🌌 Dark Matter — Galaxy Rotation Curves
One of the strongest pieces of evidence for dark matter comes from galaxy rotation curves. Stars at the outskirts of galaxies orbit much faster than Kepler's laws predict from visible mass alone. Explore the NFW dark matter halo profile and see how it fills the gap.
View
Baryonic Mass
Dark Matter Halo (NFW)
Legend
ρ(r) = ρ₀ / [(r/r_s)·(1+r/r_s)²]
v_halo² = GM_halo(r)/r
v_total² = v_disk²+v_bulge²+v_halo²
Vera Rubin (1970s) confirmed
flat curves in 200+ galaxies.
The Dark Matter Problem
According to Newtonian gravity and the visible matter in a galaxy (stars, gas, dust), orbital speeds should fall off as v ∝ r-½ at large radii — just like planets around the Sun. But observations by Vera Rubin and Kent Ford in the 1970s showed that rotation curves of spiral galaxies are flat out to many scale radii. The only way to explain this is to postulate a large, extended mass distribution — a dark matter halo — that adds mass even where no stars are visible. The NFW (Navarro-Frenk-White) profile describes the density distribution predicted by cold dark matter simulations: ρ(r) = ρ₀ / [(r/r_s)(1+r/r_s)²]. About 85% of all matter in the Universe is thought to be dark matter, yet its nature remains unknown.
About Dark Matter — Galaxy Rotation Curves
This simulation models the orbital velocities of stars and gas clouds at different radii in a spiral galaxy, comparing what Newtonian gravity predicts from visible (baryonic) matter alone against the flat rotation curves that astronomers actually observe. You can adjust the disk mass, bulge mass, and NFW dark matter halo parameters to see how each component contributes to the total circular velocity, and discover that a massive invisible halo is required to match observations.
Galaxy rotation curves became the most compelling evidence for dark matter after Vera Rubin and Kent Ford systematically measured dozens of spiral galaxies in the 1970s and 1980s, confirming that the outer regions orbit far too fast to be explained by visible stars and gas alone.
Frequently Asked Questions
What is dark matter?
Dark matter is a form of matter that does not interact with the electromagnetic force — it emits no light, reflects none, and absorbs none — yet it possesses gravitational mass. It accounts for approximately 85% of all matter in the Universe. Its exact nature is unknown: leading candidates include weakly interacting massive particles (WIMPs), axions, and sterile neutrinos, but none has been directly detected in a laboratory so far.
How do I use this simulation?
Use the sliders in the control panel to adjust the disk mass, disk scale radius, bulge mass, dark matter halo mass, and the NFW scale radius. The Rotation Curve view plots circular velocity versus radius in kiloparsecs, showing separate coloured lines for the disk (yellow), bulge (red), dark matter halo (purple), and the total (cyan). Set the halo mass to zero to see the Keplerian drop-off without dark matter, then increase it to match the flat observed curve. Switch to the Galaxy view to see how the extended halo surrounds the visible stellar disk.
Why do rotation curves stay flat instead of dropping off?
Without a dark matter halo, the circular velocity beyond the visible disk should fall roughly as v ∝ r-½ — the same Keplerian decline seen among planets in the Solar System. Observations show instead that velocity stays roughly constant (flat) out to radii of 30–50 kpc and beyond. This flatness requires additional enclosed mass growing proportionally with radius, supplied by the extended dark matter halo whose density follows the NFW profile: rho(r) = rho_0 / [(r/r_s)(1+r/r_s)^2].
What is the NFW profile and why is it used?
The Navarro-Frenk-White (NFW) profile was derived in 1996 from cosmological N-body simulations of cold dark matter. It describes halo density as rho(r) = rho_0 / [(r/r_s)(1+r/r_s)^2], where r_s is the scale radius. At small radii the density rises as 1/r (a cusp), and at large radii it falls as 1/r^3. The enclosed mass grows logarithmically, producing a nearly flat rotation curve over a wide range of radii. NFW halos are characterised by just two parameters — the halo mass M_200 and the concentration c = r_200/r_s — making them very practical for fitting observations.
What real galaxies show the flattest rotation curves?
The Milky Way's rotation curve is flat at about 220 km/s from roughly 5 kpc out to at least 60 kpc. Andromeda (M31) shows similar behaviour. Among the most striking examples are low-surface-brightness (LSB) galaxies, which contain almost no visible stars in their outer regions yet show the same flat curve — meaning the dark matter halo completely dominates. The galaxy NGC 3198 became a classic textbook case after van Albada et al. (1985) demonstrated that its rotation curve out to 30 kpc could only be explained by a massive dark matter halo.
Is dark matter the only explanation for flat rotation curves?
Modified Newtonian Dynamics (MOND), proposed by Mordehai Milgrom in 1983, suggests that gravity behaves differently at very low accelerations (below about 1.2 × 10^-10 m/s^2), naturally producing flat rotation curves without dark matter. MOND fits many individual galaxies well, but it struggles to explain galaxy cluster dynamics (the Bullet Cluster in particular), the cosmic microwave background anisotropy spectrum, and large-scale structure formation. The mainstream scientific view remains that dark matter is real, though MOND-inspired theories such as TeVeS and relativistic MOND variants are still actively studied.
Who discovered flat rotation curves and when?
Fritz Zwicky first inferred missing mass in the Coma galaxy cluster in 1933 from the velocities of member galaxies. Horace Babcock measured a rising rotation curve in Andromeda as early as 1939. The systematic confirmation came from Vera Rubin and Kent Ford starting in 1970, who measured rotation curves of dozens of spiral galaxies with high-sensitivity spectrographs and showed unambiguously that the curves are flat far beyond the optical disk. Rubin's work, combined with N-body simulations in the late 1970s and 1980s, established the dark matter halo as the standard cosmological model.
What other evidence supports the existence of dark matter?
Beyond rotation curves, dark matter is supported by gravitational lensing (galaxy clusters bend light far more than their visible mass allows), the Bullet Cluster (where two colliding clusters show the gas slowing due to electromagnetism while the dark matter halos passed through each other), the cosmic microwave background power spectrum (which encodes the ratio of baryonic to dark matter), and large-scale structure simulations that only reproduce observed filaments and voids when dark matter is included. Each of these independent lines of evidence points to the same dark matter fraction of roughly 27% of the total energy density of the Universe.
How is dark matter research connected to particle physics?
The most studied candidate, WIMPs (Weakly Interacting Massive Particles), would have masses in the range of 10 GeV to a few TeV and interact via the weak nuclear force. Underground detectors such as LUX-ZEPLIN (LZ), XENONnT, and PandaX-4T search for the tiny recoil when a WIMP scatters off a heavy nucleus. The Large Hadron Collider at CERN looks for dark matter pair-production as missing transverse energy in collision events. Axion experiments (ADMX, HAYSTAC) probe a different mass range around 10^-5 eV. So far no confirmed direct detection has been reported, but limits on WIMP cross-sections have improved by many orders of magnitude since the 1990s.
What are the current open questions in dark matter research?
Despite decades of searching, dark matter has never been directly detected as a particle. The "cusp-core problem" questions whether NFW profiles accurately describe halo centres, since observations of dwarf galaxies often prefer flat-density cores rather than sharp cusps. The "missing satellites problem" notes that cold dark matter simulations predict far more small subhalos than the number of satellite galaxies observed around the Milky Way. Self-interacting dark matter (SIDM) models attempt to resolve these small-scale discrepancies. Primordial black holes and ultralight "fuzzy" dark matter are further candidates under active investigation.