Charting galactic accelerations: when and how to extract a unique potential from the distribution function

  title={Charting galactic accelerations: when and how to extract a unique potential from the distribution function},
  author={J. An and Aneesh P. Naik and N. W. Evans and Clare Burrage},
  journal={Monthly Notices of the Royal Astronomical Society},
The advent of data sets of stars in the Milky Way with 6D phase-space information makes it possible to construct empirically the distribution function (DF). Here, we show that the accelerations can be uniquely determined from the DF using the collisionless Boltzmann equation, providing the Hessian determinant of the DF with respect to the velocities is non-vanishing. We illustrate this procedure and requirement with some analytic examples. Methods to extract the potential from data sets of… Expand

Figures from this paper


The distribution function of the Galaxy's dark halo
Starting from the hypothesis that the Galaxy's dark halo responded adiabatically to the infall of baryons, we have constructed a self-consistent dynamical model of the Galaxy that satisfies a largeExpand
Is the dark halo of the Milky Way prolate
We introduce the flattening equation, which relates the shape of the dark halo to the angular velocity dispersions and the density of a tracer population of stars. It assumes spherical alignment ofExpand
Tidal Streams as Probes of the Galactic Potential
We explore the use of tidal streams from Galactic satellites for recovering the potential of the Milky Way. Our study is motivated both by the discovery of the first lengthy stellar stream in theExpand
A Universal Mass Profile for Dwarf Spheroidal Galaxies
We apply the Jeans equation to estimate masses for eight of the brightest dwarf spheroidal (dSph) galaxies. For Fornax, the dSph with the largest kinematic data set, we obtain a model-independentExpand
First Gaia dynamical model of the Milky Way disc with six phase space coordinates: a test for galaxy dynamics
We construct the first comprehensive dynamical model for the high-quality subset of stellar kinematics of the Milky Way disc, with full 6D phase-space coordinates, provided by the Gaia Data ReleaseExpand
Dipping our toes in the water: first models of GD-1 as a stream
We present a model for producing tidal streams from disrupting progenitors in arbitrary potentials, utilizing the idea that the majority of stars escape from the progenitor's two Lagrange points. TheExpand
Haloes light and dark: dynamical models of the stellar halo and constraints on the mass of the Galaxy
We develop a flexible set of action-based distribution functions (DFs) for stellar haloes. The DFs have five free parameters, controlling the inner and outer density slope, break radius, flatteningExpand
Warp, waves, and wrinkles in the Milky Way
We derive unbiased distance estimates for the Gaia-TGAS data set by correcting for the bias due to the distance dependence of the selection function, which we measure directly from the data. FromExpand
Stellar Velocity Dispersion and Anisotropy of the Milky Way Inner Halo
We measure the three components of velocity dispersion, $\sigma_{R},\sigma_{\theta},\sigma_{\phi}$, for stars within 6 < R < 30 kpc of the Milky Way using a new radial velocity sample from the MMTExpand
The total mass of the Large Magellanic Cloud from its perturbation on the Orphan stream
In a companion paper by Koposov et al., RR Lyrae from Gaia Data Release 2 are used to demonstrate that stars in the Orphan stream have velocity vectors significantly misaligned with the stream track,Expand