Double Compton emission in radiation dominated thermal plasmas

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Abstract
We investigate the process of double Compton (DC) emission and absorption, γ + e ⇔ γ + γ + e. We derive the kinetic equation for this process in a nonrelativistic, thermal plasma and give analytic and detailed numerical solutions of this equation coupled with the Kompaneets equation, which describes redistribution of photons through γ + e → γ + e. The photon distribution function evolves in an approximately self-similar manner. In infinite media, DC achieves a Planck distribution sooner than bremsstrahlung when the ion density satisfies nι < 1030 cm-3 (kT/mc2)11/2. In general, DC will dominate bremsstrahlung as a source of photons in a sufficiently radiation dominated plasma, nγ/nι > 0.1(mc2/kT)5/2. Under the double Compton process, the photon density increases to its equilibrium value almost exponentially in time, on a time scale tDC = τc(π/8α)(mc2/kT)2, where τc = (neσTc)-1 is the ordinary Compton scattering time and α is the fine-structure constant. We also consider the emitted radiation spectrum and time evolution of the double Compton process in a finite medium. The photon number density always adjusts itself so that a finite plasma is just" critical," and this equilibrium solution is stable. A characteristic plasma parameter for the double Compton process under equilibrium conditions is ξDC ≡ (8α/π)τes2 )tes2 (kT/mc2)2, where τes is the electron scattering optical depth. In an effectively thin, DC dominated medium the equilibrium photon density depends exponentially on ξDC. The double Compton process may have applications in high energy astrophysical phenomena and in cosmology, before recombination.

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