5.2. Ionization and X-ray emission from hot, diffuse plasma
The ionization state and X-ray line and continuum emission from a low density (n 10-3 cm-3), hot (t 108 K) plasma will now be discussed. Several simple assumptions will be made. First, the time scale for elastic Coulomb collisions between particles in the plasma is much shorter than the age or cooling time of the plasma, and thus the free particles will be assumed to have a Maxwell-Boltzmann distribution at the temperature Tg (Section 5.4.1). This is the kinetic temperature of electrons, and therefore determines the rates of all excitation and ionization processes. Second, at these low densities collisional excitation and de-excitation processes are much slower than radiative decays, and thus any ionization or excitation process will be assumed to be initiated from the ground state of an ion. Three-body (or more) collisional processes will be ignored because of the low density. Third, the radiation field in a cluster is sufficiently dilute that stimulated radiative transitions are not important, and the effect of the radiation field on the gas is insignificant. Fourth, at these low densities, the gas is optically thin and the transport of the radiation field can therefore be ignored. These assumptions together constitute the 'coronal limit'. Under these conditions, ionization and emission result primarily from collisions of ions with electrons, and collisions with ions can be ignored. Finally, the time scales for ionization and recombination are generally considerably less than the age of the cluster or any relevant hydrodynamic time scale, and the plasma will therefore be assumed to be in ionization equilibrium.
In nearly all astrophysical plasmas, hydrogen is the most common element and helium is the next commonest, with all the heavier elements being considerably less abundant. For example, this is true of the abundances of elements observed on the surface of the Sun. It is conventional to use these solar abundances as a standard of comparison when studying other astrophysical systems. Since most of the electrons originate in hydrogen and helium atoms, and they are fully ionized under the conditions considered here, the electron density is nearly independent of the state of ionization and is given by ne = 1.21np, where np is the density of hydrogen.