# Physics Underlying the ATOMDB

The ATOMDB line and continuum results apply to an optically-thin thermal plasma with astronomical abundances (such as those of Anders & Grevesse, 1989, Geochimica et Cosmochimica Acta, 53, 197).

Calculating the X-ray/UV spectrum of a hot, collisionally-dominated optically-thin plasma requires knowledge of the atomic transition rates and energies of the ions involved, as well as a code to calculate the interplay between the different rates. Here we describe an outline of the relevant processes.

In most astrophysical plasmas, the following processes are important:

1. Continuum emission processes
2. 2-photon emission
2. Line emission process
2. Dielectronic recombination satellite lines
3. Inner-shell ionization

This list omits a number of processes:

• two-photon excitation and other three-body processes are omitted because the densities required for these exceed the 'optically-thin' limit.
• charge exchange processes are omitted despite their potential importance to the spectrum, because these processes usually arise from the interaction of hot ions and neutral H or He. For hot plasmas at or near equilibrium, neutral H and He do not occur in the same volume as the hot ions.
• photoexcitation and photoionization processes are omitted since this description is of a collisionally-dominated plasma.

## Plasma Emission Models

The appropriate model depends not only on the temperature of the plasma, but also its density. At sufficiently high densities, collisions completely determine the level population. As the density drops, a collisional-radiative model must be used and finally the purely radiative coronal/nebular approximation can be used. The breakpoints between these models are discussed below:

Local Thermodynamic Equilibrium (LTE)

LTE rarely applies to an optically-thin astrophysical hot collisional plasma, but when it does, the level populations determined only by collisional processes. It requires:

• At 10 MK for H-like Fe, Ne > 2x10^27 cm^-3
• At 0.1 MK for H-like O, Ne > 10^24 cm^-3

This is the most general case, where collisional excitation and de-excitation compete with radiative transitions.

• Needed for 10^14 - 10^27 cm^-3
• Also required for complex ions at somewhat lower densities

Coronal and Nebular Models

The low-density approximation, where collisional de-excitation can be ignored, so every excited level will decay via a radiative transition.

• Applicable to Ne < 10^14 - 10^16 cm^-3

### Other Common Simplifying Assumptions

Most of these assumptions break down somewhere in astrophysics. In fact, most of them break down in our own Sun! The ability to calculate more general cases is limited by availability and accuracy of atomic data (and/or by computational limits). The ability to parameterize an astrophysical plasma in full detail is a different, often more difficult, problem.
• Ionization/recombination may be solved separately from excitation/de-excitation
• Either collisional processes dominate or radiative processes dominate
• Optical depth effects may be treated in a simple way:
ignored
escape probability formalism
• Low density
• Ion population mostly in the ground state
• Coronal approximation (collisionally ionized plasmas)
• Nebular approximation (photoionized plasmas)
• Rate coefficients are not density-sensitive
• Time-independent
• Maxwellian electrons
• Electric and magnetic field effects are ignored
• No diffusion