SIMBAD references

Disc stars from the Gaia DR3 RVS catalogue are selected to explore the phase spiral 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 〈v_R〉(z, v_z): this is characteristic of a breathing mode that can in principle be produced by in-plane non-axisymmetric perturbations. The phase spiral pattern becomes single armed outside the solar radius. When a realistic analytic model with 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 〈v_R〉 map in the x-y plane. Additionally, clear breathing mode evidence at a few $\, \mathrm{km\, s}^{-1}$ level can be seen in the 〈v_z〉 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 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 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.