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
(i.e unbound to an atom) may produce
x-rays
if the electron is undergoing any one of these motions:
- accelerated past a charged particle,
- moving in a magnetic field,
- accelerated by another photon.
We discuss each of these scenarios below.
Bremsstrahlung
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, 'brems' for
braking, and 'strahlung' for 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 on encountering 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 can be regarded as producing a photon, and the energy
of the photon corresponds approximately to the change in energy suffered
during the collision. The electrons in a gas have a distribution of
energies, with the mean proportional to the temperature. The distribution
of photon energies produced by bremsstrahlung reflects the electron energy
distribution, and has an average which is proportional to temperature.
Thus, a measurement of the spectrum can be used to determine the temperature
of the gas.
Synchrotron Radiation
Synchrotron radiation is associated with the acceleration suffered by
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 objects. In 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 due to the fact
that 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-rays and beyond. Clearly, 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.
Compton Scattering
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 results in 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 constant
and the speed of light, respectively. Thus, unless kT is much
greater than mc2 (which is unlikely)
many scatterings are required in order 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 spectra are currently considered one of the most likely
mechanisms for making the hard (greater than 10 keV) X-rays observed
from many classes of objects, including active galaxies and black hole
binaries in our Galaxy.
|
