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

Soumavo Ghosh, Taavet Kalda, Paola Di Matteo, Gregory M. Green, Sergey Khoperskov, David Katz, Misha Haywood

TL;DR

The paper addresses whether the quadrupole signature in the stellar mean radial velocity <VR> can serve as a robust kinematic diagnostic to constrain Milky Way bar properties. By combining a large suite of isolated N-body barred discs with barred galaxies from the TNG50 cosmological simulation, the authors quantify the quadrupole's strength and extent via the $m=4$ Fourier moment and map these to bar strength and length, finding strong linear correlations (S_quadrupole ≈ 0.96 S_bar − 0.18 and R_quadrupole ≈ 1.06 R_bar + 0.01) with ρ ≥ 0.75. They show that the quadrupole orientation, captured by the phase φ4, traces the bar orientation and remains robust in central regions, though spirals can bias length estimates; in bar+spiral regimes φ4-based extents are more reliable. When applying Gaia-like observational effects using DR3-like errors, quadrupole properties are overestimated by ~35–45% largely due to parallax uncertainties, highlighting significant biases in MW inferences from Gaia DR3 alone and signaling the need for Gaia DR4 and complementary data. Overall, the quadrupole feature is a powerful diagnostic for bar properties in ideal data, but practical inferences require careful treatment of astrometric systematics and multi-survey constraints.

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 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, 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/thick disc stars; thereby making the quadrupole feature an excellent kinematic diagnostic for constraining the bar properties. In presence of spirals, the estimator which takes into account the phase-angle of $m = 4$ Fourier moment, serves as a more appropriate estimator for measuring the length of the quadrupole. Further, 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 ($\sim 35-45$ percent) when compared with their true values. We showed that the majority of this effect is due to the uncertainty in parallax measurement. This demonstrates that the quadrupole structure in Gaia data is likely a result of dominant Gaia parallax errors/biases, almost masking the true inherent signature of the MW bar.

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

TL;DR

The paper addresses whether the quadrupole signature in the stellar mean radial velocity <VR> can serve as a robust kinematic diagnostic to constrain Milky Way bar properties. By combining a large suite of isolated N-body barred discs with barred galaxies from the TNG50 cosmological simulation, the authors quantify the quadrupole's strength and extent via the Fourier moment and map these to bar strength and length, finding strong linear correlations (S_quadrupole ≈ 0.96 S_bar − 0.18 and R_quadrupole ≈ 1.06 R_bar + 0.01) with ρ ≥ 0.75. They show that the quadrupole orientation, captured by the phase φ4, traces the bar orientation and remains robust in central regions, though spirals can bias length estimates; in bar+spiral regimes φ4-based extents are more reliable. When applying Gaia-like observational effects using DR3-like errors, quadrupole properties are overestimated by ~35–45% largely due to parallax uncertainties, highlighting significant biases in MW inferences from Gaia DR3 alone and signaling the need for Gaia DR4 and complementary data. Overall, the quadrupole feature is a powerful diagnostic for bar properties in ideal data, but practical inferences require careful treatment of astrometric systematics and multi-survey constraints.

Abstract

The presence of a 'butterfly' or a quadrupole structure in the stellar mean radial velocity () field of the Milky Way is well known from the Gaia and the APOGEE surveys. Past studies indicated that a stellar bar can excite such a quadrupole feature in the distribution. However, a systematic study investigating the co-evolution of bar and quadrupole structure is largely missing. Furthermore, whether this quadrupole structure in 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 -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/thick disc stars; thereby making the quadrupole feature an excellent kinematic diagnostic for constraining the bar properties. In presence of spirals, the estimator which takes into account the phase-angle of Fourier moment, serves as a more appropriate estimator for measuring the length of the quadrupole. Further, 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 ( percent) when compared with their true values. We showed that the majority of this effect is due to the uncertainty in parallax measurement. This demonstrates that the quadrupole structure in Gaia data is likely a result of dominant Gaia parallax errors/biases, almost masking the true inherent signature of the MW bar.

