Astrophysics · Galactic Structure · 2025

The Mass of the Milky Way: Components, Equations and Open Problems

A complete breakdown of the main mass components of our Galaxy — from the stellar disks to the central black hole — with radial mass equations, visual simulation, and the open questions that remain unresolved.

Based on McMillan 2017 · Ou et al. 2024 · Bland-Hawthorn & Gerhard 2016

~5 × 10¹⁰ M⊙

Total stellar mass

~1.3 × 10¹² M⊙

Virial mass estimate

R₀ = 8.2 kpc

Sun’s galactic radius

V₀ = 233 km/s

Circular velocity at R₀

Thin stellar disk
Thick stellar disk
Atomic gas HI
Molecular gas H₂
Bulge and bar
Central black hole Sagittarius A*
Stellar halo
Total visible mass
The missing mass
Radial mass profile simulation
Open problems

The Milky Way is our home galaxy: a barred spiral containing roughly one hundred billion stars, a large gas disk, a stellar halo, and a central supermassive black hole. Despite being the most studied galaxy in the universe, fundamental questions remain about its total mass, its outer halo, and the invisible mass required by its rotation curve.

All masses below are expressed as radial cumulative masses: the total mass contained inside a radius r from the Galactic Center.

\(M(This is the natural observable quantity because it determines the circular velocity through Newton’s law:

[latex]V_c(r)=\sqrt{\frac{G\,M(

1. Thin Stellar Disk

Component 1 — Thin stellar disk · M ≈ 3.52 × 10¹⁰ M⊙

The thin disk is the dominant stellar component of the Milky Way. It contains the Sun, the spiral arms, young and intermediate-age stars, most of the interstellar gas and dust, and the main sites of ongoing star formation. Its vertical thickness is small compared with its radial extent.

The surface density is modeled as an exponential disk:

[latex]\Sigma_{\mathrm{thin}}(r)=\Sigma_{0,\mathrm{thin}}e^{-r/R_{d,\mathrm{thin}}}\)

Parameter	Symbol	Value	Source
Central surface density	Σ_0,thin	896 M⊙ pc⁻²	McMillan 2017
Scale radius	R_d,thin	2.50 kpc	McMillan 2017
Total mass	M_thin	3.52 × 10¹⁰ M⊙	From 2πΣ₀R_d²

The radial cumulative mass is:

\(M_{\mathrm{thin}}(This formula comes from integrating the surface density over circular rings. The thin disk mass rises rapidly inside the inner few kiloparsecs and then saturates toward its total mass.

2. Thick Stellar Disk

Component 2 — Thick stellar disk · M ≈ 1.05 × 10¹⁰ M⊙

The thick disk is an older, more diffuse stellar population that extends farther above and below the Galactic plane. Its stars have different metallicities and kinematics from the thin disk and may record earlier merger or heating events in the Milky Way.

[latex]\Sigma_{\mathrm{thick}}(r)=\Sigma_{0,\mathrm{thick}}e^{-r/R_{d,\mathrm{thick}}}\)

Parameter	Symbol	Value
Central surface density	Σ_0,thick	183 M⊙ pc⁻²
Scale radius	R_d,thick	3.02 kpc
Total mass	M_thick	1.05 × 10¹⁰ M⊙

\(M_{\mathrm{thick}}(The combined stellar disk mass is:

[latex]M_{\mathrm{disk,\star}}(

3. Atomic Gas — HI

Component 3 — Atomic hydrogen gas · M ≈ 1.1 × 10¹⁰ M⊙

The 21 cm radio line of neutral hydrogen traces a large, flared and warped gas disk extending far beyond the stellar disk. Unlike stars, HI has a central depression and peaks several kiloparsecs from the Galactic Center.

[latex]\Sigma_{\mathrm{HI}}(r)=\Sigma_{0,\mathrm{HI}}\exp\left(-\frac{R_{m,\mathrm{HI}}}{r}-\frac{r}{R_{d,\mathrm{HI}}}\right)\)

Parameter	Value	Meaning
R_m,HI	4.0 kpc	Creates the central hole
R_d,HI	7.0 kpc	Outer exponential scale
M_HI,total	1.1 × 10¹⁰ M⊙	Total atomic gas mass

\(M_{\mathrm{HI}}(The peak of the HI mass distribution is near r ≈ √(4 × 7) ≈ 5.3 kpc. HI is important both as a gas reservoir and as a tracer of the outer galactic potential.

