Synchrotron radiation

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Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity (a ⊥ v). It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.

Synchrotron radiation from a bending magnet

 

Synchrotron radiation from an undulator

History

Syncradiation was named after its discovery in Schenectady, New York from a General Electric synchrotron accelerator built in 1946 and announced in May 1947 by Frank Elder, Anatole Gurewitsch, Robert Langmuir and Herb Pollock in a letter entitled "Radiation from Electrons in a Synchrotron". Pollock recounts:

On April 24, Langmuir and I were running the machine and as usual were trying to push the electron gun and its associated pulse transformer to the limit. Some intermittent sparking had occurred and we asked the technician to observe with a mirror around the protective concrete wall. He immediately signaled to turn off the synchrotron as "he saw an arc in the tube." The vacuum was still excellent, so Langmuir and I came to the end of the wall and observed. At first we thought it might be due to Cherenkov radiation, but it soon became clearer that we were seeing Ivanenko and Pomeranchuk radiation.

Properties of synchrotron radiation

1. Broad Spectrum (which covers from microwaves to hard X-rays): the users can select the wavelength required for their experiment;
2. High Flux: high intensity photon beam allows rapid experiments or use of weakly scattering crystals;
3. High Brilliance: highly collimated photon beam generated by a small divergence and small size source (spatial coherence);
4. High Stability: submicron source stability;
5. Polarization: both linear and circular;
6. Pulsed Time Structure: pulsed length down to tens of picoseconds allows the resolution of process on the same time scale.

Emission mechanism

When high-energy particles are in acceleration, including electrons forced to travel in a curved path by a magnetic field, synchrotron radiation is produced. This is similar to a radio antenna, but with the difference that, in theory, the relativistic speed will change the observed frequency due to the Doppler effect by the Lorentz factor, γ. Relativistic length contraction then bumps the frequency observed by another factor of γ, thus multiplying the GHz frequency of the resonant cavity that accelerates the electrons into the X-ray range. The radiated power is given by the relativistic Larmor formula while the force on the emitting electron is given by the Abraham–Lorentz–Dirac force.

The radiation pattern can be distorted from an isotropic dipole pattern into an extremely forward-pointing cone of radiation. Synchrotron radiation is the brightest artificial source of X-rays.
The planar acceleration geometry appears to make the radiation linearly polarized when observed in the orbital plane, and circularly polarized when observed at a small angle to that plane. Amplitude and frequency are however focused to the polar ecliptic.

Synchrotron radiation from accelerators

Synchrotron radiation may occur in accelerators either as a nuisance, causing undesired energy loss in particle physics contexts, or as a deliberately produced radiation source for numerous laboratory applications. Electrons are accelerated to high speeds in several stages to achieve a final energy that is typically in the GeV range. In the LHC proton bunches also produce the radiation at increasing amplitude and frequency as they accelerate with respect to the vacuum field, propagating photoelectrons, which in turn propagate secondary electrons from the pipe walls with increasing frequency and density up to 7×10¹⁰. Each proton may lose 6.7 keV per turn due to this phenomenon.

Synchrotron radiation in astronomy

Messier 87's astrophysical jet, HST image. The blue light from the jet emerging from the bright AGN core, towards the lower right, is due to synchrotron radiation.

Synchrotron radiation is also generated by astronomical objects, typically where relativistic electrons spiral (and hence change velocity) through magnetic fields. Two of its characteristics include non-thermal power-law spectra, and polarization.

History of detection

It was first detected in a jet emitted by Messier 87 in 1956 by Geoffrey R. Burbidge, who saw it as confirmation of a prediction by Iosif S. Shklovsky in 1953, but it had been predicted earlier by Hannes Alfvén and Nicolai Herlofson in 1950. Solar flares accelerate particles that emit in this way, as suggested by R. Giovanelli in 1948 and described critically by J.H. Piddington in 1952.

T. K. Breus noted that questions of priority on the history of astrophysical synchrotron radiation are complicated, writing:

In particular, the Russian physicist V.L. Ginzburg broke his relationships with I.S. Shklovsky and did not speak with him for 18 years. In the West, Thomas Gold and Sir Fred Hoyle were in dispute with H. Alfven and N. Herlofson, while K.O. Kiepenheuer and G. Hutchinson were ignored by them.

Crab Nebula. The bluish glow from the central region of the nebula is due to synchrotron radiation.

Supermassive black holes have been suggested for producing synchrotron radiation, by ejection of jets produced by gravitationally accelerating ions through the super contorted 'tubular' polar areas of magnetic fields. Such jets, the nearest being in Messier 87, have been confirmed by the Hubble telescope as apparently superluminal, travelling at 6 × c (six times the speed of light) from our planetary frame. This phenomenon is caused because the jets are travelling very near the speed of light and at a very small angle towards the observer. Because at every point of their path the high-velocity jets are emitting light, the light they emit does not approach the observer much more quickly than the jet itself. Light emitted over hundreds of years of travel thus arrives at the observer over a much smaller time period (ten or twenty years) giving the illusion of faster than light travel. There is no violation of special relativity.

Pulsar wind nebulae

A class of astronomical sources where synchrotron emission is important is the pulsar wind nebulae, a.k.a. plerions, of which the Crab nebula and its associated pulsar are archetypal. Pulsed emission gamma-ray radiation from the Crab has recently been observed up to ≥25 GeV, probably due to synchrotron emission by electrons trapped in the strong magnetic field around the pulsar. Polarization in the Crab at energies from 0.1 to 1.0 MeV illustrates a typical synchrotron radiation.

Formulation

Liénard–Wiechert Field

We start with the expressions for the Liénard–Wiechert field:

${\displaystyle {\begin{aligned}\mathbf {B} (\mathbf {r} ,t)&=-{\frac {\mu _{0}q}{4\pi }}\left[{\frac {c\,{\hat {\mathbf {n} }}\times {\vec {\beta }}}{\gamma ^{2}R^{2}\,(1-{\vec {\beta }}\mathbf {\cdot } {\hat {\mathbf {n} }})^{3}}}+{\frac {{\hat {\mathbf {n} }}\times [\,{\dot {\vec {\beta }}}+{\hat {\mathbf {n} }}\times ({\vec {\beta }}\times {\dot {\vec {\beta }}})]}{R\,(1-{\vec {\beta }}\mathbf {\cdot } {\hat {\mathbf {n} }})^{3}}}\right]_{\mathrm {retarded} },\qquad &(1)\\\mathbf {E} (\mathbf {r} ,t)&={\frac {q}{4\pi \varepsilon _{0}}}\left[{\frac {{\hat {\mathbf {n} }}-{\vec {\beta }}}{\gamma ^{2}R^{2}\,(1-{\vec {\beta }}\mathbf {\cdot } {\hat {\mathbf {n} }})^{3}}}+{\frac {{\hat {\mathbf {n} }}\times [({\hat {\mathbf {n} }}-{\vec {\beta }})\times {\dot {\vec {\beta }}}\,]}{c\,R\,(1-{\vec {\beta }}\mathbf {\cdot } {\hat {\mathbf {n} }})^{3}}}\right]_{\mathrm {retarded} },\qquad &(2)\end{aligned}}}$

where R(t′) = r − r₀(t′), R(t′) = |R(t′)|, and n(t′) = R(t′)/R(t′), which is the unit vector between the observation point and the position of the charge at the retarded time, and t′ is the retarded time.

