Dark matter

Dark matter is an inferred gravitating component whose mass is not accounted for by the observed luminous material. Galaxy rotation curves, motions in galaxy clusters and gravitational lensing probe its gravitational contribution through different measurements.^[ref]

For illustration, circular motion in a spherical mass distribution obeys $v_c^2=GM(<r)/r$. A roughly constant orbital speed over increasing radius therefore requires enclosed mass to keep increasing in this model. A realistic inference also models visible matter and the system's geometry; a rotation curve alone is not a direct identification of a new particle.

Dark-matter direct detection searches for interactions in terrestrial targets, while indirect detection of dark matter looks for secondary products. These tests address microscopic models rather than replacing the astronomical gravitational evidence.

Dark-matter indirect detection searches for ordinary particles or radiation produced by hypothetical dark-matter annihilation or decay. Candidate signals include gamma rays, neutrinos and charged cosmic rays.

An annihilation rate is typically proportional to the square of dark-matter density, while a decay rate is proportional to density. Predicted signals therefore depend on both particle properties and the distribution of dark matter along the line of sight. Astrophysical sources can produce similar radiation, so a spectral excess alone is not a unique identification. Consistent spatial, spectral and multi-messenger evidence is needed to distinguish a proposed signal from backgrounds.

Direct detection measures scattering or absorption of incident halo particles in a target. Indirect detection searches for secondary products from annihilation or decay. Recording those secondary particles directly does not turn an indirect search into a direct halo-scattering measurement.

A search for interactions of passing dark matter with a terrestrial target, for example nuclear recoils from elastic scattering. Predicting a count requires the local density and velocity distribution, interaction cross section, target response and detector acceptance. A background-compatible count gives a conditional interaction bound, rather than a measurement of the cosmological relic density.

An elastic recoil interaction whose leading coherent nuclear amplitude does not depend on nuclear spin. At low momentum transfer, proton and neutron amplitudes add; equal couplings give an $A$-fold amplitude and the displayed cross-section scaling, with reduced masses ${\mu }_A$ and ${\mu }_p$. A finite-momentum nuclear form factor reduces coherence. Unequal nucleon couplings or other interactions change how experiments on different targets should be compared.

A low-momentum dark-matter–nucleon elastic cross section and a high-energy collider pair-production cross section are different observables. Crossing of amplitudes does not equate their numerical values. Mediator masses, couplings, nuclear matrix elements, parton distributions and kinematics enter the relation. Collider sensitivity further requires a trigger, visible recoil, acceptance and background treatment. Multiplying a direct-detection cross section by collider luminosity is therefore only a hypothetical dimensional estimate unless a production model justifies the substitution.

The Earth's changing velocity relative to a halo changes the recoil-rate integral above a detector threshold. Its phase and energy dependence depend on the velocity distribution and interaction, so a sinusoidal fit is a model approximation. Seasonal instrumental or environmental backgrounds can also vary annually; energy radiation spectrum, multiple-hit samples, time stability and independent targets help test a proposed dark-matter interpretation.

A cryogenic direct-detection search using scintillating crystal calorimeters. Calcium-tungstate modules measure deposited energy through phonons and compare a separate light signal to discriminate recoil populations. Oxygen, calcium and tungsten recoil differently for a given WIMP mass; a model fit must include their responses and backgrounds.^[ref]

Cryogenic germanium or silicon detectors combining phonon and ionization signals. Relative charge yield discriminates electron and nuclear recoils, while phonon timing helps identify surface backgrounds. Lower thresholds extend light-WIMP sensitivity but require renewed efficiency, energy-scale and leakage studies.^[ref]

A low-threshold point-contact germanium ionization search. The small readout capacitance supports sensitivity to low-energy interactions. Bulk/surface charge collection, internal lines, threshold response and time dependence must be controlled before interpreting an excess or modulation as a WIMP recoil.^[ref]

An underground NaI(Tl) particle scintillation experiment seeking annual variation in low-energy single-hit rates. Its reported modulation is an observable; mapping it to a WIMP mass and cross section requires assumptions about the interaction, halo distribution and detector recoil response. Multiple-hit and other-energy samples test some backgrounds, but particle scintillation alone does not label every interaction as a nuclear recoil.^[ref]

A compact astronomical object proposed as a constituent of a galactic dark matter halo. It can be sought through gravitational microlensing even if its emitted light is undetectable. Stellar objects and remnants consume the cosmological baryon budget; primordial black holes do not obey that particular formation-budget argument. Exclusion bounds depend on the object's mass, the halo model and survey selection.

A matter component with relativistic motion during an important part of structure formation. Its free streaming suppresses small-scale perturbations. Making a light thermal neutrino Majorana rather than Dirac does not by itself turn this component into cold dark matter.

The maximum primordial occupation of a collisionless fermion distribution limits the coarse-grained phase-space density attainable in a halo. Combining that bound with an observed velocity dispersion and mass density gives a lower candidate mass. This tests light-fermion halo models independently of whether the candidate is optically visible.^[ref]

Fine-grained occupation is conserved along trajectories of a collisionless distribution. Coarse graining cannot increase its maximum. For fermions the primordial occupation is bounded, so a measured halo density and velocity scale restrict the particle mass required to produce that halo.

For identical self-conjugate dark matter particles, the pair-annihilation rate per volume is $⟨\sigma v⟩n_{\chi }^2/2$. If each annihilation releases radiated energy $E_a$, volume emissivity is $j=E_a⟨\sigma v⟩{\rho }^2/(2m_{\chi }^2)$. Optically thin isotropic surface brightness is $(4\pi {)}^{-1}\int jdz$. The squared-density dependence assumes a spatially constant rate coefficient and a smooth density; unresolved substructure changes the average of the square.

The line-of-sight, solid-angle integral of squared dark-matter density used for annihilation fluxes with a position-independent rate coefficient. It separates an astrophysical density model from particle yields and annihilation rates. A decay signal instead scales with a single power of density. Substructure or spatially varying velocity-dependent rates can prevent a simple smooth-density factorization.

If a dark matter particle of mass $m_{\chi }$ radiates power $ϵ$ independently of its neighbours, optically thin isotropic emission has volume emissivity $j=ϵ\rho /m_{\chi }$. Its surface brightness is $I=(4\pi {)}^{-1}\int jdz$ and therefore traces the mass column rather than its square.

A weakly interacting massive particle is a massive dark-matter candidate whose interaction strength permits thermal production and later cosmological particle freeze-out. Its relic abundance depends on the annihilation rate and cosmological history, not on its mass alone. At nucleosynthesis temperatures a 50 GeV example is nonrelativistic: its equilibrium density is reduced by Boltzmann suppression, while an already frozen relic population need not follow the equilibrium density. Its effect on nucleosynthesis depends on whether the surviving energy density is appreciable or whether it injects reaction-altering products.

Cold dark matter is nonrelativistic early enough that its primordial free-streaming length is small compared with the cosmological structures of interest.

Warm dark matter has a primordial collisionless free streaming length large enough to suppress the formation of low-mass haloes, while remaining nonrelativistic early enough to cluster on galactic and larger scales.