5.2.2. X-ray emission
The X-ray continuum emission from a hot diffuse plasma is due primarily to three processes, thermal bremsstrahlung (free-free emission), recombination (free-bound) emission, and two-photon decay of metastable levels. The emissivity for thermal bremsstrahlung is given by equation (5.11) above. The radiative recombination (bound-free) continuum emissivity is usually calculated by applying the Milne relation for detailed balance to the photoionization cross sections, which gives (Osterbrock, 1974)
Here, l sums over all of the energy levels of the ion Xi, gs refers to the ground state of the recombining ion Xi+1, are the statistical weights of the levels, al is the photoionization cross section, and l(Xi) is the ionization potential for each energy level in the ion.
The two-photon continuum comes from the metastable 2s states of hydrogenic and heliumlike ions. These levels are excited by the same processes, discussed below, that excite line emission from less forbidden transitions. For hydrogenic ions, the spectral distribution of two-photon emission is given by Spitzer and Greenstein (1951).
At the high temperatures which predominate in clusters (outside of accretion flows), thermal bremsstrahlung is the predominant X-ray emission process. For solar abundances, the emission is primarily from hydrogen and helium.
Processes that contribute to the X-ray line emission from a diffuse plasma include collisional excitation of valence or inner shell electrons, radiative and dielectronic recombination, inner shell collisional ionization, and radiative cascades following any of these processes. The emissivity due to a collisionally excited line is usually written (Osterbrock, 1974)
where h is the energy of the transition, E is the excitation energy above the ground state of the excited level, B is the branching ratio for the line (the probability that the upper state decays through this transition), and is the 'collision strength', which is often a slowly varying function of temperature. Recent compilations of emissivities for X-ray lines and continua include Kato (1976), Raymond and Smith (1977), Mewe and Gronenschild (1981), Shull (1981), Hamilton et al. (1983), and Gaetz and Salpeter (1983). Lines and line ratios that are particularly suited for determining the temperature, ionization state, and elemental abundances in the intracluster gas are described in Bahcall and Sarazin (1978).
Shapiro and Bahcall (1980) and Basko et al. (1981) have suggested that X-ray absorption lines due to intracluster gas might be observed in the spectra of background quasars.