Investigation of the mean photon energy in Kompaneets spectra

Sammanfattning: The Kompaneets equation describes the spectrum formation when hot fermions are injected into an opaque fermion-photon plasma in thermal equilibrium and inverse Compton-scatterings occur. The equation has three free parameters, the initial plasma thermal energy θ_u, the final plasmathermal energy θ_r and the average photon energy gain y_r. In this study I use the parameters R = θ_r/θ_u, θ_r and y_r. The created spectrum has different properties, of which an important one is the mean photon energy ε_d. In this thesis, I aim to find the dependencies of the mean photon energy on the three Kompaneets parameters. I chart the parameter spaces and find correlation between the mean photon energy and the individual parameters. I describe the relations between the mean photon energy and the Kompaneets quantities empirically, constructing a function where I try to separate the variables as far as possible. For general results, I study a wide range of each parameter, which forces me to make a broken power-law description of the mean energy. I arrive at a function of the form ε_d(R, y_r, θ_r) = g(R, y_r) R^k(y_r) 3θ_r. I perform an error analysis and see that the majority of the errors of the new method is ≲ 2%, while the previous (tabulated value based approximation) method had the majority of the errors ≲ 70%. This means an effective improvement of the method by a factor 35. Then, I discuss the behaviour of the mean energy in the Kompaneets parameterspace. Finally, I outline a similar analysis of another property of the Kompaneets spectrum, the Compton temperature.