In equation (1), and (2), the first terms for B and E resulting from the particle fall off as the inverse square of the distance from the particle, and this first term is called the generalized Coulomb field or velocity field. These terms represents the particle static field effect, which is a function of the component of its motion that has zero or constant velocity, as seen by a distant observer at r. By contrast, the second terms fall off as the inverse first power of the distance from the source, and these second terms are called the acceleration field or radiation field because they represent components of field due to the charge's acceleration (changing velocity), and they represent E and B which are emitted as electromagnetic radiation from the particle to an observer at r.

If we ignore the velocity field in order to find the power of emitted EM radiation only, the radial component of Poynting's vector resulting from the Liénard–Wiechert fields can be calculated to be

${\displaystyle [\mathbf {S\cdot } {\hat {\mathbf {n} }}]={\frac {q^{2}}{16\pi ^{2}\varepsilon _{0}c}}\left\{{\frac {1}{R^{2}}}\left|{\frac {{\hat {\mathbf {n} }}\times [({\hat {\mathbf {n} }}-{\vec {\beta }})\times {\dot {\vec {\beta }}}]}{(1-{\vec {\beta }}\mathbf {\cdot } {\hat {\mathbf {n} }})^{3}}}\right|^{2}\right\}_{\text{retarded}}.\qquad \qquad (3)}$

Note that

• The spatial relationship between β→ and .→β determines the detailed angular power distribution.
• The relativistic effect of transforming from the rest frame of the particle to the observer's frame manifests itself by the presence of the factors (1 − β→⋅n̂) in the denominator of Eq. (3).
• For ultrarelativistic particles the latter effect dominates the whole angular distribution.

The energy radiated into per solid angle during a finite period of acceleration from t′ = T₁ to t′ = T₂ is

${\displaystyle {\begin{aligned}{\frac {\mathrm {d} P}{\mathrm {d} {\mathit {\Omega }}}}&=R(t')^{2}\,[\mathbf {S} (t')\mathbf {\cdot } {\hat {\mathbf {n} }}(t')]\,{\frac {\mathrm {d} t}{\mathrm {d} t'}}=R(t')^{2}\,\mathbf {S} (t')\mathbf {\cdot } {\hat {\mathbf {n} }}(t')\,[1-{\vec {\beta }}(t')\mathbf {\cdot } {\hat {\mathbf {n} }}(t')]\\&={\frac {q^{2}}{16\pi ^{2}\varepsilon _{0}c}}\,{\frac {|{\hat {\mathbf {n} }}(t')\times \{[{\hat {\mathbf {n} }}(t')-{\vec {\beta }}(t')]\times {\dot {\vec {\beta }}}(t')\}|^{2}}{[1-{\vec {\beta }}(t')\mathbf {\cdot } {\vec {\mathbf {n} }}(t')]^{5}}}.\qquad \qquad (4)\end{aligned}}}$

Integrating Eq. (4) over the all solid angles, we get the relativistic generalization of Larmor's formula

${\displaystyle P={\frac {e^{2}}{6\pi \varepsilon _{0}c}}\gamma ^{6}\left[\left|{\dot {\vec {\beta }}}\right|^{2}-\left|{\vec {\beta }}\times {\dot {\vec {\beta }}}\right|^{2}\right].\qquad (5)}$

However, this also can be derived by relativistic transformation of the 4-acceleration in Larmor's formula.

Velocity perpendicular to acceleration (v ⟂ a): synchrotron radiation

When the electron velocity approaches the speed of light, the

emission pattern is sharply collimated forward.

When the charge is in instantaneous circular motion, its acceleration .→β is perpendicular to its velocity β→. Choosing a coordinate system such that instantaneously β→ is in the z direction and .→β is in the x direction, with the polar and azimuth angles θ and φ defining the direction of observation, the general formula Eq. (4) reduces to

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} {\mathit {\Omega }}}}={\frac {q^{2}}{16\pi ^{2}\epsilon _{0}c}}{\frac {|{\dot {\vec {\beta }}}|^{2}}{(1-\beta \cos \theta )^{3}}}\left[1-{\frac {\sin ^{2}\theta \cos ^{2}\phi }{\gamma ^{2}(1-\beta \cos \theta )^{2}}}\right].\qquad (6)}$

In the relativistic limit ${\displaystyle (\gamma \gg 1)}$, the angular distribution can be written approximately as

${\displaystyle {\frac {\mathrm {d} P}{\mathrm {d} {\mathit {\Omega }}}}\simeq {\frac {2}{\pi }}{\frac {e^{2}}{c^{3}}}\gamma ^{6}{\frac {|{\dot {\mathbf {v} }}|^{2}}{(1+\gamma ^{2}\theta ^{2})^{3}}}\left[1-{\frac {4\gamma ^{2}\theta ^{2}\cos ^{2}\phi }{(1+\gamma ^{2}\theta ^{2})^{2}}}\right].\qquad \qquad (7)}$

The factors (1 − βcosθ) in the denominators tip the angular distribution forward into a narrow cone like the beam of a headlight pointing ahead of the particle. A plot of the angular distribution (dP/dΩ vs. γθ) shows a sharp peak around θ = 0.

Integration over the whole solid angle yields the total power radiated by one electron

${\displaystyle P={\frac {e^{2}}{6\pi \epsilon _{0}c}}\left|{\dot {\vec {\beta }}}\right|^{2}\gamma ^{4}={\frac {e^{2}c}{6\pi \epsilon _{0}}}{\frac {\beta ^{4}\gamma ^{4}}{\rho ^{2}}}={\frac {e^{4}}{6\pi \epsilon _{0}m^{4}c^{5}}}B^{2}E^{2}\beta ^{2}={\frac {e^{4}}{6\pi \epsilon _{0}m^{4}c^{5}}}B^{2}(E^{2}-m^{2}c^{4}),\qquad (8)}$

where E is the electron energy, B is the magnetic field, and ρ is the radius of curvature of the track in the field. Note that the radiated power is proportional to 1/m⁴, 1/ρ², and B². In some cases the surfaces of vacuum chambers hit by synchrotron radiation have to be cooled because of the high power of the radiation.

Using

${\displaystyle B={\frac {E\beta }{e\,r\sin(\alpha )}},}$

where α is the angle between the velocity and the magnetic field and r is the radius of the circular acceleration, the power emitted is:

${\displaystyle P={\frac {e^{2}}{6\pi \epsilon _{0}m^{4}c^{5}r^{2}\sin ^{2}(\alpha )}}E^{4}\beta ^{4}={\frac {e^{2}}{6\pi \epsilon _{0}m^{4}c^{5}r^{2}\sin ^{2}(\alpha )}}(E^{2}-m^{2}c^{4})^{2}.}$

Thus the power emitted scales as energy to the fourth, and decreases with the square of the radius and the fourth power of particle mass. This radiation is what limits the energy of an electron-positron circular collider. Generally, proton-proton colliders are instead limited by the maximum magnetic field; this is why, for example, the LHC has a center-of-mass energy 70 times higher than the LEP even though the proton mass is 2000 times the electron mass.

