Weighing the Invisible
Section 11 of 11
Summary
Summary
Motion is a mass measurement. S-star orbits reveal the compact mass at the Milky Way’s center. Galaxy rotation curves reveal mass extending far beyond the bright stellar disk. Cluster collisions separate hot gas from gravitational mass. Redshift surveys show a cosmic web shaped by gravity over billions of years. Across all these scales, the method is the same: observe motion or lensing, model with gravity, infer the mass distribution.
A galaxy’s rotation curve stays flat far beyond its bright disk. Using , explain what that implies about the enclosed mass — and then name one independent line of evidence that the missing mass is real, not a flaw in the rotation-curve method.
A flat curve means is roughly constant, so keeps rising in proportion to : gravitating mass extends well beyond the light. An independent line of evidence is the Bullet Cluster, where gravitational lensing locates most of the mass offset from the collisional hot X-ray gas — a completely different observable and physical setup that still requires dark matter (gravitational lensing of clusters and the gravitationally grown cosmic web are equally valid alternatives).
Glossary
- Active galactic nucleus
A luminous galactic center powered by accretion onto a supermassive black hole. The black hole itself emits no light; the brightness comes from infalling gas releasing gravitational energy outside the event horizon.
- Bullet Cluster
A colliding galaxy-cluster system where the hot X-ray-emitting gas and the gravitational-lensing mass are spatially separated. The offset is strong evidence that most of the gravitating mass is collisionless and not the ordinary hot gas.
- Cosmic web
The large-scale network of filaments, walls, clusters, and voids traced by galaxies and shaped by gravity. It is evidence that gravity has amplified small early density differences into the structure we observe today.
- Dark matter
A gravitating component inferred from motion, lensing, and structure formation that does not emit, absorb, or scatter enough light to be seen directly. “Dark” means electromagnetically dark — visible through gravity, not through ordinary light. This reading, built on rotation curves and the Bullet Cluster, is its canonical home in the course.
- Enclosed mass
The amount of mass inside radius , written , inferred from orbital motion or other gravitational effects. It is the total gravitating mass interior to the orbit — not necessarily the mass that emits light.
- Flat rotation curve
A galaxy rotation curve in which orbital speed stays roughly constant with radius. Through , a flat speed implies an enclosed mass that rises in proportion to radius — the signature of an extended dark-matter halo.
- Galaxy cluster
A gravitationally bound system of many galaxies, hot X-ray-emitting intracluster gas, and dark matter. The galaxies are the easiest part to see, but they are not most of the cluster’s ordinary matter — and ordinary matter is not most of its total mass.
- Gravitational lensing
Bending of light by mass, used to map total gravitating matter whether or not it emits light. Because lensing responds to all mass, it weighs dark matter directly — independent of any rotation-curve argument.
- Large-scale structure
The distribution of matter on scales larger than individual galaxies, including galaxy groups, clusters, filaments, walls, and voids. Its pattern records the gravitational growth of small early density differences over cosmic time.
- Local Group
The gravitationally bound galaxy group containing the Milky Way, Andromeda, Triangulum, and many dwarf galaxies. Because it is bound, its members’ motions are governed by local gravity rather than by cosmic expansion.
- Rotation curve
A plot of orbital speed versus distance from the center of a galaxy. Its shape encodes how mass is distributed: a falling curve means a central mass concentration; a flat curve means mass that keeps growing outward.
- Supermassive black hole
A black hole with millions to billions of solar masses, commonly found in galactic centers. The Milky Way’s is Sagittarius A*, about four million solar masses, inferred from the orbits of stars that pass close to it.