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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:

• 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 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 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 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.

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 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 constant and 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.