17. Galaxies, Dark Matter & Dark Energy
CollegeThe visible universe of stars and galaxies is a small fraction of everything that exists. This chapter confronts the evidence for the invisible majority.
Rotation curves and the case for dark matter
If a spiral galaxy's mass were concentrated where its visible stars are, orbital speeds at large radii should fall off as v ∝ 1/√r (like the planets around the Sun). Instead, observed galaxy rotation curves stay roughly flat far beyond the visible disc — meaning far more mass exists than can be seen, dubbed dark matter. Independent evidence comes from gravitational lensing (mass bends light more than visible matter alone can explain) and the Bullet Cluster, where colliding galaxy clusters show the mass (mapped by lensing) has separated from the visible hot gas (mapped by X-rays).
Separately, observations of distant Type Ia supernovae (reliable "standard candles" of known intrinsic brightness) in the late 1990s revealed the universe's expansion is not slowing under gravity, as expected, but accelerating — attributed to a mysterious dark energy, often modelled as Einstein's cosmological constant Λ.
The cosmic composition, and what dark matter is not
Current measurements (largely from the CMB, via missions like Planck) suggest the universe's total mass-energy is roughly 5% ordinary (baryonic) matter, 27% dark matter, and 68% dark energy. Dark matter is not simply "matter we haven't lit up yet" — it does not interact with light at all (hence "dark"), interacts only gravitationally (and perhaps very weakly otherwise), and candidate particles like WIMPs or axions have so far evaded direct detection despite extensive searches.
Worked example — mass implied by a flat rotation curve
A star orbits at r = 5.0×10²⁰ m from a galaxy's centre with an observed (flat) orbital speed of v = 2.2×10⁵ m/s (220 km/s). Estimate the total mass enclosed within that radius, assuming circular orbit.
- For circular orbital motion, gravity supplies centripetal force: GM/r² = v²/r, so M = v²r/G.
- Compute v² = (2.2×10⁵)² = 4.84×10¹&sup0;.
- Multiply by r: 4.84×10¹&sup0; × 5.0×10²⁰ = 2.42×10&sup4;¹.
- Divide by G: M = 2.42×10&sup4;¹ / 6.674×10⁻¹¹ ≈ 3.6×10&sup5;¹ kg — about 1.8×10¹¹ solar masses.
Answer: since the visible stars and gas at this radius account for only a fraction of that mass, the shortfall is attributed to an unseen dark matter halo extending well beyond the visible galaxy.
Test your understanding
What observation about galaxy rotation curves points to dark matter?
Orbital speeds of stars and gas stay roughly flat far beyond a galaxy's visible edge, instead of falling off as expected if all the mass were concentrated in the visible disc — implying a large amount of unseen mass, distributed in an extended halo.
What does the Bullet Cluster show, and why is it strong evidence for dark matter?
In the Bullet Cluster, two galaxy clusters have collided; X-ray observations show the hot, ordinary gas (most of the visible mass) concentrated near the collision centre, slowed by the impact, while gravitational lensing shows most of the total mass has passed through relatively undisturbed, offset from the gas. This separation is very difficult to explain without a form of matter that does not interact electromagnetically like ordinary gas does.
What evidence led to the discovery of dark energy?
Observations of distant Type Ia supernovae in the late 1990s, used as standard candles to measure cosmic distances precisely, showed the universe's expansion rate is accelerating rather than decelerating under gravity's pull — implying a repulsive component, dark energy, dominating the universe's large-scale dynamics.
Roughly what fraction of the universe's total mass-energy is ordinary matter?
Only about 5%. The rest is split between roughly 27% dark matter and 68% dark energy — meaning the stars, planets, and everything we can directly observe make up a small minority of the universe's total content.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1A galaxy's rotation curve stays flat at v = 200 km/s out to r = 30 kpc. Estimate the enclosed mass (M = v^2 r / G).
- Convert: v = 2e5 m/s, r = 30 kpc = ~9.3e20 m
- M = v^2 r / G = (2e5)^2 x 9.3e20 / 6.67e-11
- M = 4e10 x 9.3e20 / 6.67e-11 = ~5.6e41 kg (~3e11 solar masses)
Example 2Why do flat rotation curves argue for dark matter?
- Visible mass predicts orbital speeds falling off beyond the disc
- Observed speeds stay flat far out
- Extra unseen mass in a halo is needed to hold those speeds
Now you try
Work each one out first, then tap to reveal the worked answer.