Hierarchical bayesian inference: constraining population distribution of dark matter halo shapes via stellar streams

TL;DR

This work addresses inferring the population-level distribution of dark matter halo shapes from 2D stellar stream tracks in external galaxies. It introduces a hierarchical Bayesian framework that combines multiple low-information streams using a fast, JAX-accelerated forward-modeler (StreaMAX) to infer the distribution of halo flattening $q$ in axisymmetric NFW potentials. Individual 2D stream fits yield broad, potentially multimodal constraints on $q$ and orientation due to projection degeneracies; however, aggregating ~35 simulated streams via hierarchical reweighting recovers the population mean and dispersion of $q$, yielding clear discrimination among oblate, spherical, and prolate populations. The approach scales linearly with sample size and is poised to exploit forthcoming data from Euclid and Rubin/LSST to perform population-level inferences of halo morphology with no kinematic information.

Abstract

Stellar streams, the debris of tidally disrupted satellites, trace their host's gravitational potential and thus probe dark matter halo structure. While six-dimensional phase-space data of Galactic streams enable precise dark matter halo modelling in the Milky Way, streams around external galaxies are typically available only as low surface brightness features without kinematics (i.e. two-dimensional photometric data), providing only weak constraints when considered individually. We present a hierarchical Bayesian framework that infers the population distribution of halo flattening using only projected stream tracks. Streams are forward-modelled in StreaMAX, a new JAX-accelerated particle-spray package that achieves orders of magnitude faster stream generation when compared to traditional methods. For each stream we fit an axisymmetric dark matter halo model and obtain a posterior on the flattening. These posteriors are then combined through hierarchical reweighting to constrain the population distribution. Using mock data, we show that individual fits recover the correct flattening with modest precision and exhibit projection-induced multi-modalities. Nevertheless, aggregating these fits yields accurate and confident constraints on the underlying population distribution of dark matter halo morphologies, clearly distinguishing between oblate, spherical, and prolate populations. The total computational cost scales linearly with sample size. Our results demonstrate that ensembles of purely photometric streams carry sufficient information to constrain dark matter halo shapes in external galaxies at the population level. With the forthcoming samples from Euclid and Rubin/LSST, this approach offers a practical path to population-level inferences of halo morphology without any kinematic measurements.

Figures (9)

• Figure 1: Time required to model a tidal stream as a function of the number of particles, using identical integration settings across Gala and StreaMAX on both CPU and GPU. CPU tests were performed on a 44-core node, and GPU tests use an NVIDIA L4. StreaMAX outperforms the conventional package, with the GPU version delivering the fastest and flattest scaling with particle number.
• Figure 2: Schematic representation showing the coordinate system of the axisymmetric NFW potential (grey grid), the halo flattened axis $\boldsymbol{r}$, and the progenitor’s present-day phase-space location (black circle). The origin is fixed and taken as the centre of the DM halo.
• Figure 3: Corner plot for a single projected stream fit (13 parameters). Posteriors are shown in blue and the ground truth in red. The mock data include 2% Gaussian radial noise. Overall, the posteriors recover the truth, though several degeneracies remain (see Section \ref{['Degen']}).
• Figure 4: Summary of the 1000 samples drawn uniformly at random from the posterior (blue) compared to the ground truth (red) for a single stream. Shading indicates the 1, 2, and 3$\sigma$ drawned sample envelopes. Left: Comparison between the samples to the mock data on the $XY$ plane. Middle: Same comparaison in the radial distance versus angle plan, where the likelihood is evaluated as the radial difference at fixed angle bins. Right: Radius residuals (data minus model) as a function of angle. Fits track the mock data well; larger deviations near the ends of the stream reflect lower particle counts and increased sampling noise. Residuals show no obvious bias.
• Figure 5: Joint posterior distributions showing the degeneracy of the mass of the halo ($\log_{10}(M \ [M_{\odot}])$) as a function of the mass of the progenitor ($\log_{10}(m \ [M_{\odot}])$), the velocity ($\log_{10}(\text{v} \ [\text{km/s}])$) and integration time. Ground truth is shown is red. Increasing the mass of the halo can be compensated by also increasing the mass and velocity of the progenitor while reducing the time. Without kinematic data these degeneracies cannot be broken.