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

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.

14 pages, 5 Figures. Accepted by ApJ

References in corpus (7)

• The Uchuu Simulations: Data Release 1 and Dark Matter Halo Concentrations
• Large-scale dark matter simulations
• The Universe at z>10: Predictions for JWST from the UniverseMachine DR1
• Virial halo mass function in the $Planck$ cosmology
• A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function
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• A Stochastic Theory of the Hierarchical Clustering II. Halo progenitor mass function and large-scale bias

Cited by in corpus (1)

• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales