![Radio galaxy 3C31](https://upload.wikimedia.org/wikipedia/commons/e/e4/Radio_galaxy_3C31.png)
Relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which
relativistic effects
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of ...
modify the apparent luminosity of emitting matter that is moving at speeds close to the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. In an astronomical context, relativistic beaming commonly occurs in two oppositely-directed
relativistic jet
An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets bec ...
s of
plasma
Plasma or plasm may refer to:
Science
* Plasma (physics), one of the four fundamental states of matter
* Plasma (mineral), a green translucent silica mineral
* Quark–gluon plasma, a state of matter in quantum chromodynamics
Biology
* Blood pla ...
that originate from a central
compact object that is
accreting matter. Accreting compact objects and relativistic jets are invoked to explain
x-ray binaries
X-ray binaries are a class of binary stars that are luminous in X-rays.
The X-rays are produced by matter falling from one component, called the ''donor'' (usually a relatively normal star), to the other component, called the ''accretor'', which ...
,
gamma-ray burst
In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten milli ...
s, and, on a much larger scale,
active galactic nuclei
An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
(
quasar
A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s are also associated with an accreting compact object, but are thought to be merely a particular variety of active galactic nuclei, or
AGNs).
Beaming affects the apparent brightness of a moving object. Consider a cloud of gas moving relative to the observer and emitting electromagnetic radiation. If the gas is moving towards the observer, it will be brighter than if it were at rest, but if the gas is moving away, it will appear fainter. The magnitude of the effect is illustrated by the
AGN jets of the galaxies
M87 and
3C 31 (see images at right). M87 has twin jets aimed almost directly towards and away from Earth; the jet moving towards Earth is clearly visible (the long, thin blueish feature in the top image), while the other jet is so much fainter it is not visible. In 3C 31, both jets (labeled in the lower figure) are at roughly right angles to our line of sight, and thus, both are visible. The upper jet actually points slightly more in Earth's direction and is therefore brighter.
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
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
changes the energy of the photons by red- or blue-shifting them. Finally, time intervals as measured by clocks moving alongside the emitting object are different from those measured by an observer on Earth due to
time dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
and photon arrival time effects. How all of these effects modify the brightness, or apparent luminosity, of a moving object is determined by the equation describing the
relativistic Doppler effect
The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special rel ...
(which is why relativistic beaming is also known as Doppler beaming).
A simple jet model
The simplest model for a jet is one where a single, homogeneous sphere is travelling towards the Earth at nearly the speed of light. This simple model is also an unrealistic one, but it does illustrate the physical process of beaming quite well.
Synchrotron spectrum and the spectral index
Relativistic jet
An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets bec ...
s emit most of their energy via
synchrotron emission
Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in ...
. In our simple model the sphere contains highly relativistic electrons and a steady magnetic field. Electrons inside the blob travel at speeds just a tiny fraction below the speed of light and are whipped around by the magnetic field. Each change in direction by an electron is accompanied by the release of energy in the form of a photon. With enough electrons and a powerful enough magnetic field the relativistic sphere can emit a huge number of photons, ranging from those at relatively weak radio frequencies to powerful X-ray photons.
The figure of the sample spectrum shows basic features of a simple synchrotron spectrum. At low frequencies the jet sphere is opaque and its luminosity increases with frequency until it peaks and begins to decline. In the sample image this ''peak frequency'' occurs at
. At frequencies higher than this the jet sphere is transparent. The luminosity decreases with frequency until a ''break frequency'' is reached, after which it declines more rapidly. In the same image the break frequency occurs when
. The sharp break frequency occurs because at very high frequencies the electrons which emit the photons lose most of their energy very rapidly. A sharp decrease in the number of high energy electrons means a sharp decrease in the spectrum.
The changes in slope in the synchrotron spectrum are parameterized with a ''spectral index''. The spectral index, α, over a given frequency range is simply the slope on a diagram of
vs.
. (Of course for α to have real meaning the spectrum must be very nearly a straight line across the range in question.)
Beaming equation
In the simple jet model of a single homogeneous sphere the observed luminosity is related to the intrinsic luminosity as
:
where
:
The observed luminosity therefore depends on the speed of the jet and the angle to the line of sight through the Doppler factor,
, and also on the properties inside the jet, as shown by the exponent with the spectral index.
The beaming equation can be broken down into a series of three effects:
* Relativistic aberration
* Time dilation
* Blue- or redshifting
Aberration
Aberration is the change in an object's
apparent direction caused by the relative transverse motion of the observer. In inertial systems it is equal and opposite to the
light time correction
Light-time correction is a displacement in the ''apparent'' position of a celestial object from its ''true'' position (or geometric position) caused by the object's motion during the time it takes its light to reach an observer.
Light-time corr ...
.
In everyday life aberration is a well-known phenomenon. Consider a person standing in the rain on a day when there is no wind. If the person is standing still, then the rain drops will follow a path that is straight down to the ground. However, if the person is moving, for example in a car, the rain will appear to be approaching at an angle. This apparent change in the direction of the incoming raindrops is aberration.
The amount of aberration depends on the speed of the emitted object or wave relative to the observer. In the example above this would be the speed of a car compared to the speed of the falling rain. This does not change when the object is moving at a speed close to
. Like the classic and relativistic effects, aberration depends on: 1) the speed of the emitter at the time of emission, and 2) the speed of the observer at the time of absorption.
In the case of a relativistic jet, beaming (emission aberration) will make it appear as if more energy is sent forward, along the direction the jet is traveling. In the simple jet model a homogeneous sphere will emit energy equally in all directions in the rest frame of the sphere. In the rest frame of Earth the moving sphere will be observed to be emitting most of its energy along its direction of motion. The energy, therefore, is ‘beamed’ along that direction.
Quantitatively, aberration accounts for a change in luminosity of
:
Time dilation
Time dilation is a well-known consequence of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
and accounts for a change in observed luminosity of
:
Blue- or redshifting
Blue- or
redshifting can change the observed luminosity at a particular frequency, but this is not a beaming effect.
Blueshifting accounts for a change in observed luminosity of
:
Lorentz invariants
A more-sophisticated method of deriving the beaming equations starts with the quantity
. This quantity is a Lorentz invariant, so the value is the same in different reference frames.
Terminology
; beamed, beaming : shorter terms for ‘relativistic beaming’
; beta : the ratio of the jet speed to the speed of light, sometimes called ‘relativistic beta’
; core : region of a galaxy around the central
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
; counter-jet : the jet on the far side of a source oriented close to the line of sight, can be very faint and difficult to observe
; Doppler factor : a mathematical expression which measures the strength (or weakness) of relativistic effects in
AGN, including beaming, based on the jet speed and its angle to the line of sight with Earth
; flat spectrum : a term for a non-thermal
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
that emits a great deal of energy at the higher frequencies when compared to the lower frequencies
; intrinsic luminosity : the
luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...
from the jet in the rest frame of the jet
; jet (often termed '
relativistic jet
An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets bec ...
'): a high velocity (close to c) stream of plasma emanating from the polar direction of an AGN
; observed luminosity : the
luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...
from the jet in the rest frame of Earth
; spectral index :a measure of how a non-thermal
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
changes with frequency. The smaller
α is, the more significant the energy at higher frequencies is. Typically α is in the range of 0 to 2.
; steep spectrum : a term for a non-thermal
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
that emits little energy at the higher frequencies when compared to the lower frequencies
Physical quantities
; angle to the line-of-sight with Earth :
; jet speed :
; intrinsic luminosity :
(sometimes called emitted luminosity)
; observed Luminosity :
; spectral index :
where
;
Speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
:
m/s
Mathematical expressions
; relativistic beta :
; Lorentz factor :
; Doppler factor :
See also
*
Astrophysical jet
An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation. When this greatly accelerated matter in the beam approaches the speed of light, astrophysical jets bec ...
*
List of plasma physics articles
This is a list of plasma physics topics.
A
* Ablation
* Abradable coating
* Abraham–Lorentz force
* Absorption band
* Accretion disk
* Active galactic nucleus
* Adiabatic invariant
* ADITYA (tokamak)
* Aeronomy
* Afterglow plasma
* Air ...
*
Relativistic Doppler effect
The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special rel ...
*
Relativistic particle
A relativistic particle is a particle which moves with a relativistic speed; that is, a speed comparable to the speed of light. This is achieved by photons to the extent that effects described by special relativity are able to describe those of su ...
*
Relativistic plasma Relativistic plasmas in physics are plasmas for which relativistic corrections to a particle's mass and velocity are important. Such corrections typically become important when a significant number of electrons reach speeds greater than 0.86 c (Lo ...
*
Relativistic similarity parameter
In relativistic laser-plasma physics the relativistic similarity parameter ''S'' is a dimensionless parameter defined as
: S=\frac,
where is the electron plasma density, is the critical plasma density and is the normalized vector potential. H ...
*
Relativistic wave equations
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the con ...
References
External links
Detailed explanation of relativistic aberration
{{DEFAULTSORT:Relativistic Beaming
Astrophysics