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📘 Why do we still need dark matter?

Expert-level survey of dark matter evidence, candidates, and probes

13
lessons
~30 min
to learn
Adults
level
Start the course →

What you’ll learn

  1. Galactic Rotation Curves and the Missing Mass ProblemQuantify the discrepancy between luminous and dynamical mass using observed rotation curves and derive the required halo density profile.Rotation curves provide the first quantitative evidence for non-baryonic mass. The flatness at large radii rules out Keplerian decline and demands an extended halo. NFW and Einasto parametrizations are introduced as standard benchmarks for later chapters.
  2. Virial Masses in Galaxy ClustersApply the virial theorem and hydrostatic equilibrium to cluster observables and extract the dark-matter fraction.Cluster dynamics independently require dominant non-baryonic mass. The measured gas fraction combined with nucleosynthesis bounds excludes baryons as the sole constituent. These results set the stage for cosmological density parameters.
  3. Strong and Weak Gravitational LensingReconstruct three-dimensional mass distributions from strong- and weak-lensing shear and convergence fields.Lensing measures total mass irrespective of dynamical state. The offset between lensing mass and baryonic tracers in merging systems supplies direct visual evidence for collisionless dark matter.
  4. The Bullet Cluster and Collisionless DynamicsInterpret the separation of collisional gas from collisionless mass and place limits on dark-matter self-interaction.The Bullet Cluster supplies the cleanest empirical demonstration that the dominant mass component is effectively collisionless on cluster scales. This constraint eliminates many strongly self-interacting models.
  5. CMB Power Spectrum and Baryon Acoustic OscillationsExtract the cold dark matter density parameter from CMB anisotropies and BAO measurements.The CMB fixes the total matter density and the baryon fraction to percent precision. The required non-baryonic fraction is 84 percent of the matter budget and must be cold by z = 1090.
  6. N-Body Simulations and Halo AssemblyUse N-body results to predict halo density profiles, substructure statistics, and assembly bias.High-resolution simulations establish the universal NFW form and its scatter. They also quantify the missing-satellites and too-big-to-fail problems that motivate baryonic or dark-sector solutions.
  7. WIMP Candidates and Thermal Freeze-OutCalculate the thermal relic density for a generic WIMP and map viable parameter space.The WIMP miracle links the observed abundance to electroweak-scale physics. Direct and indirect detection rates are now expressed in terms of the same annihilation cross-section.
  8. Axions and Ultralight Dark MatterDerive axion relic density from the misalignment angle and contrast wave-like versus particle-like regimes.Axions evade the WIMP paradigm yet remain testable through cavity and NMR techniques. Ultralight scalars alter halo cores and soliton formation, offering distinct observational signatures.
  9. Underground Direct Detection ExperimentsTranslate nuclear recoil spectra into WIMP-nucleon cross-section limits and assess irreducible neutrino backgrounds.Current tonne-scale detectors have reached the neutrino floor for spin-independent scattering. Next-generation experiments must discriminate solar neutrino coherent scattering from dark-matter signals.
  10. Indirect detection and modified-gravity testsCompute expected fluxes from prompt and secondary photons, neutrinos, and charged cosmic rays. Compare MOND and emergent-gravity predictions against cluster lensing and cosmological data.Indirect searches constrain the same annihilation cross-section that sets the relic density. Astrophysical foregrounds and propagation uncertainties remain the dominant systematics. Modified-gravity alternatives succeed on galactic scales yet fail on cluster and cosmological scales. The data therefore continue to favor a particle or field dark-matter component.
  11. Halo Substructure and the Missing-Satellites ProblemQuantify the subhalo mass function and map suppression mechanisms to observed satellite luminosity functions.Baryonic physics plus reionization largely resolves the missing-satellites discrepancy. The remaining tension lies in the too-big-to-fail problem for the most massive subhalos.
  12. Collider and Accelerator ConstraintsTranslate LHC missing-energy signatures into limits on dark-matter mediator and coupling parameters.Collider bounds close the low-mass window left open by direct detection. Effective-field-theory operators are matched to UV-complete models to maintain consistency across experiments.
  13. Future Surveys and Theoretical FrontiersForecast parameter constraints from Stage-IV surveys and next-generation direct-detection technologies.The combination of cosmological surveys, terrestrial detectors, and collider data will either discover the dark-matter particle or push its interactions far below the thermal-relic benchmark. Persistent null results will sharpen the case for non-thermal or hidden-sector scenarios.

Questions this course answers

A newly observed spiral shows v = 180 km s⁻¹ flat beyond 12 kpc. If its baryonic mass inside 12 kpc is 1.5 × 10¹⁰ M⊙, what dark-matter fraction is required inside 36 kpc?

M_dyn(36 kpc) = v² r / G = 2.7 × 10¹¹ M⊙, so the dark fraction is 1 − 1.5e10/2.7e11 ≈ 0.83.

A newly observed relaxed cluster at z = 0.2 shows f_gas = 0.14 inside r_500 and a weak-lensing M_500 = 8 × 10¹⁴ M_⊙. What dark-matter fraction is implied?

Subtracting the observed gas plus stellar fraction (~0.16) from unity leaves a dark-matter fraction of ~0.84, matching the canonical value for massive clusters.

Which observable directly constrains the inner logarithmic slope of the 3D density after tomographic inversion?

Astrometric residuals inside the strong-lensing regime are most sensitive to the central density gradient once the smooth model is subtracted; outer shear and source redshifts constrain the envelope and geometry but not the inner slope at the same precision.

If dark matter had a self-interaction cross section of 5 cm² g⁻¹, which observable would be absent in a system like the Bullet Cluster?

A large cross section would couple the dark-matter halos to the gas, preventing the observed separation of collisionless mass from collisional plasma.

Given Ω_m h² = 0.143 and Ω_b h² = 0.0224 from Planck+BAO, what value of Ω_c h² is required?

Subtracting the baryon density from the total matter density isolates the cold dark matter contribution: 0.143 – 0.0224 = 0.1206, which rounds to the measured 0.120–0.121 value.

A new 50 GeV Majorana fermion couples to the Z with strength 0.3 g_w. Its thermally averaged annihilation cross section at freeze-out is 8 × 10^{-27} cm³ s^{-1}. Does it produce the observed dark-matter density?

The cross section is roughly 3.5 times smaller than the canonical 3 × 10^{-26} value, yielding Ωh² ≈ 0.42, which exceeds the observed density.

Grounded in trusted sources

  • NASA
  • CERN
  • Fermilab
  • Particle Data Group, Review of Particle Physics — dark matter overview
  • Planck Collaboration papers — CMB constraints on dark matter density
  • Clowe et al., Bullet Cluster lensing/X-ray separation papers
  • Bertone & Hooper, dark matter review literature; PDG / Fermilab explainers
  • NASA / ESA public lensing and cluster resources

Every Wunder lesson is built from real, reputable sources — never invented.

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