Actions for axisymmetric potentials

By J. Binney. 2012

165 citations recorded by the source corpus.

We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of thick-disc stars, the errors in the actions are typically smaller than 2 per cent. We describe a scheme for obtaining actions by interpolation on tabulated values that significantly accelerates the process of calculating observables quantities, such as density and velocity moments, from a distribution function.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/5dfd78686ad991514fbb73f004c02756d0184ed8

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Citations in the corpus

The origin of accreted stellar halo populations in the Milky Way using APOGEE,Gaia, and the EAGLE simulations (2018, methodology): “…of Mackereth & Bovy (2018), which adapts the Stäckel fudge method for estimating action-angle coordinates in axisymmetric potentials (presented in Binney 2012) to directly estimate the orbital eccentricity, e, apo- and pericentre radii, rap and rperi, and the maximum vertical excursion, Zmax, to…”
Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble (2018, methodology): “In a general axisymmetric potential, the action integrals can be computed from positions and velocities, J = J(x, v), with the ‘Staeckel Fudge’ algorithm (Binney 2012).”
The GALAH+ survey: Third data release (2020, methodology): “To estimate actions, eccentricity, maximum orbit Galactocentric height, and apocentre/pericentre radii, we use galpy’s actionAngleStaeckel approximations via the Staeckel fudge (Binney 2012) with a focus of 0.45 and the method by Mackereth & Bovy (2018).”
The Sausage Globular Clusters (2018, methodology): “Historically, actions were cumbersome to calculate, but recent theoretical advances have transformed the situation (e.g., Binney 2012; Sanders & Binney 2016).”
galpy: A python LIBRARY FOR GALACTIC DYNAMICS (2014, methodology): “This gridding approach is slightly different from that of Binney (2012), who uses a grid in (Lz,E,Er ), where Er is a radial energy given by Equation (18) of Binney (2012).”
A DIRECT DYNAMICAL MEASUREMENT OF THE MILKY WAY'S DISK SURFACE DENSITY PROFILE, DISK SCALE LENGTH, AND DARK MATTER PROFILE AT 4 kpc ≲ R ≲ 9 kpc (2013, methodology): “(6) Binney (2012a) discusses how the choice of ∆ influences the precision with which the actions are calculated.”
The local dark matter density (2014, methodology): “The ‘Stäckel action’ approximation is then required in order to map the observables [x,v] onto the actions J that appear in equation 23 for a given potential Φ(R, z) (Binney, 2012a).”
Proper motions and dynamics of the Milky Way globular cluster system fromGaiaDR2 (2018, methodology): “The actions and angles are estimated using the Stäckel fudge approach (Binney 2012, see also Sanders & Binney 2016 for an overview of action computation methods), as implemented in the Agama galaxy modelling framework (Vasiliev 2018).”
Dynamics for galactic archaeology (2013, methodology): “McMillan & Binney (2012) used orbital tori to investigate our ability to infer the df of a population from various combinations of photometry, astrometry and measurements of line-of-sight velocities.”
Constraining the Galaxy's dark halo with RAVE stars (2014, methodology): “We use the ‘Stäckel Fudge’ introduced by Binney (2012a) to evaluate the Ji given phase-space coordinates (x, v).”
The Milky Way’s stellar disk (2013, methodology): “…azimuthal and vertical actions J ≡ ( JR, Jφ ≡ Lz, Jz ) of the form f(JR, Lz, Jz|λJ ) =f̃(Lz) [ κ(Lz) CR(Lz) exp ( −κ(Lz)JR CR(Lz) ) ] × [ κ(Lz) DR(Lz) exp ( −ν(Lz)Jz DR(Lz) ) ] (11) seems like a sensible choice (Binney 2012), where λJ is a set of parameters to describe the distribution function.”