A Stochastic Theory of the Hierarchical Clustering III. The Non-universality and Non-stationarity of the Halo Mass Function

TL;DR

This paper develops a stochastic Fokker-Planck framework to model the evolving halo mass function in hierarchical clustering, revealing non-universality and non-stationarity, especially at high redshifts relevant for JWST observations.

Contribution

It introduces a time-dependent stochastic model that captures the non-universal evolution of halo mass functions beyond stationary solutions, aligning with simulations and aiding future experiment design.

Findings

Stationary solutions match low-redshift simulations accurately.

Time-dependent solutions describe high-redshift halo evolution.

Predicted halo densities are higher than standard estimates at z>10.

Abstract

In the framework of the stochastic theory for hierarchical clustering, we investigate the time-dependent solutions of the Fokker-Planck equation describing the statistics of dark matter halos, and discuss the typical timescales needed for these to converge toward stationary states, far away enough from initial conditions. Although we show that the stationary solutions can reproduce the outcomes of state-of-the-art $N-$body simulations at $z\approx 0$ to a great accuracy, one needs to go beyond to fully account for the cosmic evolution of the simulated halo mass function toward high-redshift. Specifically, we demonstrate that the time-dependent solutions of the Fokker-Planck equation can describe, for reasonable initial conditions, the non-universal evolution of the simulated halo mass functions. Compared to standard theoretical estimates, our stochastic theory predicts a halo number density higher by factor of several toward $z\gtrsim 10$, an outcome which can be helpful in elucidating early and upcoming data from JWST. Finally, we point out the relevance of our approach in designing, interpreting and emulating present and future $N-$body experiments.