[Paper Review] The Pattern Speed of the Milky Way Bar/Bulge from VIRAC & Gaia

Jonathan P. Clarke, Ortwin Gerhard|arXiv (Cornell University)|Jul 22, 2021

Stellar, planetary, and galactic studies7 references4 citations

TL;DR

This study measures the Milky Way's bar pattern speed using distance-resolved proper motions from the VIRAC-Gaia (gVIRAC) data, comparing them to a grid of made-to-measure (M2M) dynamical models. It finds Ωb = 33.29 ± 1.81 km s⁻¹ kpc⁻¹, supporting the 'long-slow' bar scenario and confirming consistency with recent solar neighborhood kinematic measurements.

ABSTRACT

We compare distance resolved, absolute proper motions in the Milky Way bar/bulge region to a grid of made-to-measure dynamical models with well defined pattern speeds. The data are obtained by combining the relative VVV Infrared Astrometric Catalog v1 proper motions with the Gaia DR2 absolute reference frame. We undertake a comprehensive analysis of the various errors in our comparison, from both the data and the models, and allow for additional, unknown, contributions by using an outlier-tolerant likelihood function to evaluate the best fitting model. We quantify systematic effects such as the region of data included in the comparison, the possible overlap from spiral arms, and the choice of synthetic luminosity function and bar angle used to predict the data from the models. Resulting variations in the best-fit parameters are included in their final errors. We thus measure the bar pattern speed to be ${\Omega}_b=33.29\pm1.81 \mathrm{km \, s^{-1} \, kpc^{-1}}$ and the azimuthal solar velocity to be $V_{\phi,\,\odot} = 251.31 \pm 1.95 \mathrm{km \, s^{-1}}$. These values, when combined with recent measurements of the Galactic rotation curve, yield the distance of corotation, 6.5 < $R_{CR}$ [kpc] < 7.5, the outer Lindblad resonance (OLR), 10.7 < $R_{OLR}$ [kpc] < 12.4, and the higher order, m = 4, OLR, 8.7 < $R_{{OLR}_4}$ [kpc] < 10.0. The measured pattern speed provides strong evidence for the "long-slow" bar scenario.

Motivation & Objective

• To measure the Milky Way's bar pattern speed (Ωb) using high-precision, distance-resolved proper motions in the bar/bulge region.
• To assess systematic uncertainties from data reduction, model assumptions, and structural parameters such as bar angle and luminosity function.
• To test the robustness of the pattern speed measurement against variations in data selection, spiral arm contamination, and model assumptions.
• To provide a self-consistent dynamical constraint on the bar's properties that aligns with independent measurements from the solar neighborhood.

Proposed method

• Combines relative proper motions from the VVV Infrared Astrometric Catalog (VIRACv1) with the absolute Gaia DR2 reference frame to obtain absolute proper motions with distance resolution.
• Uses a grid of made-to-measure (M2M) dynamical models with well-defined pattern speeds, based on P17's models calibrated from star counts and line-of-sight velocities.
• Applies an outlier-tolerant likelihood function to robustly compare observed gVIRAC kinematics to model predictions, minimizing bias from measurement outliers.
• Quantifies systematic errors from magnitude-dependent proper motion errors, red clump giant (RC&B) selection, luminosity function choice, and bar angle uncertainty.
• Uses marginalized posterior probability distributions to derive final parameter estimates, including systematic errors in quadrature.
• Combines the measured Ωb with recent rotation curve data to infer corotation and Lindblad resonance radii.

Experimental results

Research questions

• RQ1 What is the precise value of the Milky Way bar's pattern speed (Ωb) based on kinematic data from the inner bar/bulge?
• RQ2 How do systematic effects—such as bar angle, luminosity function choice, and spiral arm contamination—affect the measured pattern speed?
• RQ3 Does the measured pattern speed support the 'long-slow' bar scenario over fast or short bars?
• RQ4 What are the resulting corotation and Lindblad resonance radii, and how do they align with other kinematic features like the Hercules stream?
• RQ5 Can the gVIRAC data independently confirm recent pattern speed estimates derived from solar neighborhood kinematics?

Key findings

• The bar pattern speed is measured as Ωb = 33.29 ± 1.81 km s⁻¹ kpc⁻¹, with systematic uncertainties fully accounted for.
• The solar azimuthal velocity is determined as 𝑉𝜙,⊙ = 251.31 ± 1.95 km s⁻¹, consistent with recent solar neighborhood measurements.
• Corotation radius is estimated at 6.5 < 𝑅CR [kpc] < 7.5, with the outer Lindblad resonance (OLR) at 10.7 < 𝑅OLR [kpc] < 12.4.
• The higher-order 𝑚=4 OLR is found at 8.7 < 𝑅OLR4 [kpc] < 10.0, suggesting a possible link to complex velocity structures in the solar neighborhood.
• The measured Ωb value strongly supports the 'long-slow' bar scenario, consistent with recent studies using Hercules stream kinematics.
• The model-data comparison achieves an rms precision of < 9 km s⁻¹ for the fiducial case, despite the P17 models not being fitted to gVIRAC data.