A Comprehensive Perturbative Formalism for Phase-Mixing in Perturbed Disks. I. Phase spirals in an Infinite, Isothermal Slab

Abstract

Galactic disks are highly responsive systems that often undergo external perturbations and subsequent collisionless equilibration, predominantly via phase-mixing. We use linear perturbation theory to study the response of infinite isothermal slab analogues of disks to perturbations with diverse spatio-temporal characteristics. Without self-gravity of the response, the dominant Fourier modes that get excited in a disk are the bending and breathing modes, which, due to vertical phase-mixing, trigger local phase-space spirals that are one- and two-armed, respectively. We demonstrate how the lateral streaming motion of slab stars causes phase spirals to damp out over time. The ratio of the perturbation timescale (${\tau }_{\mathrm{P}}$) to the local, vertical oscillation time (${\tau }_z$) ultimately decides which of the two modes is excited. Faster, more impulsive (${\tau }_{\mathrm{P}}<{\tau }_z$) and slower, more adiabatic (${\tau }_{\mathrm{P}}>{\tau }_z$) perturbations excite stronger breathing and bending modes, respectively, although the response to very slow perturbations is exponentially suppressed. For encounters with satellite galaxies, this translates to more distant and more perpendicular encounters triggering stronger bending modes. We compute the direct response of the Milky Way disk to several of its satellite galaxies, and find that recent encounters with all of them excite bending modes in the Solar neighborhood. The encounter with Sagittarius triggers a response that is at least $1-2$ orders of magnitude larger than that due to any other satellite, including the Large Magellanic Cloud. We briefly discuss how ignoring the presence of a dark matter halo and the self-gravity of the response might impact our conclusions.

arXiv commentAccepted for publication in ApJ; 7 figures, 1 table

References in corpus (66)

