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The inner rotation curve of the Milky Way

Y. Sofue, M. Kohno

TL;DR

This study derives the Milky Way's inner rotation curve (RC) using the terminal-velocity method (TVM) applied to HI and CO longitude–velocity diagrams, and validates the results against maser VLBI and Gaia astrometry to produce a unified RC out to roughly 25 kpc. By combining TVM-derived RCs with external astrometric RCs, the authors perform a mass decomposition into a central black hole, bulge, disc, and dark halo (NFW), obtaining a local dark-matter density of $\rho_{\rm DM}^\odot = 0.107 \pm 0.003$ GeV cm$^{-3}$ and a DM fraction $f_{\rm DM} \approx 0.1$ inside the solar circle. They also identify a prominent East–West asymmetry in the inner RC, well described by a decaying sinusoid consistent with bar-driven noncircular motions, and discuss the implications for the Galactic mass model and the limitations of axisymmetric assumptions. The results provide precise constraints on the bulge mass (~$10^{10} M_\odot$), disk dominance in the outer Galaxy, and a coherent picture of the Milky Way's mass distribution and dynamics, with clear relevance for interpreting nonaxisymmetric features. Significance lies in the robust, data-driven coupling of TVM with high-quality HI/CO surveys to benchmark Galactic mass components and local dark matter density, informing both Galactic dynamics and dark matter studies.

Abstract

We derived the inner rotation curve (RC) of the Milky Way by applying the terminal velocity method (TVM) to the longitude-velocity diagrams (LVD) made from the large-scale survey data of the Galactic plane in the HI (HI4PI whole sky survey) and CO lines (CfA-Chile 1.2-m Galactic plane survey, Nobeyama 45-m Galactic plane and Galactic Center surveys, and Mopra 22-m southern Galactic plane survey). The derived RC agrees well with the RCs derived from the astrometric measurements of the maser sources by very long baseline interferometer (VLBI) observations and the GAIA result. We combined them to construct a unified RC from $R=0$ to $\sim 25$ kpc and decomposed the curve into bulge, disc and dark halo components with high precision. The dark matter density near the Sun is estimated to be $0.107 \pm 0.003$ GeV cm$^{-3}$. We present the RC as ascii tables for the solar constants of $(R_0,V_0)=(8.178 {\rm kpc}, 235.1 {\rm km/s})$, We also obtained a detailed comparison of the eastern ($l\ge 0^\circ$) and western ($< 0^\circ$) RCs in the HI and CO lines, which allowed the creation of an E/W asymmetry curve of the velocity difference. The E/W asymmetry is fitted by a sinusoidal function of the radius with the amplitude increasing toward the Galactic Center. We consider the possibility of the origin due to a weak bar inside $\sim 4$ kpc.

The inner rotation curve of the Milky Way

TL;DR

This study derives the Milky Way's inner rotation curve (RC) using the terminal-velocity method (TVM) applied to HI and CO longitude–velocity diagrams, and validates the results against maser VLBI and Gaia astrometry to produce a unified RC out to roughly 25 kpc. By combining TVM-derived RCs with external astrometric RCs, the authors perform a mass decomposition into a central black hole, bulge, disc, and dark halo (NFW), obtaining a local dark-matter density of GeV cm and a DM fraction inside the solar circle. They also identify a prominent East–West asymmetry in the inner RC, well described by a decaying sinusoid consistent with bar-driven noncircular motions, and discuss the implications for the Galactic mass model and the limitations of axisymmetric assumptions. The results provide precise constraints on the bulge mass (~), disk dominance in the outer Galaxy, and a coherent picture of the Milky Way's mass distribution and dynamics, with clear relevance for interpreting nonaxisymmetric features. Significance lies in the robust, data-driven coupling of TVM with high-quality HI/CO surveys to benchmark Galactic mass components and local dark matter density, informing both Galactic dynamics and dark matter studies.

Abstract

We derived the inner rotation curve (RC) of the Milky Way by applying the terminal velocity method (TVM) to the longitude-velocity diagrams (LVD) made from the large-scale survey data of the Galactic plane in the HI (HI4PI whole sky survey) and CO lines (CfA-Chile 1.2-m Galactic plane survey, Nobeyama 45-m Galactic plane and Galactic Center surveys, and Mopra 22-m southern Galactic plane survey). The derived RC agrees well with the RCs derived from the astrometric measurements of the maser sources by very long baseline interferometer (VLBI) observations and the GAIA result. We combined them to construct a unified RC from to kpc and decomposed the curve into bulge, disc and dark halo components with high precision. The dark matter density near the Sun is estimated to be GeV cm. We present the RC as ascii tables for the solar constants of , We also obtained a detailed comparison of the eastern () and western () RCs in the HI and CO lines, which allowed the creation of an E/W asymmetry curve of the velocity difference. The E/W asymmetry is fitted by a sinusoidal function of the radius with the amplitude increasing toward the Galactic Center. We consider the possibility of the origin due to a weak bar inside kpc.

Paper Structure

This paper contains 21 sections, 31 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data
  3. HI
  4. CO
  5. Terminal-velocity method (TVM) to determine rotation curve
  6. Galactic constants
  7. Rotation velocity from terminal velocity
  8. Correction for line width due to local velocity dispersions
  9. Result
  10. Terminal velocity and rotation curves
  11. The inner RC of the Milky Way
  12. Discussion
  13. Dynamical mass distribution
  14. Comparison with outer RCs
  15. Model fitting: decomposition into mass components
  16. ...and 6 more sections

Figures (15)

  • Figure 1: HI and CO-line LVDs of the inner Galaxy. (a) HI 21 cm taken from the Effelsberg 100-m and Parkes 64-m radio telescopes 2016AA...594A.116H. (b) $^{12}$CO $J$ = 1--0 obtained by CfA and Chile 1.2-m telescopes 2001ApJ...547..792D. (c) $^{12}$CO $J$ = 1--0 obtained by the Nobeyama 45-m telescope with the FUGIN and Local spur CO survey project ume+2017Torii+20192022PASJ...74...24K2023PASJ...75..279F. (d) $^{12}$CO $J$ = 1--0 obtained by the Nobeyama 45-m telescope with the GC CO survey 2019PASJ...71S..19T. (e) $^{12}$CO $J$ = 1--0 taken from the Mopra Southern Galactic Plane CO Survey 2023PASA...40...47C. The white contour levels are 2, 0.25, 0.5, 1.2, and 2.8 K from (a) to (e), respectively. Alt text: HI and CO line longitude-velocity diagrams from the large-scale Galactic plane surveys.
  • Figure 2: Line profile at $l=30^\circ$ decomposed into Gaussian components. Alt text: Diagram explaining Gaussian deconvolution of a line spectrum.
  • Figure 3: [Top] HI terminal velocity $V_{\rm term}$ after correction (subtraction) of an intrinsic velocity dispersion of $\delta V_{\rm HI}=15$ km s$^{-1}$. [Bottom] RC East (dot) and RC West (circle). Large dot is the Sun. Alt text: HI-line terminal velocity and rotation curve.
  • Figure 4: [Top] $^{12}$CO -line $V_{\rm term}$ from CfA-Chile survey. [Bottom] Rotation curves in the E (dots) and W (circles) sides of GC. Big dot is the Sun. Alt text: Terminal velocity and rotation curve from CfA-Chile CO survey.
  • Figure 5: [Top] CO FUGIN Terminal velocity against longitude. [Bottom] Rotation velocity against radius. Alt text: Terminal velocity and rotation curve from FUGIN CO-line survey.
  • ...and 10 more figures