$\texttt{StreamSculptor}$: Hamiltonian Perturbation Theory for Stellar Streams in Flexible Potentials with Differentiable Simulations

TL;DR

This paper introduces a novel differentiable simulation framework combined with Hamiltonian perturbation theory to model stellar streams in complex, disequilibrium galactic potentials, enabling detailed analysis of dark matter subhalo effects.

Contribution

It develops a direct, efficient forward mode differentiation of Hamilton's equations to model stream perturbations in observable coordinates, accommodating arbitrary subhalo potentials and non-linear effects.

Findings

Predicted stream velocity dispersion as a function of subhalo properties.

Constrained low-mass subhalo population down to ~10^5 solar masses.

Observed GD-1 stream data aligns with CDM subhalo predictions.

Abstract

Stellar streams retain a memory of their gravitational interactions with small-scale perturbations. While perturbative models for streams have been formulated in action-angle coordinates, a direct transformation to these coordinates is only available for static and typically axisymmetric models for the galaxy. The real Milky Way potential is in a state of disequilibrium, complicating the application of perturbative methods around an equilibrium system. Here, we utilize a combination of differentiable simulations and Hamiltonian perturbation theory to model the leading-order effect of dark matter subhalos on stream observables. To obtain a perturbative description of streams, we develop a direct and efficient forward mode differentiation of Hamilton's equations of motion. Our model operates in observable coordinates, allowing us to treat the effects of arbitrary subhalo potentials on streams perturbatively, while simultaneously capturing non-linear effects due to other substructures like the infalling LMC or the rotating bar. The model predicts the velocity dispersion of streams as a function of subhalo statistics, allowing us to constrain the low-mass range of subhalos down to $\sim 10^5~M_\odot$. We forecast the velocity dispersion of the GD-1 stream, and find that observations are in agreement with a CDM subhalo population, with a slight preference for more dense subhalos. The method provides a new approach to characterize streams in the presence of substructure, with significantly more modeling flexibility compared to previous works.