• A Universal Density Profile from Hierarchical Clustering
• Gaia Data Release 2. Summary of the contents and survey properties
• The Gaia mission
• galpy: A Python Library for Galactic Dynamics
• SEGUE: A Spectroscopic Survey of 240,000 stars with g=14-20
• The Kinematics of the Ultra-Faint Milky Way Satellites: Solving the Missing Satellite Problem
• The Radial Velocity Experiment (RAVE): first data release
• Mass models of the Milky Way
• Gaia Data Release 2: using Gaia parallaxes
• Gaia Data Release 2: Kinematics of globular clusters and dwarf galaxies around the Milky Way
• A dynamically young and perturbed Milky Way disk
• The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution
• Vertical waves in the solar neighbourhood in Gaia DR2
• Gaia Data Release 2: Mapping the Milky Way disc kinematics
• The total mass of the Large Magellanic Cloud from its perturbation on the Orphan stream
• Galactoseismology: Discovery of Vertical Waves in the Galactic Disk
• Footprints of the Sagittarius dwarf galaxy in the $Gaia$ data set
• The wobbly Galaxy: kinematics north and south with RAVE red clump giants
• Rings and Radial Waves in the Disk of the Milky Way
• The Influence of Sagittarius and the Large Magellanic Cloud on the Milky Way Galaxy
• Vertical density waves in the Milky Way disc induced by the Sagittarius Dwarf Galaxy
• The GALAH survey and Gaia DR2: dissecting the stellar disc's phase space by age, action, chemistry and location
• Gaia Data Release 2: Properties and validation of the radial velocities
• Distribution functions for the Milky Way
• The mass and velocity anisotropy of the Carina, Fornax, Sculptor and Sextans dwarf spheroidal galaxies
• Bending and Breathing Modes of the Galactic Disk
• The origin of the Gaia phase-plane spiral
• Warp, Waves, and Wrinkles in the Milky Way
• Radial and vertical flows induced by galactic spiral arms: likely contributors to our "wobbly Galaxy''
• Chaos and Mixing in Triaxial Stellar Systems
• On the Self-Consistent Response of Stellar Systems to Gravitational Shocks
• The echo of the bar buckling: phase-space spirals in Gaia DR2
• The last breath of the Sagittarius dSph
• A re-interpretation of the Triangulum-Andromeda stellar clouds: a population of halo stars kicked out of the Galactic disk
• The Stellar Number Density Distribution in the Local Solar Neighborhood is North-South Asymmetric
• Adiabatic Invariants in Stellar Dynamics: II. Gravitational shocking
• The GALAH survey and Gaia DR2: Linking ridges, arches and vertical waves in the kinematics of the Milky Way
• Signatures of resonance and phase mixing in the Galactic disc
• The Bar--Halo Interaction--I. From Fundamental Dynamics to Revised N-body Requirements
• Excitation of coupled stellar motions in the Galactic Disk by orbiting satellites
• Adiabatic Invariants in Stellar Dynamics: I. Basic concepts
• The 4:1 Outer Lindblad Resonance of a long slow bar as a potential explanation for the Hercules stream
• The total mass and dark halo properties of the Small Magellanic Cloud
• Emergence of the Gaia Phase Space Spirals from Bending Waves
• Spiral arm crossings inferred from ridges in Gaia stellar velocity distributions
• Constraining the Milky Way Mass Profile with Phase-Space Distribution of Satellite Galaxies
• Kinematics with Gaia DR2: The Force of a Dwarf
• Modeling the Milky Way as a Dry Galaxy
• Constraints on Radial Migration in Spiral Galaxies I. Analytic Criterion for Capture at Corotation
• The velocity anisotropy of the Milky Way satellite system
• Stalling of Globular Cluster Orbits in Dwarf Galaxies
• The Stellar Distribution Function and Local Vertical Potential from Gaia DR2
• A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy
• Did Sgr cause the vertical waves in the solar neighbourhood?
• EXP: N-body integration using basis function expansions
• Vertical Phase Mixing across the Galactic Disk
• Revisiting dynamical friction: the role of global modes and local wakes
• Dynamical Friction, Buoyancy and Core-Stalling -- I. A Non-perturbative Orbit-based Analysis
• Snails Across Scales: Local and Global Phase-Mixing Structures as Probes of the Past and Future Milky Way
• A-type stars in the Canada-France Imaging Survey II. Tracing the height of the disc at large distances with Blue Stragglers
• Density Wakes due to Dynamical Friction in Cored Potentials
• Kinematics beats dust: unveiling nested substructure in the perturbed outer disc of the Milky Way
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution and the Nyquist-Shannon theorem
• Eigenfunctions of Galactic Phase Space Spirals from Dynamic Mode Decomposition
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
• A Fully General, Non-Perturbative Treatment of Impulsive Heating

Cited by in corpus (19)

• The rapid onset of stellar bars in the baryon-dominated centers of disk galaxies
• The phase spiral in Gaia DR3
• The origin and fate of the Gaia phase-space snail
• Vertical motion in the Galactic disc: unwinding the Snail
• Swing Amplification and the Gaia Phase Spirals
• Gaia DR3 features of the phase spiral and its possible relation to internal perturbations
• A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Non-responsive Dark Matter Halo
• Ripples spreading across the Galactic disc. Interplay of direct and indirect effects of the Sagittarius dwarf impact
• Growing Local arm inferred by the breathing motion
• Galactic disc heating by density granulation in fuzzy dark matter simulations
• Limitations and rotation of the two-armed phase spiral in the Milky Way stellar disc
• Two-point correlation function studies for the Milky Way: discovery of spatial clustering from disk excitations and substructure
• Galactic echoes
• Impulsive mixing of stellar populations in dwarf spheroidal galaxies
• Delayed phase mixing in the self-gravitating Galactic disc
• Minimum-entropy constraints on galactic potentials
• Chaos in violent relaxation dynamics. Disentangling micro- and macro-chaos in numerical experiments of dissipationless collapse
• The multiple corrugations in the Galactic disk derived from the LAMOST and Gaia survey data
• Correlation between the two-armed $V_R$ spiral in the $Z$--$V_Z$ plane and moving groups