Temperature-averaged and total free-free Gaunt factors for κ and Maxwellian distributions of electrons^⋆

¹ Department of Mathematics University of Évora, R. Romão Ramalho 59, 7000 Évora, Portugal
e-mail: mavillez@galaxy.lca.uevora.pt
² Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
e-mail: mavillez@astro.physik.tu-berlin.de

Received: 16 March 2015
Accepted: 6 May 2015

Abstract

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission.

Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10^-10 in units of z²Ry. We used double and quadruple precisions. The temperature-averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes.

Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.