Radiation integral

The energy received by an observer (per unit solid angle at the source) is

${\displaystyle {\frac {d^{2}W}{d\Omega }}=\int _{-\infty }^{\infty }{\frac {d^{2}P}{d\Omega }}dt=c\varepsilon _{0}\int _{-\infty }^{\infty }\left|R{\vec {E}}(t)\right|^{2}dt}$

Using the Fourier transformation we move to the frequency space

${\displaystyle {\frac {d^{2}W}{d\Omega }}=2c\varepsilon _{0}\int _{0}^{\infty }\left|R{\vec {E}}(\omega )\right|^{2}d\omega }$

Angular and frequency distribution of the energy received by an observer (consider only the radiation field)

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}=2c\varepsilon _{0}R^{2}\left|{\vec {E}}(\omega )\right|^{2}={\frac {e^{2}}{4\pi \varepsilon _{0}4\pi ^{2}c}}\left|\int _{-\infty }^{\infty }{\frac {{\hat {n}}\times \left[\left({\hat {n}}-{\vec {\beta }}\right)\times {\dot {\vec {\beta }}}\right]}{\left(1-{\hat {n}}\cdot {\vec {\beta }}\right)^{2}}}e^{i\omega (t-{\hat {n}}\cdot {\vec {r}}(t)/c)}dt\right|^{2}.\qquad (9)}$

Therefore, if we know the particle's motion, cross products term, and phase factor, we could calculate the radiation integral. However, calculations are generally quite lengthy (even for simple cases as for the radiation emitted by an electron in a bending magnet, they require Airy function or the modified Bessel functions).

Example 1: bending magnet

Integrating

Trajectory of the arc of circumference

Trajectory of the arc of circumference is

${\displaystyle {\vec {r}}(t)=\left(\rho \sin {\frac {\beta c}{\rho }}t,\rho \left(1-\cos {\frac {\beta c}{\rho }}t\right),0\right).}$

In the limit of small angles we compute

${\displaystyle {\hat {n}}\times \left({\hat {n}}\times {\vec {\beta }}\right)=\beta \left[-{\vec {\varepsilon }}_{\parallel }\sin \left({\frac {\beta ct}{\rho }}\right)+{\vec {\varepsilon }}_{\perp }\cos \left({\frac {\beta ct}{\rho }}\right)\sin \theta \right]}$

${\displaystyle \omega \left(t-{\frac {{\hat {n}}\cdot {\vec {r}}(t)}{c}}\right)=\omega \left[t-{\frac {\rho }{c}}\sin \left({\frac {\beta ct}{\rho }}\right)\cos \theta \right]}$

Substituting into the radiation integral and introducing

${\displaystyle \xi ={\frac {\rho \omega }{3c\gamma ^{3}}}\left(1+\gamma ^{2}\theta ^{2}\right)^{3/2}}$

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}={\frac {3e^{2}}{16\pi ^{3}\varepsilon _{0}c}}\left({\frac {2\omega \rho }{3c\gamma ^{2}}}\right)^{2}\left(1+\gamma ^{2}\theta ^{2}\right)^{2}\left[K_{2/3}^{2}(\xi )+{\frac {\gamma ^{2}\theta ^{2}}{1+\gamma ^{2}\theta ^{2}}}K_{1/3}^{2}(\xi )\right]\qquad (10),}$

where the function K is a modified Bessel function of the second kind.

Frequency distribution of radiated energy

Angular distribution of radiated energy

From Eq.(10), we observe that the radiation intensity is negligible for ${\displaystyle \xi \gg 1}$. Critical frequency is defined as the frequency when ξ = 1/2 and θ = 0. So,

${\displaystyle \omega _{\text{c}}={\frac {3}{2}}{\frac {c}{\rho }}\gamma ^{3},}$

and critical angle is defined as the angle for which ${\displaystyle \xi (\theta _{\text{c}})\simeq \xi (0)+1}$ and is approximately

${\displaystyle \theta _{\text{c}}\simeq {\frac {1}{\gamma }}\left({\frac {2\omega _{\text{c}}}{\omega }}\right)^{1/3}}$^.

For frequencies much larger than the critical frequency and angles much larger than the critical angle, the synchrotron radiation emission is negligible.

Integrating on all angles, we get the frequency distribution of the energy radiated.

${\displaystyle {\frac {dW}{d\omega }}=\oint {\frac {d^{3}W}{d\omega d\Omega }}d\Omega ={\frac {{\sqrt {3}}e^{2}}{4\pi \varepsilon _{0}c}}\gamma {\frac {\omega }{\omega _{\text{c}}}}\int _{\omega /\omega _{\text{c}}}^{\infty }K_{5/3}(x)dx}$

Frequency distribution of radiated energy

If we define

${\displaystyle S(y)\equiv {\frac {9{\sqrt {3}}}{8\pi }}y\int _{y}^{\infty }K_{5/3}(x)dx}$

${\displaystyle \int _{0}^{\infty }S(y)dy=1,}$

where y = ω/ω_c. Then

${\displaystyle {\frac {dW}{d\omega }}={\frac {2e^{2}\gamma }{9\varepsilon _{0}c}}S(y).\qquad (11)}$

Note that ${\displaystyle {\frac {dW}{d\omega }}\sim {\frac {e^{2}}{4\pi \varepsilon _{0}c}}\left({\frac {\omega \rho }{c}}\right)^{1/3}}$, if ${\displaystyle \omega \ll \omega _{\text{c}}}$,
and ${\displaystyle {\frac {dW}{d\omega }}\approx {\sqrt {\frac {3\pi }{2}}}{\frac {e^{2}}{4\pi \varepsilon _{0}c}}\gamma \left({\frac {\omega }{\omega _{\text{c}}}}\right)^{0.5}e^{-\omega /\omega _{\text{c}}}}$, if ${\displaystyle \omega \gg \omega _{\text{c}}}$

The formula for spectral distribution of synchrotron radiation, given above, can be expressed in terms of a rapidly converging integral with no special functions involved by means of the relation:

${\displaystyle \int _{\xi }^{\infty }K_{5/3}(x)dx={\frac {1}{\sqrt {3}}}\,\int _{0}^{\infty }\,{\frac {9+36x^{2}+16x^{4}}{(3+4x^{2}){\sqrt {1+x^{2}/3}}}}\exp \left[-\xi \left(1+{\frac {4x^{2}}{3}}\right){\sqrt {1+{\frac {x^{2}}{3}}}}\right]\ dx}$

Synchrotron radiation emission as a function of the beam energy

Relationship between power radiated and the photon energy

First, define the critical photon energy as

${\displaystyle \varepsilon _{c}=\hbar \omega _{\text{c}}={\frac {3}{2}}{\frac {\hbar c}{\rho }}\gamma ^{3}.}$

Then, the relationship between radiated power and photon energy is shown in the graph on the right side. The higher the critical energy, the more photons with high energies are generated. Note that, there is no dependence on the energy at longer wavelength.

Polarization of synchrotron radiation

In Eq.(10), the first term ${\displaystyle K_{2/3}^{2}(\xi )}$ is the radiation power with polarization in the orbit plane, and the second term ${\displaystyle {\frac {\gamma ^{2}\theta ^{2}}{1+\gamma ^{2}\theta ^{2}}}K_{1/3}^{2}(\xi )}$ is the polarization orthogonal to the orbit plane.

In the orbit plane ${\displaystyle \theta =0}$, the polarization is purely horizontal. Integrating on all frequencies, we get the angular distribution of the energy radiated

${\displaystyle {\frac {d^{2}W}{d\Omega }}=\int _{0}^{\infty }{\frac {d^{3}W}{d\omega d\Omega }}d\omega ={\frac {7e^{2}\gamma ^{5}}{64\pi \varepsilon _{0}\rho }}{\frac {1}{(1+\gamma ^{2}\theta ^{2})^{5/2}}}\left[1+{\frac {5}{7}}{\frac {\gamma ^{2}\theta ^{2}}{1+\gamma ^{2}\theta ^{2}}}\right].\qquad (12)}$

Integrating on all the angles, we find that seven times as much energy is radiated with parallel polarization as with perpendicular polarization. The radiation from a relativistically moving charge is very strongly, but not completely, polarized in the plane of motion.

Example 2: undulator

Solution of equation of motion and undulator equation

An undulator consists of a periodic array of magnets, so that they provide a sinusoidal magnetic field.

${\displaystyle {\vec {B}}=\left(0,B_{0}\sin(k_{\text{u}}z),0\right)}$

undulator

Solution of equation of motion is

${\displaystyle {\vec {r}}(t)={\frac {\lambda _{\text{u}}K}{2\pi \gamma }}\sin \omega _{\text{u}}t\cdot {\hat {x}}+\left({\bar {\beta _{z}}}ct+{\frac {\lambda _{\text{u}}K^{2}}{16\pi \gamma ^{2}}}\cos(2\omega _{\text{u}}t)\right)\cdot {\hat {z}}}$

where

${\displaystyle K={\frac {eB_{0}\lambda _{\text{u}}}{2\pi mc}},}$

and

${\displaystyle {\bar {\beta _{z}}}=1-{\frac {1}{2\gamma ^{2}}}\left(1+{\frac {K^{2}}{2}}\right),}$

and the parameter ${\displaystyle K}$ is called the undulator parameter.

Constructive interference of the beam in the undulator

Condition for the constructive interference of radiation emitted at different poles is

${\displaystyle d={\frac {\lambda _{\text{u}}}{\bar {\beta }}}-\lambda _{\text{u}}\cos \theta =n\lambda }$

Expanding ${\displaystyle \cos \theta \approx 1-{\frac {\theta ^{2}}{2}}}$ and neglecting the terms ${\displaystyle O(\theta ^{2})}$ in the resulting equation, one obtains

${\displaystyle \lambda _{n}={\frac {\lambda _{\text{u}}}{2\gamma ^{2}n}}\left({\frac {1+{\frac {K^{2}}{2}}+\gamma ^{2}\theta ^{2}}{\bar {\beta }}}\right)}$

For ${\displaystyle {\bar {\beta }}\rightarrow 1}$, one finally gets

${\displaystyle \lambda _{n}={\frac {\lambda _{\text{u}}}{2\gamma ^{2}n}}\left(1+{\frac {K^{2}}{2}}+\gamma ^{2}\theta ^{2}\right)\qquad (13).}$

This equation is called the undulator equation.

Radiation from the undulator

Radiation integral is

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}={\frac {e^{2}}{4\pi \varepsilon _{0}4\pi ^{2}c}}\left|\int _{-\infty }^{\infty }{\frac {{\hat {n}}\times \left[\left({\hat {n}}-{\vec {\beta }}\right)\times {\dot {\vec {\beta }}}\right]}{\left(1-{\hat {n}}\cdot {\vec {\beta }}\right)^{2}}}e^{i\omega (t-{\hat {n}}\cdot {\vec {r}}(t)/c)}dt\right|^{2}.}$

Using the periodicity of the trajectory, we can split the radiation integral into a sum over ${\displaystyle N}$ terms, where ${\displaystyle 2N}$ is the total number of bending magnets of the undulator.

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}={\frac {e^{2}\omega ^{2}}{4\pi \varepsilon _{0}4\pi ^{2}c}}\left|\int _{-\lambda _{u}/2{\bar {\beta }}c}^{\lambda _{u}/2{\bar {\beta }}c}{\hat {n}}\times \left({\hat {n}}\times {\vec {\beta }}\right)e^{i\omega (t-{\hat {n}}\cdot {\vec {r}}(t)/c)}dt\right|^{2}\left|1+e^{i\delta }+e^{2i\delta }+\cdots +e^{i(N_{u}-1)\delta }\right|^{2},\qquad (14)}$

where 　${\displaystyle {\bar {\beta }}=\beta \left(1-{\frac {K^{2}}{4\gamma ^{2}}}\right)}$

Peak frequencies become sharp as the number N increases

, and ${\displaystyle \delta ={\frac {2\pi \omega }{\omega _{\text{res}}(\theta )}}}$,　${\displaystyle \omega _{\text{res}}(\theta )={\frac {2\pi c}{\lambda _{\text{res}}(\theta )}}}$,　and
　${\displaystyle \lambda _{\text{res}}(\theta )={\frac {\lambda _{u}}{2\gamma ^{2}}}\left(1+{\frac {K^{2}}{2}}+\gamma ^{2}\theta ^{2}\right).}$

Only odd harmonics are radiated on-axis

 

Off-axis radiation contains many harmonics

The radiation integral in an undulator can be written as

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}={\frac {e^{2}\gamma ^{2}N^{2}}{4\pi \varepsilon _{0}c}}L\left(N{\frac {\Delta \omega _{n}}{\omega _{\text{res}}(\theta )}}\right)F_{n}(K,\theta ,\phi )\qquad (15).}$

where ${\displaystyle \Delta \omega _{n}=\omega -n\omega _{\text{res}}}$ is the frequency difference to the n-th harmonic. The sum of δ generates a series of sharp peaks in the frequency spectrum harmonics of fundamental wavelength

${\displaystyle L\left(N{\frac {\Delta \omega _{n}}{\omega _{\text{res}}(\theta )}}\right)={\frac {\sin ^{2}\left(N\pi \Delta \omega _{n}/\omega _{\text{res}}(\theta )\right)}{N^{2}\left(\pi \Delta \omega _{n}/\omega _{\text{res}}(\theta )\right)^{2}}},}$

and F_n depends on the angles of observations and K

${\displaystyle F_{n}(K,\theta ,\phi )\propto \left|\int _{-\lambda _{u}/2{\bar {\beta }}c}^{\lambda _{u}/2{\bar {\beta }}c}{\hat {n}}\times \left({\hat {n}}\times {\vec {\beta }}\right)e^{i\omega (t-{\hat {n}}\cdot {\vec {r}}(t)/c)}dt\right|^{2}.}$

On the axis (θ = 0, φ = 0), the radiation integral becomes

${\displaystyle {\frac {d^{3}W}{d\Omega d\omega }}={\frac {e^{2}\gamma ^{2}N^{2}}{4\pi \varepsilon _{0}c}}L\left(N{\frac {\Delta \omega _{n}}{\omega _{\text{res}}(0)}}\right)F_{n}(K,0,0)}$

and

${\displaystyle F_{n}(K,0,0)={\frac {n^{2}K^{2}}{1+K^{2}/2}}\left[J_{\frac {n+1}{2}}(Z)-J_{\frac {n-1}{2}}(Z)\right]^{2},}$

where ${\displaystyle Z={\frac {nK^{2}}{4(1+K^{2}/2)}}.}$

Note that only odd harmonics are radiated on-axis, and as K increases higher harmonic becomes stronger.

Radio galaxy

From Wikipedia, the free encyclopedia

False-colour image of the nearby radio galaxy Centaurus A, showing radio (red), 24-micrometre infrared (green) and 0.5-5 keV X-ray emission (blue). The jet can be seen to emit synchrotron radiation in all three wavebands. The lobes only emit in the radio frequency range, and so appear red. Gas and dust in the galaxy emits thermal radiation in the infrared. Thermal X-ray radiation from hot gas and non-thermal emission from relativistic electrons can be seen in the blue 'shells' around the lobes, particularly to the south (bottom).

Radio galaxies and their relatives, radio-loud quasars and blazars, are types of active galaxy nuclei that are very luminous at radio wavelengths, with luminosities up to 10³⁹ W between 10 MHz and 100 GHz. The radio emission is due to the synchrotron process. The observed structure in radio emission is determined by the interaction between twin jets and the external medium, modified by the effects of relativistic beaming. The host galaxies are almost exclusively large elliptical galaxies.  Radio-loud active galaxies can be detected at large distances, making them valuable tools for observational cosmology. Recently, much work has been done on the effects of these objects on the intergalactic medium, particularly in galaxy groups and clusters.

