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We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a nonresponsive dark matter (DM) halo to various perturbations like bars, spiral arms, and encounters with satellite galaxies. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Ω_z), radial (Ω_r), and azimuthal (Ω_ϕ) frequencies, triggering local phase-space spirals. The detailed galactic potential dictates the shape of phase spirals: phase mixing occurs more slowly and thus phase spirals are more loosely wound in the outer disk and in the presence of an ambient DM halo. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes superexponential damping of the phase spiral amplitude. Thez–v_zphase spiral is one-armed (two-armed) for vertically antisymmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (τ_P) comparable to the vertical oscillation period (τ_z∼ 1/Ω_z) can trigger vertical phase spirals. Each (n,l,m) mode of the response to impulsive (τ_P<τ= 1/(nΩ_z+lΩ_r+mΩ_ϕ)) perturbations is power-law (∼τ_P/τ) suppressed, but that to adiabatic (τ_P>τ) perturbations is exponentially weak ($\sim \exp \left[-{\left({\tau }_{\mathrm{P}}/\tau \right)}^{\alpha }\right]$) except for resonant (τ→ ∞ ) modes. Slower (τ_P>τ_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. Sagittarius (Sgr) dominates the solar neighborhood response of the Milky Way (MW) disk to satellite encounters. Thus, if the Gaia phase spiral was triggered by a MW satellite, Sgr is the leading contender. However, the survival of the phase spiral against collisional damping necessitates an impact ∼0.6–0.7 Gyr ago.

 

Many disc galaxies host galactic bars, which exert time-dependent, non-axisymmetric forces that can alter the orbits of stars. There should be both angle and radius dependences in the resulting radial rearrangement of stars (‘radial mixing’) due to a bar; we present here novel results and trends through analysis of the joint impact of these factors. We use an N-body simulation to investigate the changes in the radial locations of star particles in a disc after a bar forms by quantifying the change in orbital radii in a series of annuli at different times post bar formation. We find that the bar induces both azimuth angle- and radius-dependent trends in the median distance that stars have travelled to enter a given annulus. Angle-dependent trends are present at all radii we consider, and the radius-dependent trends roughly divide the disc into three ‘zones’. In the inner zone, stars generally originated at larger radii and their orbits evolved inwards. Stars in the outer zone likely originated at smaller radii and their orbits evolved outwards. In the intermediate zone, there is no net inwards or outwards evolution of orbits. We adopt a simple toy model of a radius-dependent initial metallicity gradient and discuss recent observational evidence for angle-dependent stellar metallicity variations in the Milky Way in the context of this model. We briefly comment on the possibility of using observed angle-dependent metallicity trends to learn about the initial metallicity gradient(s) and the radial rearrangement that occurred in the disc.

 

Studying coupling between different galactic components is a challenging problem in galactic dynamics. Using basis function expansions (BFEs) and multichannel singular spectrum analysis (mSSA) as a means of dynamical data mining, we discover evidence for two multicomponent disc–halo dipole modes in a Milky-Way-like simulated galaxy. One of the modes grows throughout the simulation, while the other decays throughout the simulation. The multicomponent disc–halo modes are driven primarily by the halo, and have implications for the structural evolution of galaxies, including observations of lopsidedness and other non-axisymmetric structure. In our simulation, the modes create surface density features up to 10 per cent relative to the equilibrium model stellar disc. While the simulated galaxy was constructed to be in equilibrium, BFE + mSSA also uncovered evidence of persistent periodic signals incited by aphysical initial conditions disequilibrium, including rings and weak two-armed spirals, both at the 1 per cent level. The method is sensitive to distinct evolutionary features at and even below the 1 per cent level of surface density variation. The use of mSSA produced clean signals for both modes and disequilibrium, efficiently removing variance owing to estimator noise from the input BFE time series. The discovery of multicomponent halo–disc modes is strong motivation for application of BFE + mSSA to the rich zoo of dynamics of multicomponent interacting galaxies.

 

We present a novel method for constraining the length of the Galactic bar using 6D phase-space information to directly integrate orbits. We define a pseudo-length for the Galactic bar, named RFreq, based on the maximal extent of trapped bar orbits. We find the RFreq measured from orbits is consistent with the RFreq of the assumed potential only when the length of the bar and pattern speed of said potential is similar to the model from which the initial phase-space coordinates of the orbits are derived. Therefore, one can measure the model’s or the Milky Way’s bar length from 6D phase-space coordinates by determining which assumed potential leads to a self-consistent measured RFreq. When we apply this method to ≈210 000 stars in APOGEE DR17 and Gaia eDR3 data, we find a consistent result only for potential models with a dynamical bar length of ≈3.5 kpc. We find the Milky Way’s trapped bar orbits extend out to only ≈3.5 kpc, but there is also an overdensity of stars at the end of the bar out to 4.8 kpc which could be related to an attached spiral arm. We also find that the measured orbital structure of the bar is strongly dependent on the properties of the assumed potential.

 

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 analogs of disks to perturbations with diverse spatiotemporal 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 (τ_P) to the local, vertical oscillation time (τ_z) ultimately decides which of the two modes is excited. Faster, more impulsive (τ_P<τ_z) and slower, more adiabatic (τ_P>τ_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.

 

ABSTRACT Flattened axisymmetric galactic potentials are known to host minor orbit families surrounding orbits with commensurable frequencies. The behaviour of orbits that belong to these orbit families is fundamentally different than that of typical orbits with non-commensurable frequencies. We investigate the evolution of stellar streams on orbits near the boundaries between orbit families (separatrices) in a flattened axisymmetric potential. We demonstrate that the separatrix divides these streams into two groups of stars that belong to two different orbit families, and that as a result, these streams diffuse more rapidly than streams that evolve elsewhere in the potential. We utilize Hamiltonian perturbation theory to estimate both the time-scale of this effect and the likelihood of a stream evolving close enough to a separatrix to be affected by it. We analyse two prior reports of stream-fanning in simulations with triaxial potentials, and conclude that at least one of them is caused by separatrix divergence. These results lay the foundation for a method of mapping the orbit families of galactic potentials using the morphology of stellar streams. Comparing these predictions with the currently known distribution of streams in the Milky Way presents a new way of constraining the shape of our Galaxy’s potential and distribution of dark matter.