Synchrotron radiation is commonly observed from astronomical
phenomena involving large amounts of energy, particularly in quasars and
active galaxies, and in supernovae. In these objects,
electrons are ejected from the central power source like a supermassive black hole or (in
supernovae) are accelerated by shocks in a process called Fermi
acceleration. These electrons can be accelerated to extremely high energies,
reaching speeds very near the speed of light (often much more than .999 c).
When these electrons encounter a magnetic field, they
move in circular orbits around the field lines, due to the Lorentz force.
Any charged particle gives off radiation when it accelerates, and circular
motion is essentially a constant acceleration with a changing direction,
so the electrons radiate like crazy.
The amount of energy extragalactic radio sources put out is enormous,
often amounting to millions of times the energy output of the Sun, just in
radio waves. Supernovae are also very luminous synchrotron sources, and
because they accelerate electrons to very high energies the synchrotron
emission can extend into optical and X-Ray wavelengths as well.
Synchrotron radiation has some useful properties that make it a useful
diagnostic tool in astronomy. For one, synchrotron radiation is
highly linearly polarized, and this can tell us about the
energy spectrum of the electrons, and also about the ambient magnetic fields
in the source. One good example of this is the Crab Nebula. Here, the
electron energies are so high that some of the optical light is actually
synchrotron emission. When you observe the Crab Nebula through a polarizing
filter, you can see the features change as you rotate the polarization axis.
The spectrum of synchrotron radiation can also tell us
about the electrons that made it. If the electron energy distribution follows
N(E)dE = const × E-p dE
(N(E)dE is the number of electrons at a given energy, and p is the
slope of the electron distribution) then the synchrotron spectrum will
P(nu) = const × nu-(p-1)/2
where P is the total emitted power, and nu is the frequency.
One more note about synchrotron radiation: the observed shape of the spectrum
can also tell you about the "age" of the parent electrons. As the electrons
radiate they lose energy, and the electrons at high energies (radiating
at high frequencies) lose energy faster. Thus, the spectral slope
-(p-1)/2 will steepen at higher frequencies as these electrons are
depleted, and the frequency of this "knee" can tell you something about the
electrons. At very low frequencies, the synchrotron radiation generated by
the electrons will end up being Compton scattered in
a process called synchrotron self-absorption or synchrotron
self-Compton (often abbreviated SSC). Thus if you were to make a plot of
a synchrotron spectrum, it would look something like a tilted letter n.
Sources: Radiative Processes in Astrophysics by Rybicki and Lightman, and
more lectures on radio galaxies than I care to remember....