Emission processes

The radio emission from radio-loud active galaxies is synchrotron emission, as inferred from its very smooth, broad-band nature and strong polarization. This implies that the radio-emitting plasma contains, at least, electrons with relativistic speeds (Lorentz factors of ~10⁴) and magnetic fields. Since the plasma must be neutral, it must also contain either protons or positrons. There is no way of determining the particle content directly from observations of synchrotron radiation. Moreover, there is no way to determine the energy densities in particles and magnetic fields from observation: the same synchrotron emissivity may be a result of a few electrons and a strong field, or a weak field and many electrons, or something in between. It is possible to determine a minimum energy condition which is the minimum energy density that a region with a given emissivity can have, but for many years there was no particular reason to believe that the true energies were anywhere near the minimum energies.

A sister process to the synchrotron radiation is the inverse-Compton process, in which the relativistic electrons interact with ambient photons and Thomson scatter them to high energies. Inverse-Compton emission from radio-loud sources turns out to be particularly important in X-rays, and, because it depends only on the density of electrons, a detection of inverse-Compton scattering allows a somewhat model-dependent estimate of the energy densities in the particles and magnetic fields. This has been used to argue that many powerful sources are actually quite near the minimum-energy condition.

Synchrotron radiation is not confined to radio wavelengths: if the radio source can accelerate particles to high enough energies, features that are detected in the radio wavelengths may also be seen in the infrared, optical, ultraviolet or even X-ray. In the latter case the responsible electrons must have energies in excess of 1 TeV in typical magnetic field strengths. Again, polarization and continuum spectrum are used to distinguish the synchrotron radiation from other emission processes. Jets and hotspots are the usual sources of high-frequency synchrotron emission. It is hard to distinguish observationally between the synchrotron and inverse-Compton radiation, making them a subject of ongoing research.

Processes, collectively known as particle acceleration, produce populations of relativistic and non-thermal particles that give rise to synchrotron and inverse-Compton radiation. Fermi acceleration is one plausible particle acceleration process in radio-loud active galaxies.

Radio structures

Pseudo-colour image of the large-scale radio structure of the FRII radio galaxy 3C98. Lobes, jet and hotspot are labelled.

Radio galaxies, and to a lesser extent, radio-loud quasars display a wide range of structures in radio maps. The most common large-scale structures are called lobes: these are double, often fairly symmetrical, roughly ellipsoidal structures placed on either side of the active nucleus. A significant minority of low-luminosity sources exhibit structures usually known as plumes which are much more elongated. Some radio galaxies show one or two long narrow features known as jets (the most famous example being the giant galaxy M87 in the Virgo cluster) coming directly from the nucleus and going to the lobes. Since the 1970s, the most widely accepted model has been that the lobes or plumes are powered by beams of high-energy particles and magnetic field coming from close to the active nucleus. The jets are believed to be the visible manifestations of the beams, and often the term jet is used to refer both to the observable feature and to the underlying flow.

Pseudo-colour image of the large-scale radio structure of the FRI radio galaxy 3C31. Jets and plumes are labelled.

In 1974, radio sources were divided by Fanaroff and Riley into two classes, now known as Fanaroff and Riley Class I (FRI), and Class II (FRII). The distinction was originally made based on the morphology of the large-scale radio emission (the type was determined by the distance between the brightest points in the radio emission): FRI sources were brightest towards the centre, while FRII sources were brightest at the edges. Fanaroff and Riley observed that there was a reasonably sharp divide in luminosity between the two classes: FRIs were low-luminosity, FRIIs were high luminosity. With more detailed radio observations, the morphology turns out to reflect the method of energy transport in the radio source. FRI objects typically have bright jets in the centre, while FRIIs have faint jets but bright hotspots at the ends of the lobes. FRIIs appear to be able to transport energy efficiently to the ends of the lobes, while FRI beams are inefficient in the sense that they radiate a significant amount of their energy away as they travel.

In more detail, the FRI/FRII division depends on host-galaxy environment in the sense that the FRI/FRII transition appears at higher luminosities in more massive galaxies. FRI jets are known to be decelerating in the regions in which their radio emission is brightest, and so it seems that the FRI/FRII transition reflects whether a jet/beam can propagate through the host galaxy without being decelerated to sub-relativistic speeds by interaction with the intergalactic medium. From analysis of relativistic beaming effects, the jets of FRII sources are known to remain relativistic (with speeds of at least 0.5c) out to the ends of the lobes. The hotspots that are usually seen in FRII sources are interpreted as being the visible manifestations of shocks formed when the fast, and therefore supersonic, jet (the speed of sound cannot exceed c/√3) abruptly terminates at the end of the source, and their spectral energy distributions are consistent with this picture. Often multiple hotspots are seen, reflecting either continued outflow after the shock or movement of the jet termination point: the overall hotspot region is sometimes called the hotspot complex.

Names are given to several particular types of radio source based on their radio structure:

• Classical double refers to an FRII source with clear hotspots.
• Wide-angle tail normally refers to a source intermediate between standard FRI and FRII structure, with efficient jets and sometimes hotspots, but with plumes rather than lobes, found at or near the centres of clusters.
• Narrow-angle tail or Head-tail source describes an FRI that appears to be bent by ram pressure as it moves through a cluster.
• Fat doubles are sources with diffuse lobes but neither jets nor hotspots. Some such sources may be relics whose energy supply has been permanently or temporarily turned off.

Life cycles and dynamics

The largest radio galaxies have lobes or plumes extending to megaparsec scales (more in the case of giant radio galaxies like 3C236), implying a timescale for growth of the order of tens to hundreds of millions of years. This means that, except in the case of very small, very young sources, we cannot observe radio source dynamics directly, and so must resort to theory and inferences from large numbers of objects. Clearly radio sources must start small and grow larger. In the case of sources with lobes, the dynamics are fairly simple: the jets feed the lobes, the pressure of the lobes increases, and the lobes expand. How fast they expand depends on the density and pressure of the external medium. The highest-pressure phase of the external medium, and thus the most important phase from the point of view of the dynamics, is the X-ray emitting diffuse hot gas. For a long time it was assumed that powerful sources would expand supersonically, pushing a shock through the external medium. However, X-ray observations show that the internal lobe pressures of powerful FRII sources are often close to the external thermal pressures and not much higher than the external pressures, as would be required for supersonic expansion. The only unambiguously supersonically expanding system known consists of the inner lobes of the low-power radio galaxy Centaurus A which are probably a result of a comparatively recent outburst of the active nucleus.

Host galaxies and environments

These radio sources are almost universally found hosted by elliptical galaxies, though there is one well-documented exception, namely NGC 4151. Some Seyfert galaxies show weak, small radio jets, but they are not radio-luminous enough to be classified as radio-loud. Such information as there is about the host galaxies of radio-loud quasars and blazars suggests that they are also hosted by elliptical galaxies.

There are several possible reasons for this very strong preference for ellipticals. One is that ellipticals generally contain the most massive black holes, and so are capable of powering the most luminous active galaxies (see Eddington luminosity). Another is that ellipticals generally inhabit richer environments, providing a large-scale intergalactic medium to confine the radio source. It may also be that the larger amounts of cold gas in spiral galaxies in some way disrupts or stifles a forming jet. To date there is no compelling single explanation for the observations.

