Implications of a time-varying Galactic potential for determinations of the dynamical surface density

Recent studies have shown that the passage of a massive satellite through the disk of a spiral galaxy can induce vertical wobbles in the disk and produce features such as in-plane rings and phase-space spirals. Here we analyze a high-resolution N-body simulation of a live stellar disk perturbed by the recent passage of a massive dwarf galaxy that induces such perturbations. We study the implications of the phase-space structures for the estimate of the matter density through traditional Jeans modelling. The dwarf satellite excites rapid time-variations in the potential, leading to a significant bias of the local matter surface density determined through such a method. In particular, while the Jeans modelling gives reasonable estimates in the most overdense regions of the disk, we show that it tends to overestimate the dynamical surface density in underdense regions. In these regions, the phase-space spiral is indeed more marked in the surface of section of height vs. vertical velocity. This prediction can be verified with future Gaia data releases. Our finding is highly relevant for future attempts at determining the dynamical surface density of the outer Milky Way disk as a function of radius. The outer disk of the Milky Way is indeed heavily perturbed, and \textit{Gaia} DR2 data have clearly shown that such phase-space perturbations are even present locally. While our results show that traditional Jeans modelling should give reliable results in overdense regions of the disk, the important biases in underdense regions call for the development of non-equilibrium methods to estimate the dynamical matter density locally and in the outer disk.