Inner cusps of the first dark matter haloes: Formation and survival in a cosmological context

Understand

We use very high resolution cosmological zoom simulations to follow the early evolution of twelve first-generation haloes formed from gaussian initial conditions with scale-free power spectra truncated on small scales by a gaussian in wavenumber.

• Initial collapse occurs with a diverse range of sheet- or filament-like caustic morphologies, but in almost all cases it gives rise to a numerically converged density cusp with $\rho = Ar^{-3/2}$ and total mass comparable to that of the corresponding peak in the initial linear density field.
• The constant $A$ can be estimated to within about 10 per cent from the properties of this peak.
• This outcome agrees with earlier work on the first haloes in cold and warm dark matter universes.