Unified models

The different types of radio-loud active galaxies are linked by unified models. The key observation that led to the adoption of unified models for powerful radio galaxies and radio-loud quasars was that all quasars appear to be beamed towards us, showing superluminal motion in the cores and bright jets on the side of the source nearest to us (the Laing-Garrington effect:). If this is the case, there must be a population of objects not beamed towards us, and, since we know the lobes are not affected by beaming, they would appear as radio galaxies, provided that the quasar nucleus is obscured when the source is seen side-on. It is now accepted that at least some powerful radio galaxies have 'hidden' quasars, though it is not clear whether all such radio galaxies would be quasars if viewed from the right angle. In a similar way, low-power radio galaxies are a plausible parent population for BL Lac objects.

Uses of radio galaxies

Distant sources

Radio galaxies and radio-loud quasars have been widely used, particularly in the 80s and 90s, to find distant galaxies: by selecting based on radio spectrum and then observing the host galaxy it was possible to find objects at high redshift at modest cost in telescope time. The problem with this method is that hosts of active galaxies may not be typical of galaxies at their redshift. Similarly, radio galaxies have in the past been used to find distant X-ray emitting clusters, but unbiased selection methods are now preferred.

Standard rulers

Some work has been done attempting to use radio galaxies as standard rulers to determine cosmological parameters. This method is fraught with difficulty because a radio galaxy's size depends on both its age and its environment. When a model of the radio source is used, though, methods based on radio galaxies can give good agreement with other cosmological observations.

Effects on environment

Whether or not a radio source is expanding supersonically, it must do work against the external medium in expanding, and so it puts energy into heating and lifting the external plasma. The minimum energy stored in the lobes of a powerful radio source might be 10⁵³ J. The lower limit on the work done on the external medium by such a source is several times this. A good deal of the current interest in radio sources focuses on the effect they must have at the centres of clusters at the present day. Equally interesting is their likely effect on structure formation over cosmological time: it is thought that they may provide a feedback mechanism to slow the formation of the most massive objects.

Terminology

Widely used terminology is awkward now that it is generally accepted that quasars and radio galaxies are the same objects (see above). The acronym DRAGN (for 'Double Radiosource Associated with Galactic Nucleus') has been coined. but has not yet taken off. Extragalactic radio source is common but can lead to confusion, since many other extragalactic objects are detected in radio surveys, notably starburst galaxies. Radio-loud active galaxy is unambiguous, and so is often used in this article.

Active galactic nucleus

From Wikipedia, the free encyclopedia

Inner structure of a galaxy with an active galactic nucleus

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 produced by stars. Such excess non-stellar emission has been observed in the radio, microwave, infrared, optical, ultra-violet, X-ray and gamma ray wavebands. A galaxy hosting an AGN is called an "active galaxy". The radiation from an AGN is believed to result from the accretion of matter by a supermassive black hole at the center of its host galaxy.

Active galactic nuclei are the most luminous persistent sources of electromagnetic radiation in the universe, and as such can be used as a means of discovering distant objects; their evolution as a function of cosmic time also puts constraints on models of the cosmos.

The observed characteristics of an AGN depend on several properties such as the mass of the central black hole, the rate of gas accretion onto the black hole, the orientation of the accretion disk, the degree of obscuration of the nucleus by dust, and presence or absence of jets.

Numerous subclasses of AGN have been defined based on their observed characteristics; the most powerful AGN are classified as quasars. A blazar is an AGN with a jet pointed toward the Earth, in which radiation from the jet is enhanced by relativistic beaming.

History

Early photographic observations of nearby galaxies detected some characteristic signatures of AGN emission, although there was not yet a physical understanding of the nature of the AGN phenomenon. Some early observations included the first spectroscopic detection of emission lines from the nuclei of NGC 1068 and Messier 81 by Edward Fath (published in 1909), and the discovery of the jet in Messier 87 by Heber Curtis (published in 1918). Further spectroscopic studies by astronomers including Vesto Slipher, Milton Humason, and Nicholas Mayall noted the presence of unusual emission lines in some galaxy nuclei. In 1943, Carl Seyfert published a paper in which he described observations of nearby galaxies having bright nuclei that were sources of unusually broad emission lines. Galaxies observed as part of this study included NGC 1068, NGC 4151, NGC 3516, and NGC 7469. Active galaxies such as these are known as Seyfert galaxies in honor of Seyfert's pioneering work.

The development of radio astronomy was a major catalyst to understanding AGN. Some of the earliest detected radio sources are nearby active elliptical galaxies such as Messier 87 and Centaurus A. Another radio source, Cygnus A, was identified by Walter Baade and Rudolph Minkowski as a tidally distorted galaxy with an unusual emission-line spectrum, having a recessional velocity of 16,700 kilometers per second. The 3C radio survey led to further progress in discovery of new radio sources as well as identifying the visible-light sources associated with the radio emission. In photographic images, some of these objects were nearly point-like or quasi-stellar in appearance, and were classified as quasi-stellar radio sources (later abbreviated as "quasars").

A major breakthrough was the measurement of the redshift of the quasar 3C 273 by Maarten Schmidt, published in 1963. Schmidt noted that if this object was extragalactic (outside the Milky Way, at a cosmological distance) then its large redshift of 0.158 implied that it was the nuclear region of a galaxy about 100 times more powerful than other radio galaxies that had been identified. Shortly afterward, optical spectra were used to measured the redshifts of a growing number of quasars including 3C 48, even more distant at redshift 0.37.

The enormous luminosities of these quasars as well as their unusual spectral properties indicated that their power source could not be ordinary stars. Accretion of gas onto a supermassive black hole was suggested as the source of quasars' power in papers by Edwin Salpeter and Yakov Zel'Dovich in 1964. In 1969 Donald Lynden-Bell proposed that nearby galaxies contain supermassive black holes at their centers as relics of "dead" quasars, and that black hole accretion was the power source for the non-stellar emission in nearby Seyfert galaxies.^[13] In the 1960s and 1970s, early X-ray astronomy observations demonstrated that Seyfert galaxies and quasars are powerful sources of X-ray emission, which originates from the inner regions of black hole accretion disks.

Today, AGN are a major topic of astrophysical research, both observational and theoretical. AGN research encompasses observational surveys to find AGN over broad ranges of luminosity and redshift, examination of the cosmic evolution and growth of black holes, studies of the physics of black hole accretion and the emission of electromagnetic radiation from AGN, examination of the properties of jets and outflows of matter from AGN, and the impact of black hole accretion and quasar activity on galaxy evolution.

Models

UGC 6093 is classified as an active galaxy, which means that it hosts an active galactic nucleus.

 

For a long time it has been argued that an AGN must be powered by accretion of mass onto massive black holes (10⁶ to 10¹⁰ times the Solar mass). AGN are both compact and persistently extremely luminous. Accretion can potentially give very efficient conversion of potential and kinetic energy to radiation, and a massive black hole has a high Eddington luminosity, and as a result, it can provide the observed high persistent luminosity. Supermassive black holes are now believed to exist in the centres of most if not all massive galaxies since the mass of the black hole correlates well with the velocity dispersion of the galactic bulge (the M-sigma relation) or with bulge luminosity. Thus AGN-like characteristics are expected whenever a supply of material for accretion comes within the sphere of influence of the central black hole.

Accretion disc

In the standard model of AGN, cold material close to a black hole forms an accretion disc. Dissipative processes in the accretion disc transport matter inwards and angular momentum outwards, while causing the accretion disc to heat up. The expected spectrum of an accretion disc peaks in the optical-ultraviolet waveband; in addition, a corona of hot material forms above the accretion disc and can inverse-Compton scatter photons up to X-ray energies. The radiation from the accretion disc excites cold atomic material close to the black hole and this in turn radiates at particular emission lines. A large fraction of the AGN's radiation may be obscured by interstellar gas and dust close to the accretion disc, but (in a steady-state situation) this will be re-radiated at some other waveband, most likely the infrared.

