From metallicity distributions to mutual information: A new perspective on stellar halo assembly

TL;DR

This work presents an information-theoretic framework to quantify the spatial–chemical structure of Milky Way–mass stellar halos by computing the mutual information $I_r(X;Z)$ between angular position and metallicity class, using five Aquarius halos. By analyzing MDFs, whole-sky anisotropy, and angular–metallicity coupling—with and without bound satellites—the authors show that the outer halo preserves stronger spatial–chemical coherence tied to accreted substructures, while satellite debris largely drives the full-halo signal. The results highlight a consistent pattern: low-metallicity stars are more anisotropic and more strongly coupled to sky position, reflecting numerous disrupted progenitors, whereas high-metallicity stars retain memory of a few massive, centrally deposited mergers. The information-theoretic diagnostics complement traditional MDF and anisotropy analyses, offering a robust, model‑independent tool for comparing simulations with future high-dimensional Galactic survey data and for tracing the fossil record of hierarchical halo assembly.

Abstract

The metallicity structure of stellar halos encodes the fossil record of galaxy assembly, tracing the chemical evolution and dynamical imprint of past mergers. Using five Milky Way-mass halos from the Aquarius simulations, we introduce an information-theoretic framework to quantify spatial-chemical correlations through the mutual information (MI) between angular position and metallicity. We divide stars in each halo into high- and low-metallicity populations based on their median metallicity and examine their metallicity distribution functions (MDFs), spatial anisotropies, and angular-metallicity couplings as a function of galactocentric radius. The MDFs exhibit remarkable diversity, ranging from single-peaked distributions dominated by one or two massive progenitors to broad or bimodal forms shaped by multiple accretion events, revealing the stochastic nature of halo assembly. The low-metallicity stars, primarily contributed by disrupted satellites, display higher spatial anisotropy and stronger angular clustering than their metal-rich counterparts. After removing bound satellites, anisotropy decreases significantly, yet high-metallicity stars remain marginally more anisotropic, reflecting the lingering debris of massive, centrally deposited progenitors. The mutual information between angular position and metallicity increases with radius before saturating in the outskirts, with the difference between the data and randomized controls confined mainly to the inner halo signifying residual spatial-chemical coupling driven by incomplete phase mixing. Our results demonstrate that information-theoretic diagnostics provide a powerful and intuitive way to quantify the chemical complexity of stellar halos and offer a promising route to compare simulations with forthcoming high-dimensional Galactic survey data.

Figures (7)

• Figure 1: This shows the metallicity distribution functions (MDFs) for the five Aquarius stellar halos. Red curves show the MDF of the total stellar halo, black curves correspond to the halo after removing bound satellites, and blue curves represent the contribution from satellites alone. The variation in MDF shape among the halos from single-peaked to bimodal and satellite-dominated reflects their diverse chemical and dynamical assembly histories.
• Figure 2: This shows the spatial anisotropy parameter as a function of galactocentric distance for high- and low-metallicity stellar populations in the five Aquarius halos with bound satellites. Each panel corresponds to one halo (Aq-A to Aq-E) including satellites. The low-metallicity stars generally exhibit stronger anisotropy, reflecting their origin in spatially coherent accreted substructures, while high-metallicity stars tend to be more isotropically distributed. The 1$\sigma$ error bars shown here are obtained from 10 jackknife samples drawn from the respective datasets.
• Figure 3: This shows the spatial anisotropy parameter as a function of galactocentric distance for high- and low-metallicity stellar populations in the five Aquarius halos after removing bound satellites. Each panel corresponds to one halo (Aq-A to Aq-E). The overall anisotropy decreases significantly after satellite removal, but a subtle trend remains: high-metallicity stars are systematically more anisotropic than their low-metallicity counterparts, reflecting the less isotropic spatial distribution of stars originating from a few massive, early-accreted progenitors. The 1$\sigma$ error bars are computed using 10 jackknife resamples generated from each dataset.
• Figure 4: This shows the mutual information $I_{r}(X;Z)$ between angular position ($X$) and metallicity ($Z$) as a function of galactocentric distance for the five Aquarius stellar halos (Aq-A to Aq-E), including satellites. The dot-dashed black lines show the actual halos, while the solid green lines correspond to randomized controls with shuffled metallicity labels. The steady increase and divergence from the randomized curves demonstrate that spatial-chemical correlations strengthen with radius, tracing the growing dominance of anisotropic, chemically distinct accreted substructures. The outer plateau marks the transition to a smoother, dynamically mixed halo component. The 1$\sigma$ errorbars are derived from 10 jackknife samples taken from the underlying datasets.
• Figure 5: This shows the radial profiles of the difference $\Delta I_{r}(X;Z) = I_{r}^{\mathrm{data}} - I_{r}^{\mathrm{rand}}$ for the five Aquarius stellar halos. This difference isolates the genuine spatial-chemical coupling beyond random expectation. The increasing $\Delta I_{r}(X;Z)$ with galactocentric distance indicates that the outer halos are chemically and spatially more correlated, retaining signatures of their hierarchical assembly.