4. Molecular Gas — H₂

Component 4 — Molecular hydrogen · M ≈ 1.2 × 10⁹ M⊙

Molecular hydrogen is concentrated in the inner Galaxy and is closely associated with giant molecular clouds and star formation. It is typically traced through CO emission, which introduces uncertainty through the CO-to-H₂ conversion factor.

[latex]\Sigma_{\mathrm{H_2}}(r)=\Sigma_{0,\mathrm{H_2}}\exp\left(-\frac{R_{m,\mathrm{H_2}}}{r}-\frac{r}{R_{d,\mathrm{H_2}}}\right)\)

Parameter	Value
R_m,H₂	12.0 kpc
R_d,H₂	1.5 kpc
M_H₂,total	1.2 × 10⁹ M⊙

\(M_{\mathrm{H_2}}(

5. Bulge and Bar

Component 5 — Central bulge and galactic bar · M ≈ 9.23 × 10⁹ M⊙

The Milky Way is a barred spiral galaxy. Its central bulge and bar contain old stars and strongly influence gas flows and stellar dynamics in the inner Galaxy. The bar is difficult to measure from our position inside the disk, making the inner mass distribution uncertain.

[latex]\rho_{\mathrm{bulge}}(r)\propto e^{-(r/r_b)^2}\) \(r_b\approx0.5\,\mathrm{kpc}\)

A useful spherical approximation for the cumulative mass is:

\(M_{\mathrm{bulge}}(Almost all the bulge mass lies inside a few kiloparsecs. Beyond the bar region, its contribution to the enclosed mass changes very little.

The bar problem

The bar half-length, pattern speed and orientation remain uncertain. This uncertainty propagates directly into mass estimates inside roughly 5 kpc.

6. Central Black Hole — Sagittarius A*

Component 6 — Sagittarius A* · M = 4.0 × 10⁶ M⊙

At the dynamical centre of the Milky Way lies the supermassive black hole Sagittarius A*. Its mass is measured with high precision by tracking stellar orbits near the Galactic Center.

[latex]\rho_{\mathrm{Sgr\,A^\ast}}(\mathbf{r})=M_{\mathrm{Sgr\,A^\ast}}\delta^{(3)}(\mathbf{r})\) \(M_{\mathrm{Sgr\,A^\ast}}(0\)

Although famous, Sagittarius A* contributes negligibly to the global mass budget. Its importance is dynamical in the innermost parsec.

7. Stellar Halo

Component 7 — Stellar halo · M ≈ 5 × 10⁸ to 10⁹ M⊙

The stellar halo is a diffuse, roughly spherical population of old, metal-poor stars surrounding the disk. It includes globular clusters and stellar streams from disrupted dwarf galaxies.

\(\rho_{\mathrm{halo,\star}}(r)=\rho_{0,\star}\left(\frac{r_0}{r}\right)^n,\qquad n\approx3\text{–}4\)

For n not equal to 3, the cumulative mass is:

\(M_{\mathrm{halo,\star}}(For n = 3:

[latex]M_{\mathrm{halo,\star}}(The stellar halo is useful as a kinematic tracer, but its total mass is much smaller than the invisible mass inferred from the rotation curve.

8. Total Visible Mass

The total visible mass is the sum of the disk, gas, bulge, stellar halo and central black hole:

[latex]M_{\mathrm{visible}}(The expanded form is:

[latex]M_{\mathrm{visible}}(

Component	Total mass	Dominant radii
Thin disk	3.52 × 10¹⁰ M⊙	0–15 kpc
Thick disk	1.05 × 10¹⁰ M⊙	0–15 kpc
Bulge and bar	9.23 × 10⁹ M⊙	0–4 kpc
HI gas	1.1 × 10¹⁰ M⊙	3–20 kpc
H₂ gas	1.2 × 10⁹ M⊙	2–8 kpc
Stellar halo	~10⁹ M⊙	5–200 kpc
Sagittarius A*	4 × 10⁶ M⊙	r = 0
Total visible	≈ 6.7 × 10¹⁰ M⊙	—

9. The Missing Mass — The Central Problem

If only visible baryonic matter existed, the rotation speed would decline at large radius:

[latex]V_{\mathrm{exp}}(r)=\sqrt{\frac{GM_{\mathrm{visible}}(Instead, the observed rotation curve stays approximately flat to large radius and only declines in the outer Gaia-era measurements. The dynamical mass inferred from kinematics is:

[latex]M_{\mathrm{dyn}}(The invisible mass is:

[latex]\boxed{M_{\mathrm{invisible}}(At the solar circle, with r = 8.2 kpc and V_c = 233 km/s:

[latex]M_{\mathrm{dyn}}(<8.2\,\mathrm{kpc})=2.325\times10^5\times233^2\times8.2\approx1.04\times10^{11}M_\odot[/latex] [latex]M_{\mathrm{visible}}(<8.2\,\mathrm{kpc})\approx4.5\times10^{10}M_\odot[/latex] [latex]M_{\mathrm{invisible}}(<8.2\,\mathrm{kpc})\approx5.5\times10^{10}M_\odot[/latex]

Already at the Sun’s radius, the invisible mass is comparable to the visible mass. At larger radii, the invisible component dominates.

