About Galaxy Rotation Curves
The rotation curve of a galaxy plots the orbital velocity of stars and gas as a function of their distance from the galactic center. Newtonian gravity predicts that beyond the visible stellar disk, orbital velocity should fall off as v ∝ 1/√r (Keplerian decline), as planets do in the outer solar system where most mass is concentrated in the Sun. Instead, since the 1970s, Vera Rubin and others found that galactic rotation curves are remarkably flat—velocities remain constant or even rise at large radii where virtually no luminous matter is visible.
The most widely accepted explanation for flat rotation curves is the existence of dark matter—a massive, non-luminous component extending far beyond the visible disk in a spherical halo. If dark matter density falls as ρ ∝ 1/r², the enclosed mass M(r) ∝ r, and the orbital velocity v = √(GM/r) becomes constant, matching observed curves. The total mass of dark matter halos is typically 5–10 times the mass of visible matter. Dark matter makes up ~27% of the universe's energy density but interacts only gravitationally (and possibly weakly), making it invisible to electromagnetic observations.
This simulator lets you build a galaxy model by specifying the disk mass profile and dark matter halo parameters, then computes the predicted rotation curve. You can compare models with and without dark matter halos, adjust halo mass and scale radius, and see how the visible disk, central bulge, and dark matter halo each contribute to the total rotation curve at different radii—reconstructing the evidence for dark matter that has convinced the astronomical community.
Frequently Asked Questions
Why do we expect velocities to decrease with radius beyond the galactic disk?
Kepler's third law, derived from Newton's gravity, shows that for a circular orbit around a central mass M, v = √(GM/r). This means velocity falls as 1/√r when all mass is contained within the orbit radius. Our solar system follows this: Mercury orbits at ~48 km/s, Neptune at only ~5 km/s. If galaxy mass were concentrated in the visible disk and bulge (as the light distribution suggests), outer stars should show the same Keplerian decline. The flatness of observed rotation curves is a direct indicator that significant mass extends far beyond the visible galaxy.
What evidence supports the existence of dark matter besides rotation curves?
Multiple independent lines of evidence point to dark matter: gravitational lensing (galaxy clusters bend background light more than their visible mass can explain); the Bullet Cluster (two merging clusters where the gas was slowed by collisions while invisible dark matter passed through, observed separately via lensing); the cosmic microwave background power spectrum (baryon acoustic oscillations require dark matter to seed structure formation); and the large-scale distribution of galaxies (simulations with dark matter match observations; without it they fail). These independent methods converge on the same dark matter fraction.
Could modified gravity theories explain flat rotation curves without dark matter?
Modified Newtonian Dynamics (MOND), proposed by Mordehai Milgrom in 1983, modifies Newton's second law at very low accelerations (below 1.2×10⁻¹⁰ m/s²) to produce flat rotation curves without dark matter. MOND successfully predicts rotation curves of individual galaxies with fewer free parameters than dark matter models. However, MOND cannot explain the Bullet Cluster (where the gravitational center is offset from the gas), the CMB power spectrum, or galaxy cluster dynamics as naturally as particle dark matter. Relativistic extensions struggle with cosmological data.
What is the dark matter halo profile and how is it measured?
Dark matter halo density profiles are inferred by fitting rotation curves and gravitational lensing data. The NFW (Navarro-Frenk-White) profile, derived from N-body simulations, predicts ρ ∝ 1/[r(1+r/rₛ)²] with a central cusp (density rising as 1/r toward the center). Observationally, some galaxies (especially dwarf galaxies) show central cores rather than cusps—the "cusp-core problem." This tension between simulations and observations motivates study of dark matter self-interactions, baryonic feedback effects from supernovae that can redistribute dark matter, and alternative dark matter models.
How does dark matter influence galaxy formation?
Dark matter halos form first through gravitational collapse of small density fluctuations in the early universe, providing the gravitational potential wells into which ordinary (baryonic) matter falls to form galaxies. The mass, concentration, and merger history of dark matter halos largely determine the size, rotation speed, and star formation history of the galaxies they host. The Tully-Fisher relation—an empirical correlation between galaxy luminosity and maximum rotation velocity—reflects this fundamental connection between dark matter halo mass and galaxy properties, making rotation curves a primary probe of the dark matter–galaxy connection.