Distribution functions for resonantly trapped orbits in the Galactic disc

Abstract

The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric system. Such an Eulerian linearized treatment however leads to singularities at resonances, which prevent quantitative comparisons with data. Here, we manage to capture the behaviour of the distribution function (DF) at a resonance in a Lagrangian approach, by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then follow the prescription of Binney (2016), assigning to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits only depends on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of distribution functions in action space.

8 pages, 7 figures, accepted for publication in MNRAS

References in corpus (15)

• The Gaia mission
• The Structure of the Milky Way's Bar Outside the Bulge
• Rings and Radial Waves in the Disk of the Milky Way
• Transient spirals as superposed instabilities
• Bending and Breathing Modes of the Galactic Disk
• Age velocity dispersion relations and heating histories in disc galaxies
• The power spectrum of the Milky Way: Velocity fluctuations in the Galactic disk
• Tracing the Hercules stream with Gaia and LAMOST: new evidence for a fast bar in the Milky Way
• A centrally heated dark halo for our Galaxy
• The vertical effects of disc non-axisymmetries from perturbation theory: the case of the Galactic bar
• Staying away from the bar: the local dynamical signature of slow and fast bars in the Milky Way
• A fast algorithm for estimating actions in triaxial potentials
• The structural evolution of galaxies with both thin and thick discs
• Managing resonant trapped orbits in our Galaxy
• Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs

Cited by in corpus (17)

• Resonance sweeping by a decelerating Galactic bar
• Trapped orbits and solar-neighbourhood kinematics
• Orbital tori for non-axisymmetric galaxies
• Trimodal structure of Hercules stream explained by originating from bar resonances
• Galactic Bar Resonances Inferred from Kinematically Hot Stars in Gaia EDR3
• Identifying resonances of the Galactic bar in Gaia DR2: II. Clues from angle space
• Oscillating dynamical friction on galactic bars by trapped dark matter
• Tracing Hercules in Galactic azimuth with Gaia DR2
• The bar resonances and low angular momentum moving groups in the Galaxy revealed by stellar ages
• On the phase-mixed eccentricity and inclination distributions of wide binaries in the Galaxy
• The ACTIONFINDER: An unsupervised deep learning algorithm for calculating actions and the acceleration field from a set of orbit segments
• Impact of bar resonances in the velocity-space distribution of the solar neighbourhood stars in a self-consistent $N$-body Galactic disc simulation
• Radial and azimuthal gradients of the moving groups in Gaia DR3: The slow/fast bar degeneracy problem
• A non-axisymmetric potential for the Milky Way disk
• Dynamical streams in the local stellar halo
• Galactic echoes
• Perturbed distribution functions with accurate action estimates for the Galactic disc