Bremsstrahlung is radiation associated with the acceleration of electrons in the electrostatic fields of the ions and the nuclei of atoms in the material through which the electron is passing. In the 1930s, scientists noticed that the ionization loss rate that was expected for an electron underestimated the true value as the electron became relativistic. It was realized that an additional loss mechanism was present and associated with the radiation of electromagnetic waves because of the acceleration of the electron in the electrostatic field of the nucleus. This radiation is called 'braking radiation' or, in German, bremsstrahlung. In fact, whenever a charged particle is accelerated or decelerated, it emits bremsstrahlung radiation. There are two kinds of bremsstrahlung, thermal and non-thermal, which are reflective of the number distribution of the electrons. For hot gases, the number distribution is Maxwellian and thermal bremsstrahlung results. For a power law distribution of electrons, non-thermal bremsstrahlung results.

In certain astrophysical contexts, such as the hot (T~10⁸ K ) intergalactic gas in clusters of galaxies, the X-ray emitting plasma is very low in density. This results in the emitted X-rays getting "out " of the plasma without interacting with the gas, which is to say the gas is "optically thin". Thus, the X-ray spectrum we detect is a true representation of the emission process occurring in the plasma. In very hot plasmas (T>10⁸ K), almost all of the elements are fully ionized and the X-ray emission is dominated by bremsstrahlung from hydrogen and helium. The thermal bremsstrahlung radiation spectrum is characterized by the equation:

So what is a blackbody? Let us think of it this way. All objects radiate energy (unless they have a temperature of absolute zero). The maximum energy which can be radiated by an object is called blackbody radiation. A blackbody is a theoretical object which is a perfect absorber and emitter. The radiation given off by a blackbody occurs over a broad spectrum of energies, but has a peak in the emission at a wavelength which is mathematically determined by the temperature of the body. The equation which reflects this relationship is called Planck's Law, which gives the energy density as

Real objects such as stars and planets can, in fact, closely approximate a theoretical blackbody. Each such object can be treated as a blackbody, giving off energy at a rate determined by its temperature.

One of the most exciting uses of X-ray spectroscopy is as a probe of the extreme physical environments associated with objects such as accreting white dwarfs, neutron stars, and black holes. In such cases, the X-ray emission is derived from the release of gravitational potential energy by accreting matter. Here, the gas flows will most likely be optically thick, i.e., the X-ray will most likely scatter off something before it exits the plasma. This results in the X-ray spectrum containing not only clues about the primary emission mechanism, but also about the material flow which feeds it . Thus, understanding the observed spectrum requires understanding how X-ray spectra are modified by passage through an optically thick medium.

One of the two temperatures which occur naturally in accretion flows is the blackbody temperature. For white dwarfs, kT_BB is usually less than 0.2 keV, while for neutron stars it is of order 2 keV. For a stellar mass black hole, it is typically around 1 keV.

Highly relativistic electrons moving through a magnetic field with a component perpendicular to the electron velocity will produce X-rays by synchrotron radiation in most astrophysical sources. Inverse Compton radiation, in which a low energy photon is scattered by a relativistic electron, also can produce photons with energies above 1 keV.

Synchrotron and inverse Compton scattering are formally very similar. Both produce power law spectra with spectral index a = (GAMMA-1)/2, if the relativistic electron number spectrum is a power law with number index GAMMA. Specifically,

for synchrotron radiation

and for inverse Compton radiation

Synchrotron radiation and Compton scattered radiation are major components of the diffuse X-ray background and emission from active galaxies.

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