The dynamical memory of tidal stellar streams: Joint inference of the Galactic potential and the progenitor of GD-1 with flow matching

TL;DR

This paper tackles the challenge of jointly constraining the Milky Way potential and the GD-1 stream progenitor from Gaia-era data using a likelihood-free approach. It introduces a framework that combines a differentiable N-body forward model (Odisseo) with Flow Matching SBI to learn the posterior over progenitor and host parameters from stream phase-space data. Validation on a fiducial GD-1 simulation shows accurate recovery of true parameters, well-calibrated posteriors, and realistic parameter degeneracies between progenitor and host properties. The approach offers a scalable, amortized path toward Galactic Archaeology and can be extended to multi-stream analyses and more realistic observational effects.

Abstract

Stellar streams offer one of the most sensitive probes of the Milky Way`s gravitational potential, as their phase-space morphology encodes both the tidal field of the host galaxy and the internal structure of their progenitors. In this work, we introduce a framework that leverages Flow Matching and Simulation-Based Inference (SBI) to jointly infer the parameters of the GD-1 progenitor and the global properties of the Milky Way potential. Our aim is to move beyond traditional techniques (e.g. orbit-fitting and action-angle methods) by constructing a fully Bayesian, likelihood-free posterior over both host-galaxy parameters and progenitor properties, thereby capturing the intrinsic coupling between tidal stripping dynamics and the underlying potential. To achieve this, we generate a large suite of mock GD-1-like streams using our differentiable N-body code \textsc{\texttt{Odisseo}}, sampling self-consistent initial conditions from a Plummer sphere and evolving them in a flexible Milky Way potential model. We then apply conditional Flow Matching to learn the vector field that transports a base Gaussian distribution into the posterior, enabling efficient, amortized inference directly from stream phase-space data. We demonstrate that our method successfully recovers the true parameters of a fiducial GD-1 simulation, producing well-calibrated posteriors and accurately reproducing parameter degeneracies arising from progenitor-host interactions. Flow Matching provides a powerful, flexible framework for Galactic Archaeology. Our approach enables joint inference on progenitor and Galactic parameters, capturing complex dependencies that are difficult to model with classical likelihood-based methods.

Figures (11)

• Figure 1: Stream morphology in different Galactic potentials. The black scatter plot is the output of the simulation for the fiducial values of BovyMWPotential2014 and the same in each sub-panel. We show the results for various combinations of 20% offset of the mass of the NFW halo and its scale radius as indicated in the legend of each sub-panel.
• Figure 2: Tidal stripping of N=$10^4$ stars from a Plummer sphere over a 3 Gyr evolution. The parameters to set this simulation where the fiducial BovyMWPotential2014 for the Galaxy and $(M_{Plummer}, a_{Plummer}) = (10^{4.05} \text{M}_\odot, 100 \; \text{pc})$ for the progenitor. The colorbar indicates the initial radial distance from the progenitor.
• Figure 3: Comparison between Rejection Sampling and Inverse Sampling of the interpolated inverse for the module of the velocity of particles sampled from a Plummer sphere.
• Figure 4: Schematic of flow matching for posterior estimation with Odisseo. The training set is generated by sampling $i=0, ..., N$ parameters $\theta^i$ from the prior $p(\theta)$, and then forward model using Odisseo to obtain the observation $d^i \sim p(d\mid\theta)$. Following the flow described in Sec. \ref{['subsection:flow_matching']}, we sample $t\sim U(0, 1)$ to train a NN to approximate the vector field $v_\phi(t, d^i, \theta^i)$. In the lower section, we report a simplified Flow matching objective for a 1D case. The NN is called for different $t$ to regress the vector field that governs the ODE to transform the sampling distribution $q_{t=0} = \mathcal{N}(0, I)$ into the posterior distribution $q_{t=1} = p(\theta \mid d)$. Note that in this schematic we refer to $\theta_1$ described in Sec. \ref{['subsection:flow_matching']} as $\theta$.
• Figure 5: Flow matching SetTransformer. We indicate with $\tilde{d}$ both the observation $d$ and the intermediate output of the layers. To embed each of the stars in the observation $d$, the parameter state $\theta_t$ at the ODE time $t$ we have used a simple MLP with 128 neurons with a SiLU activation function. Then we passed $\tilde{d}$ through 3 stacked SAB with skip connection (dashed line) to encode the correlations between the particles, modulating the output of each block on $t$ using FiLM. Then we used a CAB, with FiLM modulation, to focus the Attention mechanism on finding the relevant feature in $\tilde{d}$ to regress the parameters $\theta$. The vector field $v_\phi$ is obtained by compressing the output of the CAB through an MLP with output dimension equal to the dimensionality of $\theta$, in our case 13 dimensions.