Kinematic diagnostics for non-axisymmetry in the Milky Way's nuclear stellar disc

There is now strong evidence that the Milky Way (MW) hosts a nuclear stellar disc (NSD). However, whether the NSD is purely axisymmetric or contains a nuclear bar remains unresolved. Since approximately 50% of barred galaxies with MW-like mass in the local Universe host a nuclear bar, investigating whether the MW hosts one is of interest. We conducted a systematic analysis to identify robust kinematic diagnostics capable of determining whether the MW hosts a nuclear bar. Using N-body simulations, we explored the kinematic signatures indicative of a nuclear bar. Using the phase-space coordinates longitude (), we tested various diagnostics assuming different nuclear bar orientations. We also evaluated how sample size, dust extinction, and bar amplitude influence the efficacy of the diagnostics. We identify two independent kinematic diagnostics capable of revealing a nuclear bar in the MW: (1) the vertex deviation, l_̊m v, of the (v_ and latitude (b), proper motions (μ_), and line-of-sight velocity (v_ and μ_ ̊m b ̊m los -v_ ̊m los) velocity ellipse and (2) the asymmetry in the μ_ versus ell distribution. While both are impacted by the sample size and extinction, the vertex deviation proves more robust, especially when combining stars from multiple observational fields. We also assessed the correlation between the line-of-sight velocity and the h₃ Gauss-Hermite moment (‘skewness') of the line-of-sight velocity but find no clear distinction between an NSD and a nuclear bar based on this metric. Our results suggest that data from the current KMOS survey may allow a marginal detection of a nuclear bar using the vertex deviation method. A companion paper provides further validation and detailed analysis of this approach. Nonetheless, future surveys will provide the high-quality data necessary to fully exploit the diagnostics outlined in this study.