Growing Local arm inferred by the breathing motion

Theoretical models of spiral arms suggest that the spiral arms provoke a vertical bulk motion in disc stars. By analysing the breathing motion, a coherent asymmetric vertical motion around the mid-plane of the Milky Way disc, with $\textit{Gaia}$ DR3, we found that a compressing breathing motion presents along the Local arm. On the other hand, with an $N$-body simulation of an isolated Milky Way-like disc galaxy, we found that the transient and dynamic spiral arms induce compressing breathing motions when the arms are in the growth phase, while the expanding breathing motion appears in the disruption phase. The observed clear alignment of the compressing breathing motion with the Local arm is similar to what is seen in the growth phase of the simulated spiral arms. Hence, we suggest that the Local arm's compressing breathing motion can be explained by the Local arm being in the growth phase of a transient and dynamic spiral arm. We also identified the tentative signatures of the expanding breathing motion associated with the Perseus arm and also the Outer arm coinciding with the compressing breathing motion. This may infer that the Perseus and Outer arms are in the disruption and growth phases, respectively.