25.3 The Mass of the Galaxy

Measuring the Milky Way's Mass

Orbital Velocities and Dark Matter Detection

To figure out the Milky Way's total mass, astronomers measure how fast objects (stars, gas clouds) orbit the Galactic center. The logic is straightforward: faster orbits require more gravitational pull, which means more mass.

Kepler's third law connects orbital velocity to the enclosed mass within a given orbit:

$v = \sqrt{\frac{GM}{r}}$

• $v$ = orbital velocity
• $G$ = gravitational constant
• $M$ = total mass enclosed within the orbit
• $r$ = orbital radius (distance from the Galactic center)

If you rearrange this equation, you can solve for $M$ once you know how fast something is orbiting and how far out it is.

Here's the problem: when astronomers measure orbital velocities across the Milky Way's disk, the speeds are too high to be explained by visible matter alone. According to the equation above, velocities should drop off at larger radii (farther from the center, less enclosed mass, slower orbit). But they don't. Orbital velocities stay roughly constant even at large distances from the Galactic center.

This flat rotation curve is the key evidence for dark matter. Something massive but invisible must be providing the extra gravitational pull that keeps those outer stars moving so fast.

Distribution of Dark Matter in the Galaxy

Dark matter doesn't sit in the disk like stars and gas. Instead, it forms a roughly spherical halo that envelops the entire Milky Way, extending far beyond the visible disk.

• The dark matter halo is far more massive than all the visible components combined. Roughly 90% of the Galaxy's total mass is dark matter.
• The total mass of the Milky Way (including dark matter) is estimated at $1\text{–}2 \times 10^{12} \, M_{\odot}$, compared to only about $10^{11} \, M_{\odot}$ for visible matter alone. That's roughly 10 to 20 times more dark matter than visible matter.
• Dark matter density is highest near the Galactic center and decreases with distance, but it falls off much more gradually than visible matter does.

That gradual falloff is exactly why orbital velocities stay high at large radii. The dark matter halo keeps adding enclosed mass even where there are very few visible stars.

Candidates for Dark Matter Composition

So what is dark matter made of? There are two broad categories of candidates.

Baryonic matter (ordinary protons, neutrons, electrons) was an early suggestion. Maybe the "missing" mass is just dim objects we can't easily see, like brown dwarfs, rogue black holes, or cold gas clouds. However, baryonic dark matter has been largely ruled out. Observations of the cosmic microwave background and calculations of Big Bang nucleosynthesis show that baryonic matter accounts for only a small fraction of the Universe's total matter. There simply isn't enough ordinary matter to explain the missing mass.

Non-baryonic matter is now the favored explanation. These are hypothetical particles that have mass but interact very weakly (or not at all) with light, which is why we can't see them directly.

• WIMPs (Weakly Interacting Massive Particles) are the leading candidates. They would have significant mass but interact with ordinary matter only through gravity and the weak nuclear force. Supersymmetric particles like neutralinos are one proposed type of WIMP.
• Axions are another possibility. These would have extremely low mass and an incredibly weak coupling to ordinary matter.

Despite extensive searches using underground detectors, particle accelerators, and space-based instruments, no dark matter particle has been directly detected yet. The true nature of dark matter remains one of the biggest open questions in physics and astronomy.

Additional Methods for Detecting Dark Matter

Beyond rotation curves, astronomers have other tools:

• Mass-to-light ratio analysis compares a galaxy's total gravitational mass to the amount of light it emits. A high ratio (lots of mass, relatively little light) signals the presence of dark matter.
• Gravitational lensing occurs when a massive object bends light from a more distant source. By measuring how much light bends around galaxy clusters, astronomers can map out the total mass present, including dark matter that produces no light of its own.