Dark matter

Dark matter is matter inferred from its gravitational effects that does not emit, absorb, or scatter enough electromagnetic radiation to account for those effects as ordinary baryonic matter.

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.

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.