Evidence for dark matter

The missing mass problem

Dark matter refers to matter that gravitates but does not emit, absorb, or reflect enough electromagnetic radiation to be seen directly. It is inferred from gravity. The evidence comes from galaxies, clusters, gravitational lensing, and cosmology.

Dark matter is not simply ordinary dust or faint stars. Observations strongly suggest it is a nonluminous component that behaves differently from normal baryonic matter.

Galaxy rotation curves

For a star orbiting a galaxy at radius $r$, circular motion gives

v_c^2=rac{GM(r)}{r}

If most mass were concentrated in the visible inner galaxy, then far outside the bright region we would expect

v_cpropto rac{1}{sqrt{r}}

similar to planets orbiting the Sun.

Instead, many spiral galaxies have flat rotation curves:

$v_capprox constant$

This implies

$M(r)propto r$

meaning mass continues to increase with radius beyond the visible disk.

Galaxy clusters

Galaxy clusters also show missing mass. Galaxy velocities inside clusters are too high for the clusters to remain bound by visible matter alone. Hot intracluster gas emits X-rays and contributes baryonic mass, but still not enough.

The virial theorem relates kinetic and potential energy in a bound system:

$2K+U=0$

Applying it to clusters implies much more gravitating mass than the visible galaxies and gas provide.

Gravitational lensing

Mass bends light. Gravitational lensing maps the total mass distribution, regardless of whether the matter shines. Strong lensing creates arcs and multiple images. Weak lensing statistically distorts background galaxy shapes.

Lensing observations often find more mass than can be explained by stars and gas. They also map dark matter halos around galaxies and clusters.

Bullet Cluster

The Bullet Cluster is an important example. It appears to be a collision between galaxy clusters. Hot gas, which contains most ordinary baryonic mass, was slowed by collision and observed in X-rays. Gravitational lensing shows most mass offset from the gas, near the collisionless galaxies.

This separation supports the idea of collisionless dark matter rather than a simple modification tied only to visible matter.

Cosmological evidence

The cosmic microwave background, large-scale structure, and Big Bang nucleosynthesis also support dark matter. The pattern of CMB temperature fluctuations fits a universe with far more nonbaryonic matter than ordinary matter.

Structure formation also requires dark matter to seed gravitational wells before ordinary matter fully decoupled from radiation.

Alternatives and modified gravity

Some theories attempt to modify gravity instead of adding dark matter. Modified gravity can address some galaxy rotation curves, but explaining all evidence, especially lensing, clusters, the CMB, and structure formation, is difficult.

Dark matter remains the leading framework, though its particle nature is still unknown.

The big idea

Dark matter is inferred from multiple independent gravitational observations. Flat rotation curves, cluster dynamics, gravitational lensing, the Bullet Cluster, and cosmology all point to unseen mass. The mystery is not whether extra gravity is present, but what physical substance or theory explains it.