Explaining dark matter halo density profiles with neural networks

TL;DR

The paper tackles why dark matter halos exhibit universal density profiles and whether the full halo mass accretion history can be inferred from present-day density profiles. It introduces an interpretable variational encoder (IVE) that compresses the 3D density field into a low-dimensional, disentangled latent space, predicting the density profile via a decoder that takes the latent $\boldsymbol{z}$ and the query radius $\log(r)$ as input. Mutual information analyses show that three latent components encode the profile normalization and the inner and outer shapes, with the inner latent linked to early assembly via $M(z)$ and the later-time accretion rate captured by the outer latent over the dynamical time $t_{\mathrm{dyn}}$. The approach reproduces the known inner-profile–formation-time relation and reveals that the outer outskirts are governed by a single parameter capturing the most recent accretion, enabling inference of accretion histories from density profiles and extending to hydrodynamical simulations.

Abstract

We use explainable neural networks to connect the evolutionary history of dark matter halos with their density profiles. The network captures independent factors of variation in the density profiles within a low-dimensional representation, which we physically interpret using mutual information. Without any prior knowledge of the halos' evolution, the network recovers the known relation between the early time assembly and the inner profile, and discovers that the profile beyond the virial radius is described by a single parameter capturing the most recent mass accretion rate. The results illustrate the potential for machine-assisted scientific discovery in complicated astrophysical datasets.

Figures (5)

• Figure 1: A neural network is trained to discover the underlying degrees of freedom in halo density profiles in the form of a latent representation, when presented with the full 3D density structure of a halo. We physically interpret the discovered representation by measuring the MI between the latent parameters and the assembly history of the halos.
• Figure 2: The MI between the latent parameters and the ground-truth halo profiles $\rho_\mathrm{true}(r)$ for the IVE$_{\mathrm{infall}}$ (top) and the IVE$_{\mathrm{virial}}$ (bottom) models. In the IVE$_{\mathrm{virial}}$ case, we also show MI with the NFW concentration. (For clarity we do not show the IVE$_{\mathrm{virial}}$ normalization latent, since it behaves identically to the IVE$_{\mathrm{infall}}$ normalization latent.)
• Figure 3: The MI between the latent parameters and the mass accretion histories (denoted MI$_{M(z)}$; top row), and that between the latent parameters and the mass accretion rate (denoted MI$_{\mathrm{d}M(z)/\mathrm{d}z}$; bottom row). The inner shape latent and the NFW concentration carry memory of the early-time mass assembly history, as well as the later-time mass accretion rate. The outer shape latent carries information about the halos' most recent mass accretion rate over the past dynamical time (indicated by the arrow).
• Figure S.1: Mean and 90$\%$ confidence interval of the residuals $\log [\rho_{\rm predicted}/\rho_{\rm true}]$ of the IVE$_{\mathrm{virial}}$ and IVE$_{\mathrm{infall}}$ models, as a function of $r_{\rm eff}$ defined as the median radius in each bin. The grey band shows the NFW residuals.
• Figure S.2: The MI between the densities on two fixed radial scales, $\rho(r_1)$ and $\rho(r_2)$, and (i) the mass accretion histories (top row) and (ii) the mass accretion rate (bottom row). The two radial scales, $r_1$ and $r_2$, are the locations at which the MI between the ground-truth profile and the inner shape latent peaks (Fig \ref{['fig:MI_latents_truth']}, bottom panel).