Prompt Cusp Formation and Angular Momentum

In this study, we expand on White’s model proposed in [1], which explores the post-collapse evolution of density peaks while incorporating the influence of angular momentum. Within a time scale smaller than the peak collapse, denoted as \({{t}_{0}}\), the inner regions of the peak reach an equilibrium state, forming a cuspy profile, consistent with White’s findings. However, the power-law density profile is slightly flatter, specifically \(\rho \propto {{r}^{{ - 1.52}}}\), due to the incorporation of the specific angular momentum \(J\) obtained from theoretical models of its evolution in CDM universes, represented as \(J \propto {{M}^{{2/3}}}\). The outcome above demonstrates the impact of angular momentum on the slope of the density profile, allowing us to reproduce a slightly flatter profile similar to the one observed in high-resolution numerical simulations, where \(\rho \propto {{r}^{\alpha }}\) with \(\alpha \simeq - 1.5\). Notably, our model, like the simulations, does not account for adiabatic contraction. Therefore, conducting more comprehensive simulations may yield different values for the slope of the density profile, presenting an opportunity to enhance and refine our model.