Relativistic beaming

Relativistic beaming is the forward concentration of electromagnetic radiation emitted by a source moving at relativistic speed v = βc. In the source's instantaneous rest frame the emission pattern may be the familiar sin²θ doughnut of non-relativistic dipole radiation (roughly isotropic). After Lorentz-boosting into the laboratory frame, however, that pattern collapses into a narrow cone of half-angle θ_beam ≈ 1/γ centred on the direction of motion. A source with γ = 10 beams 97% of its radiation into a 5.7° cone; a blazar jet with γ = 30 beams into a 2° cone; a pulsar with γ = 10⁶ beams into a sub-arcsecond cone.

The mechanism is geometric: solid-angle elements in the rest frame dΩ′ transform to laboratory solid-angle elements dΩ = dΩ′/δ², where the Doppler factor δ = 1/[γ(1 − β·n̂)] exceeds unity in the forward direction and is much less than unity in the backward hemisphere. Photons emitted forward arrive blueshifted and concentrated; photons emitted backward arrive redshifted and dispersed. The observable signatures are dramatic. A relativistic source moving toward the observer brightens by a factor δ^(3+α) (where α is the spectral index) relative to its rest-frame luminosity — a "boost" of orders of magnitude. This is why blazar jets, viewed down the jet axis, outshine their host galaxies; why quasar superluminal motion (apparent velocities > c) is observed on VLBI maps; and why pulsars appear as on-off sources rather than steady glows (the beam points at the observer only during a small fraction of each rotation). The contrast ratio between beam-on and beam-off intensity scales as δ^4 ∼ γ^4, which for γ = 10⁶ is 10²⁴ — the pulsar regime.