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Bremsstrahlung (German for "braking radiation") is a type of electromagnetic radiation emitted by high-temperature plasmas -- where atoms are ionized -- when free electrons interact with the electric field surrounding atomic nuclei. Bremsstrahlung is also known as free-free emission because the electrons merely pass by the atomic nuclei, and are not locked into the electron orbitals.

Whenever a free electron encounters a positively charged ion, it will undergo an acceleration. As the electron moves past, the dipole of the electron and ion changes with time, which results in the emission of energy in the form of photons. The frequency of the emitted photons will depend upon how fast the electrons are moving, the charge on the ions, and the density of electrons and ions in the plasma.

A common physical situation is the case of thermal bremsstrahlung, where the electron velocities follow a Maxwell-Boltzmann distribution. In astronomy, we observe thermal bremsstrahlung from many sources containing hot, optically thin plasmas like supernova remnants, accretion disks, and the hot gas within Abell clusters. Thermal bremsstrahlung is also emitted in hot laboratory plasmas, and in the fireballs of nuclear explosions.

The emission coefficient for thermal bremsstrahlung is given by

εν = 6.8 × 10-38 Z2 ne ni T-1/2 e-hν/kT g (erg s-1 cm-3 Hz-1)

where ε is the emitted energy per unit volume per unit frequency (ν), Z is the charge on the ions (for protons, it's just +1),ne,i are the electron and ion densities, T is the temperature, h is Planck's constant, k is Boltzmann's constant, and g is the Gaunt factor, a quantum mechanical correction to the classical scattering equations used here. The Gaunt factor has a small dependence on the photon frequency ν -- of order ν-1/2 -- which means that when you put everything together, you find that the emission from a given volume of plasma has a nearly flat spectrum (i.e. only a weak dependence on the frequency). This distinguishes it from the sharply-peaked blackbody radiation spectrum, and the synchrotron radiation spectrum. So, when you measure the spectrum of a given source, you can use the shape of the spectrum to determine whether you are observing black body radiation, bremsstrahlung, synchrotron radiation, or perhaps something else (a hot, Comptonized spectrum perhaps, or discrete emission lines). This in turn can tell you about the physical properties of what you're observing -- is it a thin gas or a dense gas, what is its temperature, what is it made of, et cetera.

Note: bremsstrahlung is fundamentally different from synchrotron radiation, also sometimes seen in high-energy plasmas. Bremsstrahlung comes entirely from the interactions of particles within a plasma, while synchrotron radiation comes from the interaction of charges (mostly electrons) with magnetic fields.

Source: mostly Radiative Processes in Astrophysics by Rybicki and Lightman. A discussion of Gaunt factors can be found in some quantum books -- R and L cite Novikov and Thorne's article in Black Holes, Gordon and Breach (1973).

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