A review of action estimation methods for galactic dynamics

Abstract

We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent, or iterative, methods are able to recover the actions to arbitrarily high accuracy given sufficient computing time. Faster non-convergent methods rely on the potential being sufficiently close to a separable potential and the accuracy of the action estimate cannot be improved through further computation. We critically compare the accuracy of the methods and the required computation time for a range of orbits in an axisymmetric multi-component Galactic potential. We introduce a new method for estimating actions that builds on the adiabatic approximation of Schönich & Binney (2012) and discuss the accuracy required for the actions, angles and frequencies using suitable distribution functions for the thin and thick discs, the stellar halo and a star stream. We conclude that for studies of the disc and smooth halo component of the Milky Way the most suitable compromise between speed and accuracy is the Stäckel Fudge, whilst when studying streams the non-convergent methods do not offer sufficient accuracy and the most suitable method is computing the actions from an orbit integration via a generating function. All the software used in this study can be downloaded from https://github.com/jls713/tact.

15 pages, 7 figures, accepted for publication in MNRAS (new subsection on resonant trapping), associated software downloadable at https://github.com/jls713/tact

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Cited by in corpus (73)

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• The Sausage Globular Clusters
• Dark matter local density determination: recent observations and future prospects
• Isochrone ages for ~3 million stars with the second Gaia data release
• The mass of our Milky Way
• The Galactic Disc in Action Space as seen by Gaia DR2
• The Milky Way Halo in Action Space
• The signatures of the resonances of a large Galactic bar in local velocity space
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• Stellar Initial Mass Function Varies with Metallicities and Time
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• Dark Shards: velocity substructure from Gaia and direct searches for dark matter
• Bending Waves in the Milky Way's disc from halo substructure
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• Stellar ages, masses, extinctions and orbital parameters based on spectroscopic parameters of Gaia DR3
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• Stellar halo substructure generated by bar resonances
• Cosmic phylogeny: reconstructing the chemical history of the solar neighbourhood with an evolutionary tree
• The dynamically selected stellar halo of the Galaxy with Gaia and the tilt of the velocity ellipsoid
• Trojans in the Solar Neighborhood
• Galactic potential constraints from clustering in action space of combined stellar stream data
• Action-based distribution function modelling for constraining the shape of the Galactic dark matter halo
• A self-consistent dynamical model of the Milky Way disc adjusted to Gaia data
• Migration and Mixing in the Galactic Disc from Encounters between Sagittarius and the Milky Way
• Modelling the Milky Way's globular cluster system
• The Gaia-ESO Survey: Dynamical models of flattened, rotating globular clusters
• Orbital Torus Imaging: Using Element Abundances to Map Orbits and Mass in the Milky Way
• Measuring the vertical response of the Galactic disc to an infalling satellite
• Spiral-like features in the disc revealed by Gaia DR3 radial actions
• Action-based Dynamical Modelling for the Milky Way Disk
• Predicting the dark matter velocity distribution in galactic structures: tests against hydrodynamic cosmological simulations
• Variations in $\alpha$-element ratios trace the chemical evolution of the disk
• Age dissection of the vertical breathing motions in Gaia DR2: evidence for spiral driving
• Action-based models for dwarf spheroidal galaxies and globular clusters
• Managing resonant trapped orbits in our Galaxy
• A kinematic calibration of the O-rich Mira variable period-age relation from Gaia
• A new resonance-like feature in the outer disc of the Milky Way
• A new dynamically self-consistent version of the Besançon Galaxy Model
• The Implications of Local Fluctuations in the Galactic Midplane for Dynamical Analysis in the Gaia Era
• Action-based Dynamical Modeling for the Milky Way Disk: The Influence of Spiral Arms
• Dark matter local density determination based on recent observations
• The ACTIONFINDER: An unsupervised deep learning algorithm for calculating actions and the acceleration field from a set of orbit segments
• Towards a more rigorous treatment of uncertainties on the velocity distribution of dark matter particles for capture in stars
• Torus Models of the Outer Disc of the Milky Way using LAMOST Survey Data
• Time-dependent Pattern Speeds in Barred Galaxies
• Dwarf spheroidal $J$-factor likelihoods for generalized NFW profiles
• Characterizing the 3D Kinematics of Young Stars in the Radcliffe Wave
• Classification of gamma-ray targets for velocity-dependent and subhalo-boosted dark-matter annihilation
• Deciphering the Milky Way disc formation time encrypted in the bar chrono-kinematics
• A non-axisymmetric potential for the Milky Way disk
• Exploring the ex-situ components within Gaia DR3
• Self-consistent modelling of our Galaxy with Gaia data
• Orbital phase-driven biases in Galactic mass constraints from stellar streams
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• Fundamental limits to orbit reconstruction due to non-conservation of stellar actions in a Milky Way-like simulation
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• An Empirical Proxy for the Second Integral of Motion in Rotating Barred or Tri-axial Potentials
• N-body self-consistent stars-halo modeling of the Fornax dwarf galaxy
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• Self-consistent modelling of the Milky Way's Nuclear Stellar Disc
• Dynamical Models of the Milky Way in Action Space with LAMOST DR8 and GAIA EDR3