2023ApJ...952...65B

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 ($\sim \exp \left[-{\left({\tau }_{{\rm{P}}}/\tau \right)}^{\alpha }\right]$) 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.