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Astron. Astrophys. 356, 1149-1156 (2000)

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Appendix A: how to average Gaunt factors for free-free emission

The free-free emissivity is the density of electrons and ions multiplied by the differential cross section integrated over the initial velocity distribution [FORMULA]. We use the mean energy of the electrons

[EQUATION]

to obtain the scale-free kinetic energy of the final electrons

[EQUATION]

The averaged Gaunt factor can be expressed in terms of a modified distribution function [FORMULA] and gives

[EQUATION]

where the velocity is a function of y. In the case of a thermal distribution we obtain

[EQUATION]

The standard form for the thermally averaged Gaunt factor is [FORMULA] divided by the average obtained from the semi-classical expression of Kramers and Wentzel. This leads to

[EQUATION]

The Gaunt factor [FORMULA] does not contain the exponential [FORMULA] of Eq. A.4 which arises as the integral over initial electron velocities is limited to [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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