Continued-Fraction Solutions for the Variation of the Electron Temperature in Comptonizing Plasmas
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**Session 106 -- AGN**
*Display presentation, Saturday, January 15, 9:30-6:45, Salons I/II Room (Crystal Gateway)*

## [106.05] Continued-Fraction Solutions for the Variation of the Electron Temperature in Comptonizing Plasmas

*P. A. Becker (CSI/Physics, George Mason University, Fairfax, VA 22030)*

During radiation-dominated X-ray transients in AGNs, energy
is rapidly transferred between the photons and the electrons
until the electron temperature ($T_e$) has equilibrated to the
inverse-Compton temperature of the radiation ($T_{\rm IC}$).
This occurs on a much shorter timescale than the equilibration
of the radiation into a Wien distribution.
Once the temperatures have equilibrated, the condition
$T_e=T_{\rm IC}$ continues to be enforced by the Compton
exchange of energy between the photons and the electrons.
The radiative transfer problem then becomes highly nonlinear,
since the variation of the electron
temperature determines the spectrum (through the Kompaneets
equation), while the spectrum determines the electron temperature
(through the condition $T_e=T_{\rm IC}$). It is therefore
extremely useful to develop techniques for independently
calculating the electron temperature as a function of time
for an arbitrary initial radiation
spectrum. In this paper we develop a general technique
for determining the electron temperature by using
the frequency moments of the initial spectrum to construct
a continued fraction with dramatic convergence properties.
Resulting expressions for $T_e$ are presented for a variety
of initial spectra.

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