The ionization and recombination rates for astrophysical plasmas have usually been calculated for a Maxwellian electron distribution (e.g., Arnaud & Rothenflug 1985; Arnaud & Raymond 1992; Mazzotta et al. 1998). However, in many low-density astrophysical plasmas, electron distributions may differ from the Maxwellian distribution. The degree of ionization of a plasma depends on the shape of the electron distribution, as well as on the electronic temperature. This has been studied for the solar corona (e.g. Roussel-Dupré 1980; Owocki & Scudder 1983; Dzifcáková 1992; Dzifcáková 1998) and for evaporating interstellar clouds (Ballet et al. 1989), where a non-thermal electron distribution occurs in places where there are high gradients of density or temperature.
A non-thermal electron population is expected in various astrophysical
plasmas. Strong shocks can convert a large fraction of their energy
into the acceleration of relativistic particles by the diffusive shock
acceleration process (e.g., Drury 1983; Blandford &
Eichler 1987; Jones & Ellison 1991; Kang
& Jones 1991). Direct evidence for the presence of
accelerated electrons up to relativistic energies (
GeV)
comes from the observations of radio synchrotron emission in supernova
remnants and in clusters of galaxies. More recently, non-thermal X-ray
emission has been reported in several shell-like supernova remnants and
interpreted as synchrotron radiation from cosmic-ray electrons up to
TeV (Koyama et al. 1995; Allen et al.
1997; Koyama et al.
1997; Slane et al. 1999; Slane et al.
2001).
A number of recent works have focused on the non-thermal emission from supernova remnants (e.g., Laming 2001; Ellison et al. 2000; Berezhko & Völk 2000; Bykov et al. 2000b; Baring et al. 1999; Gaisser et al. 1998; Reynolds 1996,1998; Sturner et al. 1997) and clusters of galaxies (e.g., Sarazin 1999; Bykov et al. 2000a; Sarazin & Kempner 1999). The impact of efficient acceleration on the hydrodynamics and thermal X-ray emission has been investigated (Decourchelle et al. 2000; Hughes et al. 2000).
When the acceleration is efficient, the non-thermal population is expected to modify directly the ionization rates in the plasma as well as the line excitation (e.g. Dzifcáková 2000; Seely et al. 1987). A hybrid electron distribution (Maxwellian plus power-law tail) is expected from diffusive shock acceleration (e.g., Berezhko & Ellison 1999; Bykov & Uvarov 1999). The low energy end of the power-law electron distribution (which connects to the Maxwellian thermal population) is likely to enhance the ionization rates and to significantly modify the degree of ionization of the plasma, which is used as a diagnostic of the plasma electron temperature.
In this paper, we shall examine the influence of a power-law non-thermal electron distribution (connecting to the falling Maxwellian thermal population) on the ionization and recombination rates for C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni. For different characteristic values of the power-law electron distribution, the mean electric charge of these elements has been determined as a function of the temperature at ionization equilibrium and for different values of the ionization timescale. We intend, in this paper, to give a comprehensive study of the dependence of these quantities on the parameters of the non-thermal population, illustrated by simple examples. We do not provide tables, which would be too numerous as the ionization equilibrium depends in our model on four parameters (element, temperature of the thermal component, index and low energy break of the non-thermal population). In the appendix or directly in the text, we give the formula needed for the calculations of the rates which could be easily inserted in computer codes.
In Sect. 2, we define the Hybrid electron distribution used in this work. The calculation of the new ionization collisional rates and (radiative and dielectronic) recombination rates is discussed in Sect. 3. In Sect. 4, we present the derived mean electric charge of the elements in ionization equilibrium as well as in ionizing plasmas.
Copyright ESO 2001