How much can we learn from resolved stellar kinematics of galactic haloes using action-based dynamical models?

TL;DR

This work extends axisymmetric, action-based dynamical modelling to external galaxies to quantify how much can be learned from resolved halo tracers when phase-space information is incomplete. By combining a multi-component potential with a generalized action-space distribution function for the stellar halo and employing Bayesian inference with careful marginalisation over missing dimensions, the authors recover total and DM mass profiles robustly, while the DM halo flattening parameter $q_{DM}$ remains weakly constrained under 3D or 4D data. The results, validated on idealised mocks and a cosmological Auriga-23 halo, are corroborated by Schwarzschild orbit-superposition tests, which show the flattening degeneracy is a general feature of dynamical modelling rather than a DF-specific issue. Methodological advances in marginalisation (deprojection via Gaussians, importance sampling, and low-discrepancy sampling) improve efficiency and reliability, enabling application to nearby systems like M31. Overall, the paper demonstrates the potential and limits of action-based dynamical models for constraining galactic mass distributions with limited kinematic information, and highlights the value of combining complementary dynamical approaches and external streams to break degeneracies.

Abstract

Dynamical models are used to study dark matter (DM) in galaxies, how galaxies assemble through mergers, and to test galaxy formation models. Despite its widespread use, there has been no systematic study quantifying how much information can be obtained from just two on-sky positions and line-of-sight velocities, which are typically available for nearby external galaxies. In this work, we introduce axisymmetric, action-based dynamical models that use the positions and velocities of stellar halo stars to jointly constrain the total mass distribution of galaxies and the underlying DM component, as well as the stellar halo phase-space distribution. We rigorously test the method using both idealised equilibrium galaxy mocks and cosmological hydrodynamical simulations from the Auriga suite, systematically assessing how its performance degrades as the available phase-space information is progressively reduced. We further examine the impact of galaxy inclination, modelling assumptions, and methodological systematics on the recovered mass profiles. A crucial development in this work is the improved marginalisation of the model likelihood over missing phase-space dimensions. Our models successfully recover the total and DM mass distributions, as well as the kinematic properties of the stellar tracers, within the derived confidence intervals. However, we find that with limited (3D or 4D) phase-space information, the flattening of the DM halo cannot be constrained with any degree of certainty. Nevertheless, the recovered mass profile is insensitive to the flattening. This finding is independently validated by Schwarzschild modelling tests.

Figures (17)

• Figure 1: The different orientations investigated for the galaxy: $i=0^{\circ}$ (face-on), $i=45^{\circ}$, and $i=90^{\circ}$ (edge-on) with respect to the axisymmetry plane which is defined by the orientation of the galactic disc.
• Figure 2: The recovery of the inclination angle for the idealised mock tests with 3D phase space availability. Different coloured lines correspond to fits to four independent data realisations.
• Figure 3: Total enclosed mass profiles of the best-fit models (coloured lines) compared to the true mass distribution of the mock galaxy (black dotted line) for inclination angles (a) ${i=0^{\circ}}$, (b) ${i=45^{\circ}}$, and (c) ${i=90^{\circ}}$, where the tracers used to constrain the potential have 3D phase-space information. The different coloured lines correspond to fits to four independent data realisations. Shaded regions indicate the 1$\sigma$ uncertainties.
• Figure 4: DM enclosed mass profiles of the best-fit models (coloured lines) compared to the true mass distribution of the mock galaxy (black dotted line) for inclination angles (a) ${i=0^{\circ}}$, (b) ${i=45^{\circ}}$, and (c) ${i=90^{\circ}}$, where the tracers used to constrain the potential have 3D phase-space information. The different coloured lines correspond to fits to four independent data realisations. Shaded regions indicate the 1$\sigma$ uncertainties.
• Figure 5: The posterior distribution of the DM flattening parameter $q_\mathrm{DM}$ for all inclinations and data set realisations (coloured lines): ${i=0^{\circ}}$, ${i=45^{\circ}}$, and ${i=90^{\circ}}$, where the tracers used to constrain the potential have 3D phase-space information. The different coloured lines correspond to fits to four independent data realisations. The solid black line is the true value of the parameter used to generate the mock galaxies ($q_\mathrm{DM,\, true}=0.7$).