Formation of the Two-Armed Phase Spiral from Multiple External Perturbations

Recent studies using the Gaia DR3 data have revealed a two-armed phase spiral in the $Z-V_Z$ phase space in the inner disk. In this study, we present new features of the two-armed phase spiral revealed by the Gaia Data and a new mechanism to explain such features with multiple external perturbations. By segmenting the Gaia DR3 RVS catalog based on $J_{\phi}$ (or $R_{g}$) and $\theta_\phi$, we confirm the existence of the clear two-armed phase spiral in the inner disk. Moreover, we identify a different two-armed phase spiral pattern at slightly larger radii, resembling a weak secondary branch along with the prominent major branch. At a given radius, with the azimuthal angle increasing, we observe a systematic transition of the two-armed phase spiral, with the significance of one branch weakened and another branch enhanced. This two-armed phase spiral may be due to the overlapping of distinct one-armed phase spirals. At different radii, the perturbation times estimated from each branch of the two-armed phase spiral are $\sim 320$ Myr and $\sim 500$ Myr, respectively, suggesting that the Galactic disk could be impacted by double external perturbers separated by $\sim 180$ Myr. We also performed test particle simulations of the disk perturbed by two satellite galaxies, which successfully generated a two-armed phase spiral similar to the observation. Both the observation and simulation results suggest that the signature in the $Z-V_Z$ phase space of earlier perturbations may not be completely erased by the more recent one.