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Thermal X-ray radiation is an important diagnostic tool for studying cosmic sources where high-energy processes are important. Examples are the hot corona of the Sun and of stars, Solar and stellar flares, supernova remnants, cataclysmic variables, accretion disks in binary stars and around black holes (Galactic and extragalactic), the diffuse interstellar medium of our Galaxy or external galaxies, the outer parts of Active Galactic Nuclei (AGN), the hot intracluster medium, the diffuse intercluster medium. In all these cases there is thermal X-ray emission or absorption.

In the present paper we focus upon the properties of the X-ray spectrum in the diffuse gas within and between galaxies, clusters and the large scale structures of the Universe. As this gas has very low densities, the level populations in the atoms are not governed by Saha-like equations, but instead most of the atoms will be in or near the ground state. This simplifies the problem considerably. Furthermore, in these tenuous media we need to consider only gas with small or moderate optical depth; the radiative transport is therefore simple. Stellar coronae have similar physical conditions, but there the densities are higher so that in several cases the emergent spectrum has density-dependent features. Due to the low densities in our sources, these density effects can be ignored in most cases; however, for the lowest density gas photoionisation effects must be taken into account.

We show in this paper that it is possible to derive many different physical parameters from an X-ray spectrum: temperature, density, chemical abundances, plasma age, degree of ionisation, irradiating continuum, geometry etc.

The outline of this paper is as follows. First, we give a brief overview of atomic structure (Sect. 2). We then discuss a few basic processes that play an important role for the thermal plasmas considered here (Sect. 3). For the proper calculation of an X-ray spectrum, three different steps should be considered:

  1. the determination of the ionisation balance (Sect. 4),

  2. the determination of the emitted spectrum (Sect. 5),

  3. possible absorption of the photons on their way towards Earth (Sect. 6).

We then briefly discuss issues like the Galactic foreground emission (Sect. 7), plasma cooling (Sect. 8), the role of non-thermal electrons (Sect. 9), and conclude with a section on plasma modelling (Sect. 10).

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