Relativistic jets

Image taken by the Hubble Space Telescope of a 5000-light-year-long jet ejected from the active galaxy M87. The blue synchrotron radiation contrasts with the yellow starlight from the host galaxy.

Some accretion discs produce jets of twin, highly collimated, and fast outflows that emerge in opposite directions from close to the disc. The direction of the jet ejection is determined either by the angular momentum axis of the accretion disc or the spin axis of the black hole. The jet production mechanism and indeed the jet composition on very small scales are not understood at present due to the resolution of astronomical instruments being too low. The jets have their most obvious observational effects in the radio waveband, where very-long-baseline interferometry can be used to study the synchrotron radiation they emit at resolutions of sub-parsec scales. However, they radiate in all wavebands from the radio through to the gamma-ray range via the synchrotron and the inverse-Compton scattering process, and so AGN jets are a second potential source of any observed continuum radiation.

Radiatively inefficient AGN

There exists a class of 'radiatively inefficient' solutions to the equations that govern accretion. The most widely known of these is the Advection Dominated Accretion Flow (ADAF), but other theories exist. In this type of accretion, which is important for accretion rates well below the Eddington limit, the accreting matter does not form a thin disc and consequently does not efficiently radiate away the energy that it acquired as it moved close to the black hole. Radiatively inefficient accretion has been used to explain the lack of strong AGN-type radiation from massive black holes at the centres of elliptical galaxies in clusters, where otherwise we might expect high accretion rates and correspondingly high luminosities. Radiatively inefficient AGN would be expected to lack many of the characteristic features of standard AGN with an accretion disc.

Particle acceleration

AGN are a candidate source of high and ultra-high energy cosmic rays.

Observational characteristics

There is no single observational signature of an AGN. The list below covers some of the features that have allowed systems to be identified as AGN.

• Nuclear optical continuum emission. This is visible whenever there is a direct view of the accretion disc. Jets can also contribute to this component of the AGN emission. The optical emission has a roughly power-law dependence on wavelength.
• Nuclear infra-red emission. This is visible whenever the accretion disc and its environment are obscured by gas and dust close to the nucleus and then re-emitted ('reprocessing'). As it is thermal emission, it can be distinguished from any jet or disc-related emission.
• Broad optical emission lines. These come from cold material close to the central black hole. The lines are broad because the emitting material is revolving around the black hole with high speeds causing a range of Doppler shifts of the emitted photons.
• Narrow optical emission lines. These come from more distant cold material, and so are narrower than the broad lines.
• Radio continuum emission. This is always due to a jet. It shows a spectrum characteristic of synchrotron radiation.
• X-ray continuum emission. This can arise both from a jet and from the hot corona of the accretion disc via a scattering process: in both cases it shows a power-law spectrum. In some radio-quiet AGN there is an excess of soft X-ray emission in addition to the power-law component. The origin of the soft X-rays is not clear at present.
• X-ray line emission. This is a result of illumination of cold heavy elements by the X-ray continuum that causes fluorescence of X-ray emission lines, the best-known of which is the iron feature around 6.4 keV. This line may be narrow or broad: relativistically broadened iron lines can be used to study the dynamics of the accretion disc very close to the nucleus and therefore the nature of the central black hole.

Types of active galaxy

It is convenient to divide AGN into two classes, conventionally called radio-quiet and radio-loud. Radio-loud objects have emission contributions from both the jet(s) and the lobes that the jets inflate. These emission contributions dominate the luminosity of the AGN at radio wavelengths and possibly at some or all other wavelengths. Radio-quiet objects are simpler since jet and any jet-related emission can be neglected at all wavelengths.

AGN terminology is often confusing, since the distinctions between different types of AGN sometimes reflect historical differences in how the objects were discovered or initially classified, rather than real physical differences.

Radio-quiet AGN

• Low-ionization nuclear emission-line regions (LINERs). As the name suggests, these systems show only weak nuclear emission-line regions, and no other signatures of AGN emission. It is debatable^{[by whom?]} whether all such systems are true AGN (powered by accretion on to a supermassive black hole). If they are, they constitute the lowest-luminosity class of radio-quiet AGN. Some may be radio-quiet analogues of the low-excitation radio galaxies (see below).
• Seyfert galaxies. Seyferts were the earliest distinct class of AGN to be identified. They show optical range nuclear continuum emission, narrow and occasionally broad emission lines, occasionally strong nuclear X-ray emission and sometimes a weak small-scale radio jet. Originally they were divided into two types known as Seyfert 1 and 2: Seyfert 1s show strong broad emission lines while Seyfert 2s do not, and Seyfert 1s are more likely to show strong low-energy X-ray emission. Various forms of elaboration on this scheme exist: for example, Seyfert 1s with relatively narrow broad lines are sometimes referred to as narrow-line Seyfert 1s. The host galaxies of Seyferts are usually spiral or irregular galaxies.
• Radio-quiet quasars/QSOs. These are essentially more luminous versions of Seyfert 1s: the distinction is arbitrary and is usually expressed in terms of a limiting optical magnitude. Quasars were originally 'quasi-stellar' in optical images as they had optical luminosities that were greater than that of their host galaxy. They always show strong optical continuum emission, X-ray continuum emission, and broad and narrow optical emission lines. Some astronomers use the term QSO (Quasi-Stellar Object) for this class of AGN, reserving 'quasar' for radio-loud objects, while others talk about radio-quiet and radio-loud quasars. The host galaxies of quasars can be spirals, irregulars or ellipticals. There is a correlation between the quasar's luminosity and the mass of its host galaxy, in that the most luminous quasars inhabit the most massive galaxies (ellipticals).
• 'Quasar 2s'. By analogy with Seyfert 2s, these are objects with quasar-like luminosities but without strong optical nuclear continuum emission or broad line emission. They are scarce in surveys, though a number of possible candidate quasar 2s have been identified.

Radio-loud AGN

• Radio-loud quasars behave exactly like radio-quiet quasars with the addition of emission from a jet. Thus they show strong optical continuum emission, broad and narrow emission lines, and strong X-ray emission, together with nuclear and often extended radio emission.
• “Blazars” (BL Lac objects and OVV quasars) classes are distinguished by rapidly variable, polarized optical, radio and X-ray emission. BL Lac objects show no optical emission lines, broad or narrow, so that their redshifts can only be determined from features in the spectra of their host galaxies. The emission-line features may be intrinsically absent or simply swamped by the additional variable component. In the latter case, emission lines may become visible when the variable component is at a low level. OVV quasars behave more like standard radio-loud quasars with the addition of a rapidly variable component. In both classes of source, the variable emission is believed to originate in a relativistic jet oriented close to the line of sight. Relativistic effects amplify both the luminosity of the jet and the amplitude of variability.
• Radio galaxies. These objects show nuclear and extended radio emission. Their other AGN properties are heterogeneous. They can broadly be divided into low-excitation and high-excitation classes. Low-excitation objects show no strong narrow or broad emission lines, and the emission lines they do have may be excited by a different mechanism. Their optical and X-ray nuclear emission is consistent with originating purely in a jet. They may be the best current candidates for AGN with radiatively inefficient accretion. By contrast, high-excitation objects (narrow-line radio galaxies) have emission-line spectra similar to those of Seyfert 2s. The small class of broad-line radio galaxies, which show relatively strong nuclear optical continuum emission probably includes some objects that are simply low-luminosity radio-loud quasars. The host galaxies of radio galaxies, whatever their emission-line type, are essentially always ellipticals.
  

