Relativistic beaming

In physics, relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light.

Accreting compact objects and relativistic jets are invoked to explain x-ray binaries, gamma-ray bursts, and, on a much larger scale, (AGN) active galactic nuclei (of which quasars are a particular variety).

Consider a cloud of gas moving relative to the observer and emitting electromagnetic radiation.

[1] In 3C 31, both jets (labeled in the lower figure at right) are at roughly right angles to our line of sight, and thus, both are visible.

[2] Relativistically, moving objects are beamed due to a variety of physical effects.

Light aberration causes most of the photons to be emitted along the object's direction of motion.

The Doppler effect changes the energy of the photons by red- or blue shifting them.

The simplest model for a jet is one where a single, homogeneous sphere is travelling towards the Earth at nearly the speed of light.

In our simple model, the sphere contains highly relativistic electrons and a steady magnetic field.

Each change in direction by an electron is accompanied by the release of energy in the form of a photon.

The beaming equation can be broken down into a series of three effects: Aberration is the change in an object's apparent direction caused by the relative transverse motion of the observer.

The amount of aberration depends on the speed of the emitted object or wave relative to the observer.

In the rest frame of Earth the moving sphere will be observed to be emitting most of its energy along its direction of motion.

Blueshifting accounts for a change in observed luminosity of A more-sophisticated method of deriving the beaming equations starts with the quantity