On the self-consistent time-dependent linearized response of stellar discs to external perturbations

Dootson, Dominic; Magorrian, John

doi:10.48550/arxiv.2205.15725

“…Besides triggering coherent point mode oscillations that make the phase spiral less wound, self-gravity can also enhance the amplitude of the phase-mixing component of the response, thus increasing the density contrast of the phase spiral. Recent work by Dootson & Magorrian (2022) has shed some light on the selfgravitating response of razor-thin disks to bar perturbations, while that by Widrow (2023) has investigated the impact of self-gravity on vertical phase spirals in a shearing box for impulsive perturbations. However, a more generic theoretical description of the self-gravitating response of inhomogeneous, thick disks to general perturbations (bars, spiral arms, satellite galaxies, etc.)…”

Section: Discussionmentioning

confidence: 99%

A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Nonresponsive Dark Matter Halo

Banik

¹

,

Bosch

²

,

Weinberg

³

2023

ApJ

1

0

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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. The z–v z phase 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 ( ∼ exp − τ P / τ α ) 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.

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“…However, self-gravity can enhance the amplitude of the phase-spiral. Although recent developments (Dootson & Magorrian 2022) have shed some light on the self-gravitating response of razor-thin disks to bar perturbations, a more generic theoretical description of the self-gravitating response of inhomogeneous, thick disks to general perturbations (bars, spiral arms, satellite galaxies, etc) is still lacking. We hope to include the effects of self-gravity on disk perturbations in future work.…”

Section: Discussionmentioning

confidence: 99%

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

Banik

¹

,

Weinberg

²

,

Bosch

³

2022

ApJ

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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.

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“…The interested reader should refer to Section 3.1 for some quantitative estimates. We emphasize that we make no attempt at selfconsistency here, as we simply impose a diffusion coefficient by hand, rather than calculating it from f. Similarly, we do not account at any stage for the self-gravity of the perturbed dark matter DF; in other words, the particles interact only with the bar, not with each other (Weinberg 1985;Dootson & Magorrian 2022).…”

Section: Kinetic Theory Near a Resonancementioning

confidence: 99%

Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

Hamilton,

Tolman,

Arzamasskiy

et al. 2023

ApJ

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The secular evolution of disk galaxies is largely driven by resonances between the orbits of “particles” (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari, and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies—effects that have, with few exceptions, been previously explored only with complex N-body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles’ slow actions. We solve this equation for various values of the dimensionless diffusion strength Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 0, we find that diffusion suppresses phase mixing, leading to a finite torque. Our results suggest that stochasticity—be it physical or numerical—tends to increase bar–halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.

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On the self-consistent time-dependent linearized response of stellar discs to external perturbations

Cited by 8 publications

References 21 publications

A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Nonresponsive Dark Matter Halo

A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Nonresponsive Dark Matter Halo

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

Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

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