Paper Structure

This paper contains 17 sections, 3 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Simulated barred galaxies
  3. Isolated barred models
  4. thin+thick models:
  5. sim6 model:
  6. Barred galaxies from the TNG50 simulations
  7. Quantifying bar properties via quadrupole signature in the mean radial velocity
  8. Correlation between strength and length of the bar and the quadrupole feature
  9. Orientation of quadrupole and the bar
  10. Influence of spiral arms in measuring the quadrupole length
  11. Implication on constraining the MW's bar properties from the quadrupole feature
  12. Sample selection from Gaia DR3
  13. Building Gaia-like mock datasets
  14. Quadrupoles in Gaia-like mocks: results and limitations
  15. Summary and future direction
  16. ...and 2 more sections

Figures (13)

  • Figure 1: Tracing the bar with the quadrupole feature: distribution of stellar surface density (left panel), mean radial velocity, $\hbox{$\left<{V_R}\right>$}$ (middle panel), and radial velocity dispersion, $\sigma_R$ (right panel), calculated in the $(x-y)$-plane, for the model rthick0.0, at the end of the simulation run ($t = 9 \hbox{$\>{\rm Gyr}$}$). Black dashed lines denote the contours of constant surface density. The cyan dashed circle denotes the bar length, $R_{\rm bar}$, and the magenta dashed circle denotes the extent of the quadrupole feature, $R_{\rm quadrupole}$. The magenta points denote the spatial distribution of the phase-angle of the $m=4$ Fourier moment ($\varphi_4$). The bar excites a prominent quadrupole pattern in the mean radial velocity field, and the orientation of the quadrupole pattern agrees fairly accurately with the orientation of the bar. Here, we used a galactocentric cylindrical coordinate system ($R, \phi, z$) to calculate $\hbox{$\left<{V_R}\right>$}$ and $\sigma_R$.
  • Figure 2: Tracing the bar properties with the quadrupole feature: correlation between the bar strength, $S_{\rm bar}$ and the strength of the quadrupole, $S_{\rm quadrupole}$ (left panel), and correlation between the bar length, $R_{\rm bar}$ and the length of the quadrupole, $R_{\rm quadrupole}$ (right panel), computed using all isolated thin+thick models and the TNG50 barred galaxies (see the legend). The black dash line denotes the best-fit straight line (of the form $Y = AX+B$) while the grey shaded region denotes the 5-$\sigma$ scatter around the best-fit line. The properties of the bar (strength and extent) remain strongly correlated with the properties of the quadrupole structure (Pearson correlation coefficient, $\rho > 0.75$).
  • Figure 3: Dependence on the choice of the thin or thick disc stars: correlation between the bar strength, $S_{\rm bar}$ and the strength of the quadrupole, $S_{\rm quadrupole}$ (top row), and correlation between the bar length, $R_{\rm bar}$ and the length of the quadrupole, $R_{\rm quadrupole}$ (bottom row), computed using thin disc particles (left panels) and thick disc particles (right panels), for all thin+thick models and the sim6 model (see the legend). The black dash line denotes the best-fit straight line (of the form $Y = AX+B$) while the grey shaded region denotes the 5-$\sigma$ scatter around the best-fit line. Regardless of the choice of thin or thick disc stellar particles, the length and strength of the quadrupole remain strongly correlated with the length and the strength of the bar.
  • Figure 4: Distribution of the mean radial velocity ($\hbox{$\left<{V_R}\right>$}$) in the $(x-y)$-plane, calculated at $t=9 \hbox{$\>{\rm Gyr}$}$ for the model rthick0.0, with the bar placed at different viewing angles with respect to a hypothetical observer (shown in diamond) at a Solar-like position ($R = -8 \hbox{$\>{\rm kpc}$}$, $\phi = 0 ^\circ$, $z = 0$). The cyan circles in each sub-panel denote the variation of the phase-angle of the $m=4$ Fourier coefficient ($\varphi_4$), computed from the distribution of $\hbox{$\left<{V_R}\right>$}$. The dashed straight line denotes the 'true' bar angle, computed from the intrinsic density distribution of the stellar particles.
  • Figure 5: Top panel: Radial variation of the amplitude of the $m=4$ Fourier moment of the mean radial velocity, $\hbox{$\left<{V_R}\right>$}$, calculated at $t = 9 \hbox{$\>{\rm Gyr}$}$ for the model rthick0.0, while putting the bar at different orientations (see the legend). Bottom panel: radial variation of the corresponding phase-angle ($\varphi_4$) of $m=4$ Fourier moment of the mean radial velocity, $\hbox{$\left<{V_R}\right>$}$. The points denoting the radial variation computed from the mean radial velocity, $\hbox{$\left<{V_R}\right>$}$ while the horizontal lines denote the corresponding true bar orientation, and the shaded region around the true value denotes a $8^\circ$ scatter. 'Half-extent' refers to the scenario where stars falling only in the negative half ($x \leq 0$) are considered while computing the Fourier moments. For further details, see the text. The vertical dash-dotted black line denotes the length of the bar ($R_{\rm bar} = 5.75 \hbox{$\>{\rm kpc}$}$).
  • ...and 8 more figures