ATOMDB Units

APEC models produce line and continuum emissivity tables which are used to calculate predicted line and continuum fluxes. These predicted fluxes may in turn be compared with an observed spectrum or a subset of spectral features. For lines observed at Earth with no redshift or column density, the predicted line flux for a single temperature model with (K) is given by

Flux [ph cm $^{-2}$ s $^{-1}$ ] $= \frac{\displaystyle \epsilon(T_e)}{\displaystyle 4 \pi R^2} \int N_eN_H dV$ ,

where $\epsilon(T_e)$ is the emissivity in ph cm $^{3}$ s $^{-1}$ , R is the distance to the source in cm, and $\int N_e N_H dV$ is the emission measure in cm $^{-3}$ , generally taken over a specified temperature interval. (Since emission measures for astronomical objects tend to involve large enough numbers to incur numerical difficulties, the traditional practice in X-ray astronomy is to scale the emission measure over distance squared to obtain a more tractable normalization, or ``norm.'') For multi-temperature models the predicted flux is the sum of the flux components at each temperature.

We define the emissivity for a line transition from level to level as

$\epsilon(T_e) = N_k A_{kj}$

where is the level population of level , and $A_{kj}$ is the atomic transition probability in s $^{-1}$ . is related to the electron density by

$N_k = \frac{\displaystyle N_k}{\displaystyle N_z} \frac{\displaystyle N_z}{\dis... ...N_Z}{\displaystyle N_{Hyd}} \frac{\displaystyle N_{Hyd}}{\displaystyle N_e} N_e$ ,

where $\frac{N_k}{N_z}$ is the ratio of the level population to the ion population, solved through the level population rate matrix; $\frac{N_z}{N_Z}$ is the charge state or ionization balance, often solved in collisional ionization equilibrium; $\frac{N_Z}{N_{Hyd}}$ is the elemental abundance relative to hydrogen; and $\frac{N_{hyd}}{N_e}$ is the fraction of hydrogen to electron density, about 0.8 for cosmic plasmas. While this definition of emissivity is convenient for our calculations, other definitions of emissivity abound and may be more convenient in other situations.

The continuum spectrum produced by bremsstrahlung, radiative recombination and two-photon emission is related to the same emission measure $\int N_e N_H dV$ ; however, it is important to note that the natural units of continuum emission are ph cm s $^{-1}$ Å $^{-1}$ , since the emission is spread out over a broad band. Thus when one is calculating the spectrum from the sum of lines and continuum, the bin size must be specified. Lines may be broadened by a number of physical processes as well as by the instrumental line spread function.

Last modified: 28 June 2002

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