The abundance of dark matter haloes down to Earth mass

Understand

We use the Voids-within-Voids-within-Voids (VVV) simulations, a suite of successive nested N-body simulations with extremely high resolution (denoted, from low to high resolution, by L0 to L7), to test the Press-Schechter (PS), Sheth-Tormen (ST), and extended Press-Schechter (EPS) formulae for the halo abundance over the entire mass range, from mini-haloes of $10^{-6}\ \mathrm{M_\odot}$, to cluster haloes of $10^{15}\ \mathrm{M_\odot}$, at different redshifts, from $z=30$ to the present.

• We find that at $z=0$ and $z=2$, ST best reproduces the results of L0, which has the mean cosmic density (overdensity $\delta=0$), at $10^{11-15} ~\mathrm{M_\odot}$.
• The higher resolution levels (L1-L7) are biased underdense regions ($\delta<-0.6$).
• The EPS formalism takes this into account since it gives the mass function of a region conditioned, in this case, on having a given underdensity.