X-rays from Free Electrons
The mechanisms for producing x-rays from
free electrons are similar to those responsible for
production of other energies of electromagnetic radiation.
The motion of a free electron
(for example, one that is unbound to an atom) may produce X-rays
if the electron is undergoing any one of these motions:
We discuss each of these scenarios below.
- accelerated past a charged particle,
- moving in a magnetic field,
- accelerated by another photon.
This mechanism operates in all X-ray sources. It originates from the
acceleration of electrons in coulomb collisions with other electrons and
with ions and nuclei.
It comes from the German words "bremsen," meaning "to brake," and
"strahlung," meaning "radiation." The most common situation is the
emission from a hot gas as the electrons collide with the nuclei due to
their random thermal motions. This is called "thermal bremsstrahlung." Bremsstrahlung can also occur
when a beam of particles decelerates when it encounters an obstacle. The
X-ray machine in a dentist's office, for example, works by firing a beam
of electrons at a metal plate. When the electrons collide with the plate
they come to a stop, emitting X-rays by bremsstrahlung.
Thermal bremsstrahlung produces a characteristic spectrum.
Each collision event produces a photon, and the energy of the photon corresponds
approximately to the change in energy that occurred during the
collision. The electrons in a gas have a distribution of energies
produced by bremsstrahlung, and this reflects the electron energy
distribution, which has an average that is proportional to temperature.
Thus, a measurement of the spectrum can be used to determine the
temperature of the gas.
Synchrotron radiation is associated with the acceleration that
happens to electrons as they spiral around a magnetic
field. The force
felt by a charged particle in a magnetic field is perpendicular to the
direction of the field and to the direction of the particle's velocity.
The net effect of this is to cause the particle to spiral around the
direction of the field. Since circular motion represents acceleration
(i.e., a change in velocity), the electrons radiate photons of a
characteristic energy, corresponding to the radius of the circle. For
non-relativistic motion, the radiation spectrum is simple and is called
"cyclotron radiation". The frequency of radiation is simply the gyration
frequency, which is given in terms of the magnetic field as
where B is the field strength, e is the electric
charge, m is the particle (electron) mass, and c is the speed of light. Cyclotron and synchrotron radiation are strongly polarized;
detection of polarization is regarded as strong observational evidence
for synchrotron or cyclotron radiation.
The situation becomes more complicated when the particle energy is relativistic (i.e., their speed approaches the
speed of light). This is more common in astrophysical
this case, the radiation is compressed into a small range of angles
around the instantaneous velocity vector of the particle. This is
referred to as "beaming," and it results in a spreading of the energy
spectrum in a way that depends on the momentum of the particle in the
direction perpendicular to the field. In such a case, there is still a
maximum photon energy that can be radiated, which is proportional to the
field strength and inversely proportional to the particle momentum.
Synchrotron spectra typically have a power law shape, i.e., the flux proportional
to photon energy to
some power. This is because the particle momenta also have a power law
distribution. They are commonly observed in the radio region of the spectrum, but can extend to
the X-ray portion of the spectrum and beyond. Both synchrotron and
cyclotron emission apply only to particle motion perpendicular to the
direction of a magnetic field. Real gases must also have particle
motions parallel to the field, and radiate ordinary thermal
bremsstrahlung from this component of their motion.
This process does not generate new photons, but scatters photons from
lower to higher energies (or vice versa) in interactions with electrons
of higher (or lower) energies. The non-relativistic version is called
"Thomson scattering," and it results in a negligible change in photon
energy. In the most widely discussed scenario, low energy photons (UV,
optical, or below) scatter with relativistic electrons, making X-rays
and/or gamma rays.
This should actually be called "inverse Compton," since it is the
inverse to the process first described by Arthur Compton, but the
distinction is often not made by astronomers. The fractional energy
transfer per scattering is
where T is the electron temperature, m is the electron
mass, and k and c are the Boltzmann
the speed of
light, respectively. Thus, unless kT is much greater than
mc2 (which is unlikely), many scatterings are required
to shift an optical or UV photon into the X-ray band. The resulting
spectra are referred to as "saturated" or "unsaturated," depending on
whether sufficient scatterings have occurred to shift all the photons to
the electron energies. In the former case, the photon spectrum will
resemble the electron energy distribution. In the latter case, the
photon spectrum is a power law spectrum extending from the UV/optical up
to the electron characteristic energy. Unsaturated Compton scattering
are currently considered one of the most likely mechanisms for making
the hard X-rays
(greater than 10 keV) observed from many classes of objects, including
active galaxies and black hole
binaries in our galaxy.
Last Modified: October 2010