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

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 M halo 10 11 M , including subhalos and host halos in gravity-only simulations, as well as in the IllustrisTNG 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 selfconsistently 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.

Diffstar: A Fully Parametric Physical Model for Galaxy Assembly History

“…In the basic physical picture of the Diffstar model, we assume that baryonic matter becomes available for star formation at a rate that is closely related to the growth rate of the dark matter halo. In §3.1, we review our model for halo mass assembly history, which is the same as the Diffmah model presented in Hearin et al (2021b), to which we refer the reader for additional details. In §3.2, we motivate and discuss our use of Diffmah to approximate the rate at which baryonic mass becomes available for star formation.…”

Cosmo-Paleontology: Statistics of Fossil Groups in a Gravity-Only Simulation

“…We include an inset plot to interpret three key regions of the (α late , τ c ) parameter space. In general, halos with smaller values of any of the three DIFFMAH parameters (α early , α late , and τ c ) formed earlier than halos with larger values of the same respective parameter (Hearin et al 2021).…”

“…The transition between early and late regimes is governed by the transition time τ c and transition speed k = 3.5 Gyr −1 . In gravity-only simulations such as Last Journey, this model accurately approximates mass growth for halos of present-day mass M 0 10 11 M at times t 1 Gyr (Hearin et al 2021).…”

“…While z frac offers a straightforward way to measure the formation time of halos, this metric also vastly oversimplifies the process of halo formation, which cannot be fully captured by a single statistic. In order to obtain a more complete picture of halo formation, we turn to a differentiable model of halo mass accretion history (DIFFMAH) (Hearin et al 2021). This model is based on the current understanding that halo formation consists first of a fast accretion phase, characterized by rapid mass growth and frequent merging, and then by a slow accretion phase, in which merging is less common (Bullock et al 2001;Wechsler et al 2002;Tasitsiomi et al 2004;Zhao et al 2009).…”

Efficient Gravitational Wave Template Bank Generation with Differentiable Waveforms

“…Differentiable programming has only been applied to a few domains within astrophysics so far (see e.g. [28][29][30][31][32][33][34][35][36]), where it enables fast, fully-automated fitting and approximate Bayesian inference. Here, we utilize the Python AD framework jax [22] to create differentiable frequencydomain waveforms so that we can automatically compute their parameter space metric.…”