A Differentiable Model of the Assembly of Individual and Populations of Dark Matter Halos

Andrew P Hearin,Alex Alarcon,Mathew R Becker,Jonás Chaves-Montero

doi:10.21105/astro.2105.05859

Abstract

We present a new empirical model for the mass assembly of dark matter halos. We approximate the growth of individual halos as a simple power-law function of time, where the power-law index smoothly decreases as the halo transitions from the fast-accretion regime at early times, to the slow-accretion regime at late times. Using large samples of halo merger trees taken from high-resolution cosmological simulations, we demonstrate that our 3-parameter model can approximate halo growth with a typical accuracy of 0.1 dex for $t > 1$ Gyr for all halos of present-day mass greater than $10^{11} M_{\odot}$, including subhalos and host halos in gravity-only simulations, as well as in the TNG hydrodynamical simulation. We additionally present a new model for the assembly of halo populations, which not only reproduces average mass growth across time, but also faithfully captures the diversity with which halos assemble their mass. Our python implementation is based on the autodiff library JAX, and so our model self-consistently captures the mean and variance of halo mass accretion rate across cosmic time. We show that the connection between halo assembly and the large-scale density field, known as halo assembly bias, is accurately captured by our model, and that residual errors in our approximations to halo assembly history exhibit a negligible residual correlation with the density field. Our publicly available source code can be used to generate Monte Carlo realizations of cosmologically representative halo histories; our differentiable implementation facilitates the incorporation of our model into existing analytical halo model frameworks.

Highlights

In the standard cosmological model, the matter content of the Universe is dominated by Cold Dark Matter (CDM), and gravitationally self-bound objects referred to as dark matter halos are the fundamental building blocks of structure formation
We have shown that is our model for individual halo growth differentiable, but using the weighted sampling techniques described in Appendix C, so are one-point function predictions based on our model for the assembly of halo populations
We conclude by summarizing our primary results: 1. We have introduced a new fitting function for Mpeak(t), the evolution of cumulative peak mass of individual dark matter halos; our model approximates halo assembly as a power-law function of cosmic time with rolling index, Mpeak(t) ∝ tα(t)

Summary

Introduction

In the standard cosmological model, the matter content of the Universe is dominated by Cold Dark Matter (CDM), and gravitationally self-bound objects referred to as dark matter halos are the fundamental building blocks of structure formation (see Mo et al 2010, for a comprehensive review). Dark matter halos are the natural sites of galaxy formation (White & Rees 1978; Blumenthal et al 1984), and so a detailed understanding of the buildup and evolution of halos is a key ingredient of any theory of structure growth. The mass density profile of dark matter halos is well-described by a double power law known as the NFW profile (Navarro et al 1997), an approximation that remains reasonably accurate across most of cosmic time ( see Ludlow et al 2013, for shortcomings of this approximation). The concentration parameter that defines the NFW profile exhibits a well-known dependence upon total mass (e.g., Diemer & Kravtsov 2015; Child et al 2018), all halos in the fast-accretion phase tend to have similar values of concentration c ≈ 3 − 4 (Zhao et al 2003a), and as halos transition to the slow-accretion

Objectives

Discussion

Conclusion