole sequence of models with 0 < α < 1 are also unphysical. Together with existing work on cusps, we conclude on purely theoretical grounds that galactic nuclei are not expected to be triaxial.     

Survival of substructure within dark matter haloes

Using high-resolution cosmological N -body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as they are dissolved by dynamical friction, tidal forces and collisions with other satellites. We also analyse the evolution of their internal structure. Satellites with less than a few per cent of the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the centre of the main halo potential well and lose their identity. Penetrating encounters between satellites are frequent and may lead to significant mass loss and disruption. Only a minor fraction of cluster mass (10–15 per cent on average) is bound to substructure at most redshifts of interest. We discuss the application of these results to the survival and extent of dark matter haloes associated with galaxies in clusters, and to their interactions. We find that a minor fraction of galaxy-size dark matter haloes are disrupted by redshift z  = 0. The fraction of satellites undergoing close encounters is similar to the observed fraction of interacting or merging galaxies in clusters at moderate redshift.