Gaia DR3 features of the phase spiral and its possible relation to internal perturbations

Disc stars from the Gaia DR3 RVS catalogue are selected to explore the phase spiral as a function of position in the Galaxy. The data reveal a two-armed phase spiral pattern in the local $z-v_z$ plane inside the solar radius, which appears clearly when colour-coded by $\langle v_R \rangle (z,v_z)$: this is characteristic of a breathing mode that can in principle be produced by in-plane non-axisymmetric perturbations. We note the phase spiral pattern becomes single armed outside the solar radius. When a realistic analytic model with an axisymmetric background potential plus a steadily rotating bar and 2-armed spiral arms as perturbation is used to perform particle test integrations, the pseudo stars get a prominent spiral pattern in the $\langle v_R \rangle$ map in the $x-y$ plane. Additionally, clear breathing mode evidence at a few $\rm{kms}^{-1}$ level can be seen in the $\langle v_z \rangle$ map on the $x-z$ plane, confirming that such breathing modes are non-negligible in the joint presence of a bar and spiral arms. However, no phase-spiral is perceptible in the $(z, v_z)$ plane. When an initial vertical perturbation is added to all pseudo stars to carry out the simulation, the one-armed phase spirals can clearly be seen 500~Myr after the perturbation and gradually disappear inside-out. Finally, we show as a proof of concept how a toy model of a time-varying non-axisymmetric in-plane perturbation with varying amplitude and pattern speed can produce a strong two-armed phase-spiral. We conclude a time-varying strong internal perturbation together with an external vertical perturbation could perhaps explain the transition between the two-armed and one-armed phase-spirals around the Solar radius.