Quadrupole signature as a kinematic diagnostic to constrain bar properties: Implications for the Milky Way

¹ Department of Astronomy, Astrophysics and Space Engineering, Indian Institute of Technology Indore, 453552 Indore, India
² Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
³ Heidelberg University, Grabengasse 1, 69117 Heidelberg, Germany
⁴ LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS, 92190 Meudon, France
⁵ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany

^⋆ Corresponding author: soumavo@iiti.ac.in

Received: 21 March 2025
Accepted: 22 September 2025

Abstract

The presence of a ‘butterfly’ or a quadrupole structure in the stellar mean radial velocity (⟨V_R⟩) field of the Milky Way is well known from the Gaia and the APOGEE surveys. Past studies have indicated that a stellar bar can excite such a quadrupole feature in the ⟨V_R⟩ distribution. However, a systematic study investigating the co-evolution of bar and quadrupole structure is largely missing. Furthermore, the question of whether this quadrupole structure in ⟨V_R⟩ can be used as a robust kinematic diagnostic to constrain bar properties, particularly for the Milky Way, is still beyond our grasp. Here, we investigate the bar-induced quadrupole feature using a suite of isolated N-body models forming prominent bars and a sample of Milky Way-like barred galaxies from the TNG50 cosmological simulation. We demonstrate that the properties of the quadrupole (strength, length, and orientation) are strongly correlated with the bar properties, regardless of the choice of the thin- or thick-disc stars; thereby making the quadrupole feature an excellent kinematic diagnostic for constraining the bar properties. In the presence of spirals, the estimator that takes into account the phase-angle of m = 4 Fourier moment serves as a more appropriate estimator for measuring the length of the quadrupole. Furthermore, we constructed a novel Gaia-like mock dataset from a simulated bar model, while incorporating the dust extinction and the broad trends of observational errors of the Gaia survey. The quadrupole properties (strength and length) estimated from those Gaia-like mock data are larger (∼35 − 45 per cent) when compared to their true values. We showed that the majority of this effect is due to the uncertainty in the parallax measurement. This demonstrates that the quadrupole structure in Gaia data is likely a result of dominant Gaia parallax errors and biases, almost masking the true inherent signature of the MW bar.