[Paper Review] A direct measurement of the distance to the Galactic center using the kinematics of bar stars

Henry Leung, Jo Bovy+4 more|arXiv (Cornell University)|Apr 26, 2022

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper presents a direct measurement of the Galactic center distance $R_0 = 8.23 \pm 0.12\ \text{kpc}$ using kinematic maps of stars in the Galactic bar, derived from APOGEE DR17 and Gaia EDR3 data with spectro-photometric distances from astroNN. The method identifies the rotational velocity minimum and radial velocity quadrupole signature in the bar, yielding the most robust $R_0$ estimate to date by anchoring the measurement to the bar's dynamical center, avoiding assumptions about Sgr A* rest frame.

ABSTRACT

The distance to the Galactic center $R_0$ is a fundamental parameter for understanding the Milky Way, because all observations of our Galaxy are made from our heliocentric reference point. The uncertainty in $R_0$ limits our knowledge of many aspects of the Milky Way, including its total mass and the relative mass of its major components, and any orbital parameters of stars employed in chemo-dynamical analyses. While measurements of $R_0$ have been improving over a century, measurements in the past few years from a variety of methods still find a wide range of $R_0$ being somewhere within $8.0$ to $8.5\,\mathrm{kpc}$. The most precise measurements to date have to assume that Sgr A$^*$ is at rest at the Galactic center, which may not be the case. In this paper, we use maps of the kinematics of stars in the Galactic bar derived from APOGEE DR17 and Gaia EDR3 data augmented with spectro-photometric distances from the exttt{astroNN} neural-network method. These maps clearly display the minimum in the rotational velocity $v_T$ and the quadrupolar signature in radial velocity $v_R$ expected for stars orbiting in a bar. From the minimum in $v_T$, we measure $R_0 = 8.23 \pm 0.12\,\mathrm{kpc}$. We validate our measurement using realistic $N$-body simulations of the Milky Way. We further measure the pattern speed of the bar to be $Ω_\mathrm{bar} = 40.08\pm1.78\,\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$. Because the bar forms out of the disk, its center is manifestly the barycenter of the bar+disc system and our measurement is therefore the most robust and accurate measurement of $R_0$ to date.

Motivation & Objective

• To provide a direct, robust measurement of the distance to the Galactic center ($R_0$) independent of assumptions about Sgr A* rest frame.
• To leverage the kinematics of stars in the Galactic bar as a dynamical tracer of the barycenter, since the bar's center is the barycenter of the bar+disk system.
• To improve precision in $R_0$ by using two-dimensional kinematic maps of bar stars from high-precision astrometry and spectroscopy.
• To validate the method using realistic $N$-body simulations of the Milky Way's bar structure and dynamics.
• To measure the bar's pattern speed ($\Omega_{\text{bar}}$) as a byproduct, enhancing dynamical modeling of the inner Galaxy.

Proposed method

• Combines APOGEE DR17 radial velocities and Gaia EDR3 astrometry (positions, proper motions) for stars in the Galactic bar region.
• Applies the astroNN neural network to derive spectro-photometric distances for stars, enabling 3D phase-space reconstruction.
• Constructs 2D kinematic maps of rotational velocity ($v_T$) and radial velocity ($v_R$) across the bar to identify dynamical signatures.
• Identifies the minimum in $v_T$ and the quadrupolar pattern in $v_R$ as indicators of circular orbits around the bar's center, used to locate $R_0$.
• Performs $N$-body simulations of the Milky Way to validate the method and assess systematic biases in $R_0$ and $\Omega_{\text{bar}}$.
• Uses maximum-likelihood fitting to the kinematic maps to derive $R_0$ and $\Omega_{\text{bar}}$ with uncertainties, minimizing reliance on external assumptions.

Experimental results

Research questions

• RQ1 Can the distance to the Galactic center be measured directly using the kinematics of stars in the Galactic bar without assuming Sgr A* is at rest?
• RQ2 Does the minimum in rotational velocity $v_T$ and the quadrupolar signature in radial velocity $v_R$ provide a reliable dynamical anchor for $R_0$?
• RQ3 How does the bar's center relate to the true barycenter of the Milky Way's disk and bar system?
• RQ4 What is the pattern speed of the Galactic bar, and how does it constrain the Milky Way's dynamical structure?
• RQ5 Can this method yield a more accurate and systematic-error-free $R_0$ than orbit-based S2 measurements?

Key findings

• The paper measures $R_0 = 8.23 \pm 0.12\ \text{kpc}$ using the minimum in rotational velocity $v_T$ in the bar's kinematic map.
• The measurement is robust because the bar's center is the barycenter of the bar+disk system, avoiding assumptions about Sgr A* rest frame.
• The bar's pattern speed is measured as $\Omega_{\text{bar}} = 40.08 \pm 1.78\ \text{km\,s}^{-1}\text{\,kpc}^{-1}$, consistent with other dynamical constraints.
• Validation using $N$-body simulations confirms the method's reliability and shows minimal systematic bias in $R_0$.
• The method avoids the instrumental and reference-frame systematics affecting S2-orbit-based $R_0$ measurements, offering a more direct path to $R_0$.
• Future surveys like SDSS-V, Small-Jasmine, and Roman Telescope will extend this method with full-coverage, parallax-based distances for even higher precision.