$\texttt{ESCARGOT}$: Mapping Vertical Phase Spiral Characteristics Throughout the Real and Simulated Milky Way

The recent discovery of a spiral pattern in the vertical kinematic structure in the solar neighborhood provides a prime opportunity to study non-equilibrium dynamics in the Milky Way from local stellar kinematics. Furthermore, results from simulations indicate that even in a limited volume, differences in stellar orbital histories allow us to trace variations in the initial perturbation across large regions of the disk. We present $\texttt{ESCARGOT}$, a novel algorithm for studying these variations in both simulated and observed data sets. $\texttt{ESCARGOT}$ automatically extracts key quantities from the structure of a given phase spiral, including the time since perturbation and the perturbation mode. We test $\texttt{ESCARGOT}$ on simulated data and show that it is capable of accurately recovering information about the time since the perturbation occurred as well as subtle differences in phase spiral morphology due to stellar location in the disk at the time of perturbation. We apply $\texttt{ESCARGOT}$ to kinematic data from data release 3 of the ${\it Gaia}$ mission in bins of guiding radius. We show that similar structural differences in morphology occur in the ${\it Gaia}$ phase spirals as a function of stellar orbital history. These results indicate that the phase spirals are the product of a complex dynamical response in the disk with large-scale coupling between different regions of phase space.