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We develop a linear perturbative formalism to compute the response of aninhomogeneous stellar disk embedded in a non-responsive dark matter halo toperturbations like bars, spiral arms and satellite galaxy encounters. Withoutself-gravity to reinforce it, the response of a Fourier mode phase mixes awaydue to an intrinsic spread in the vertical ($\Omega_z$), radial ($\Omega_r$)and azimuthal ($\Omega_\phi$) frequencies, giving rise to local phase-spacespirals. Collisional diffusion due to scattering of stars by structures likegiant molecular clouds causes super-exponential damping of the phase-spiralamplitude. The $z-v_z$ phase-spiral is 1-armed (2-armed) for verticallyanti-symmetric (symmetric) bending (breathing) modes. Only transientperturbations with timescales ($\tau_{\mathrm{P}}$) comparable to the verticaloscillation period ($\tau_z \sim 1/\Omega_z$) trigger $z-v_z$ phase-spirals.Each $(n,l,m)$ mode of the response to impulsive($\tau_{\mathrm{P}}<\tau=1/(n\Omega_z+l\Omega_r+m\Omega_\phi)$) perturbationsis power law ($\sim \tau_{\mathrm{P}}/\tau$) suppressed, but that to adiabatic($\tau_{\mathrm{P}}>\tau$) perturbations is exponentially weak ($\sim\exp{\left[-\left(\tau_{\mathrm{P}}/\tau\right)^\alpha\right]}$) exceptresonant ($\tau\to \infty$) modes. Slower ($\tau_{\mathrm{P}}>\tau_z$)perturbations, e.g., distant encounters with satellite galaxies, inducestronger bending modes. If the Gaia phase-spiral was triggered by a satellite,Sagittarius is the leading contender as it dominates the Solar neighborhoodresponse of the Milky Way disk to satellite encounters. However, survivalagainst collisional damping necessitates that the impact occurred within $\sim0.6-0.7$ Gyr ago. We discuss how the detailed galactic potential dictates thephase-spiral shape: phase mixing occurs slower and phase-spirals are less woundin the outer disk and in presence of an ambient halo.

astrophysical journal/the astrophysical journal

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