Galactic Rotation and the Dark Matter Halo

The Milky Way's rotation curve stays nearly flat far beyond the visible disk, providing direct dynamical evidence for an extended dark matter halo.

Definition

The galactic rotation curve is the circular speed of stars and gas as a function of distance from the Galactic Center; its failure to decline at large radii implies a dark matter halo, an extended distribution of non-luminous mass whose gravity dominates the outer Galaxy.

Scope

This topic covers differential rotation and the Oort constants, the construction and interpretation of the Galactic rotation curve, the inference of the total enclosed mass from circular velocities, and the structure of the dark matter halo, including density profiles such as the NFW form derived from cosmological simulations.

Core questions

• How is the rotation curve of the Milky Way measured, and why does it stay flat?
• What do the Oort constants tell us about local differential rotation?
• How is the total mass of the Galaxy inferred from its kinematics?
• What density profile describes the dark matter halo, and where does it come from?

Key theories

Flat rotation curves as dark matter evidence

Circular velocities remain roughly constant well beyond the luminous disk, requiring an enclosed mass that grows with radius, which is naturally explained by an extended dark matter halo.

Differential rotation and the Oort constants

Oort showed that the local velocity field of disk stars reflects differential rotation, parameterized by the constants A and B, which encode the local rotation speed and its radial gradient.

Universal halo density profile

Cosmological simulations of hierarchical clustering predict that dark matter halos, including the Milky Way's, follow a near-universal density profile that steepens with radius, the NFW profile.

Clinical relevance

Rotation curves of the Milky Way and external spirals were a cornerstone of the case for dark matter, reshaping cosmology; the inferred halo mass also sets the gravitational environment governing satellite galaxies and the Galaxy's future mergers.

History

Oort quantified local galactic rotation in the 1930s, and neutral-hydrogen surveys later traced the rotation curve to large radii. Rubin and Ford's 1970 spectroscopy of Andromeda and subsequent spirals revealed flat rotation curves, and by the 1990s cosmological simulations provided a theoretical description of the dark matter halos responsible.

Key figures

• Jan Oort
• Vera Rubin
• Kent Ford
• Simon White

Seminal works

• rubin1970
• oort1932
• navarro1997

Frequently asked questions

Why is a flat rotation curve surprising?

If most mass followed the visible stars, rotation speeds should fall off at large radii like the orbits of planets around the Sun. The observed flat curve means there is much more mass at large radii than the light reveals, attributed to dark matter.

Can dark matter be replaced by modified gravity?

Alternatives such as modified Newtonian dynamics can fit many rotation curves, but the dark matter halo picture is favored because it also explains gravitational lensing, galaxy cluster dynamics, and the cosmic microwave background within one framework.