[latex]M_{\mathrm{Milky\ Way}}(

10. Radial Mass Profiles — Simulation

The charts below compute approximate cumulative mass curves for the main visible components, the dynamical mass, and the inferred invisible mass. They also compare the baryon-only rotation curve with a schematic observed rotation curve and Gaia-era points.

Cumulative enclosed mass M(<r) for each galactic component

Thin disk Thick disk HI gas Bulge Total visible Dynamical total Invisible mass

Observed rotation curve — visible components vs dynamical measurement

Baryons only Observed V_c(r) Gaia-era points

11. Open Problems and Fundamental Questions

1. What Is the Total Mass of the Milky Way?

Estimates of the virial mass range from about 5 × 10¹¹ to 2 × 10¹² M⊙. The Gaia-era declining rotation curve suggests a lower mass than the canonical value near 10¹² M⊙, but the result depends strongly on halo tracers, anisotropy, and assumed halo profile.

2. What Is the Nature of the Invisible Mass?

The standard interpretation invokes cold dark matter, but no particle has yet been directly detected. Alternatives include fuzzy dark matter, self-interacting dark matter, primordial black holes, modified gravity and wave-based effective mass models.

3. Why Does the Rotation Curve Decline at Large Radii?

The Gaia 2024 measurement at about 27 kpc is significantly lower than the traditional flat-curve picture. This implies a lighter halo, a steeper outer density profile, or a more complex dynamical structure.

4. The Cusp-Core Problem

Cold dark matter simulations predict cuspy inner density profiles, while many observed galaxies prefer flatter cores. In the Milky Way, baryons dominate the inner few kiloparsecs, making the dark halo shape hard to isolate.

5. The Missing Satellites Problem

Cold dark matter predicts many small subhalos around the Milky Way. Observed satellite numbers have increased, but whether they fully match theoretical expectations remains an active question.

6. The Uncertainty in the Baryonic Mass Distribution

The CO-to-H₂ conversion factor, stellar initial mass function, dust extinction, bar pattern speed, gas distribution and stellar population models all affect estimates of the visible mass. This uncertainty propagates directly into the inferred invisible mass.

7. The Outer Rotation Curve

Beyond 30 kpc, tracers become sparse and distance uncertainties become significant. A robust, model-independent outer Milky Way rotation curve remains difficult to obtain.

The fundamental equation whose right-hand side we cannot yet explain

[latex]M_{\mathrm{invisible}}(This quantity is real, reproducible and large. The physical nature of the invisible mass remains one of the deepest unsolved problems in galactic astrophysics.

A telling coincidence — the radial acceleration relation

The observed centripetal acceleration is tightly correlated with the baryonic acceleration across many galaxies. This suggests either a deep relation between dark and baryonic matter, or a modification of the effective gravitational law at low accelerations.

[latex]g_{\mathrm{obs}}=\frac{V_c^2}{r}\) \(g_{\mathrm{bar}}=\frac{GM_{\mathrm{bar}}}{r^2}\)

References

McMillan, P. J. — The mass distribution and gravitational potential of the Milky Way, MNRAS 465, 76, 2017.
Bland-Hawthorn, J., Gerhard, O. — The Galaxy in Context: Structural, Kinematic, and Integrated Properties, ARA&A 54, 529, 2016.
Ou, X., Eilers, A.-C., Necib, L., Frebel, A. — The dark matter profile of the Milky Way inferred from its circular velocity curve, MNRAS 528, 693, 2024.
Gravity Collaboration — Mass distribution in the Galactic Center based on interferometric astrometry of multiple stellar orbits, A&A 657, L12, 2022.
McGaugh, S. S., Lelli, F., Schombert, J. M. — Radial Acceleration Relation in Rotationally Supported Galaxies, PRL 117, 201101, 2016.
Navarro, J. F., Frenk, C. S., White, S. D. M. — A Universal Density Profile from Hierarchical Clustering, ApJ 490, 493, 1997.
Rubin, V. C., Ford, W. K., Thonnard, N. — Rotational properties of 21 Sc galaxies, ApJ 238, 471, 1980.

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