Features of different types of galaxies

Galaxy type	Active nuclei	Emission lines		X-rays	Excess of		Strong radio	Jets	Variable	Radio loud
		Narrow	Broad		UV	Far-IR
Normal	no	weak	no	weak	no	no	no	no	no	no
LINER	unknown	weak	weak	weak	no	no	no	no	no	no
Seyfert I	yes	yes	yes	some	some	yes	few	no	yes	no
Seyfert II	yes	yes	no	some	some	yes	few	no	yes	no
Quasar	yes	yes	yes	some	yes	yes	some	some	yes	some
Blazar	yes	no	some	yes	yes	no	yes	yes	yes	yes
BL Lac	yes	no	no/faint	yes	yes	no	yes	yes	yes	yes
OVV	yes	no	stronger than BL Lac	yes	yes	no	yes	yes	yes	yes
Radio galaxy	yes	some	some	some	some	yes	yes	yes	yes	yes

Unification of AGN species

Unified models propose that different observational classes of AGN are a single type of physical object observed under different conditions. The currently favoured unified models are 'orientation-based unified models' meaning that they propose that the apparent differences between different types of objects arise simply because of their different orientations to the observer. However, they are debated (see below).

Radio-quiet unification

At low luminosities, the objects to be unified are Seyfert galaxies. The unification models propose that in Seyfert 1s the observer has a direct view of the active nucleus. In Seyfert 2s the nucleus is observed through an obscuring structure which prevents a direct view of the optical continuum, broad-line region or (soft) X-ray emission. The key insight of orientation-dependent accretion models is that the two types of object can be the same if only certain angles to the line of sight are observed. The standard picture is of a torus of obscuring material surrounding the accretion disc. It must be large enough to obscure the broad-line region but not large enough to obscure the narrow-line region, which is seen in both classes of object. Seyfert 2s are seen through the torus. Outside the torus there is material that can scatter some of the nuclear emission into our line of sight, allowing us to see some optical and X-ray continuum and, in some cases, broad emission lines—which are strongly polarized, showing that they have been scattered and proving that some Seyfert 2s really do contain hidden Seyfert 1s. Infrared observations of the nuclei of Seyfert 2s also support this picture.

At higher luminosities, quasars take the place of Seyfert 1s, but, as already mentioned, the corresponding 'quasar 2s' are elusive at present. If they do not have the scattering component of Seyfert 2s they would be hard to detect except through their luminous narrow-line and hard X-ray emission.

Radio-loud unification

Historically, work on radio-loud unification has concentrated on high-luminosity radio-loud quasars. These can be unified with narrow-line radio galaxies in a manner directly analogous to the Seyfert 1/2 unification (but without the complication of much in the way of a reflection component: narrow-line radio galaxies show no nuclear optical continuum or reflected X-ray component, although they do occasionally show polarized broad-line emission). The large-scale radio structures of these objects provide compelling evidence that the orientation-based unified models really are true. X-ray evidence, where available, supports the unified picture: radio galaxies show evidence of obscuration from a torus, while quasars do not, although care must be taken since radio-loud objects also have a soft unabsorbed jet-related component, and high resolution is necessary to separate out thermal emission from the sources' large-scale hot-gas environment. At very small angles to the line of sight, relativistic beaming dominates, and we see a blazar of some variety.

However, the population of radio galaxies is completely dominated by low-luminosity, low-excitation objects. These do not show strong nuclear emission lines — broad or narrow — they have optical continua which appear to be entirely jet-related, and their X-ray emission is also consistent with coming purely from a jet, with no heavily absorbed nuclear component in general. These objects cannot be unified with quasars, even though they include some high-luminosity objects when looking at radio emission, since the torus can never hide the narrow-line region to the required extent, and since infrared studies show that they have no hidden nuclear component: in fact there is no evidence for a torus in these objects at all. Most likely, they form a separate class in which only jet-related emission is important. At small angles to the line of sight, they will appear as BL Lac objects.

Criticism of the radio-quiet unification

In the recent literature on AGN, being subject to an intense debate, an increasing set of observations appear to be in conflict with some of the key predictions of the Unified Model, e.g. that each Seyfert 2 has an obscured Seyfert 1 nucleus (a hidden broad-line region).

Therefore, one cannot know whether the gas in all Seyfert 2 galaxies is ionized due to photoionization from a single, non-stellar continuum source in the center or due to shock-ionization from e.g. intense, nuclear starbursts. Spectropolarimetric studies reveal that only 50% of Seyfert 2s show a hidden broad-line region and thus split Seyfert 2 galaxies into two populations. The two classes of populations appear to differ by their luminosity, where the Seyfert 2s without a hidden broad-line region are generally less luminous. This suggests absence of broad-line region is connected to low Eddington ratio, and not to obscuration.

The covering factor of the torus might play an important role. Some torus models predict how Seyfert 1s and Seyfert 2s can obtain different covering factors from a luminosity- and accretion rate- dependence of the torus covering factor, something supported by studies in the x-ray of AGN. The models also suggest an accretion-rate dependence of the broad-line region and provide a natural evolution from more active engines in Seyfert 1s to more “dead” Seyfert 2s and can explain the observed break-down of the unified model at low luminosities and the evolution of the broad-line region.

While studies of single AGN show important deviations from the expectations of the unified model, results from statistical tests have been contradictory. The most important short-coming of statistical tests by direct comparisons of statistical samples of Seyfert 1s and Seyfert 2s is the introduction of selection biases due to anisotropic selection criteria.

Studying neighbour galaxies rather than the AGN themselves first suggested the numbers of neighbours were larger for Seyfert 2s than for Seyfert 1s, in contradiction with the Unified Model. Today, having overcome the previous limitations of small sample sizes and anisotropic selection, studies of neighbours of hundreds to thousands of AGN have shown that the neighbours of Seyfert 2s are intrinsically dustier and more star-forming than Seyfert 1s and a connection between AGN type, host galaxy morphology and collision history. Moreover, angular clustering studies of the two AGN types confirm that they reside in different environments and show that they reside within dark matter halos of different masses. The AGN environment studies are in line with evolution-based unification models where Seyfert 2s transform into Seyfert 1s during merger, supporting earlier models of merger-driven activation of Seyfert 1 nuclei.

While controversy about the soundness of each individual study still prevails, they all agree on that the simplest viewing-angle based models of AGN Unification are incomplete. Seyfert-1 and Seyfert-2 seem to differ in star formation and AGN engine power.

While it still might be valid that an obscured Seyfert 1 can appear as a Seyfert 2, not all Seyfert 2s must host an obscured Seyfert 1. Understanding whether it is the same engine driving all Seyfert 2s, the connection to radio-loud AGN, the mechanisms of the variability of some AGN that vary between the two types at very short time scales, and the connection of the AGN type to small- and large-scale environment remain important issues to incorporate into any unified model of active galactic nuclei.

Cosmological uses and evolution

For a long time, active galaxies held all the records for the highest-redshift objects known either in the optical or the radio spectrum, because of their high luminosity. They still have a role to play in studies of the early universe, but it is now recognised that an AGN gives a highly biased picture of the "typical" high-redshift galaxy.

Most luminous classes of AGN (radio-loud and radio-quiet) seem to have been much more numerous in the early universe. This suggests that massive black holes formed early on and that the conditions for the formation of luminous AGN were more common in the early universe, such as a much higher availability of cold gas near the centre of galaxies than at present. It also implies that many objects that were once luminous quasars are now much less luminous, or entirely quiescent. The evolution of the low-luminosity AGN population is much less well understood due to the difficulty of observing these objects at high redshifts.