Self‐consistent Fokker‐Planck Treatment of Particle Distributions in Astrophysical Plasmas

Abstract

High-energy, multicomponent plasmas in which pair creation and annihilation, lepton-lepton scattering, lepton-proton scattering, and Comptonization all contribute to establishing the particle and photon distributions are present in a broad range of compact astrophysical objects. The different constituents are often not in equilibrium with each other, and this mixture of interacting particles and radiation can produce substantial deviations from a Maxwellian profile for the lepton distributions. Earlier work has included much of the microphysics needed to account for electron-photon and electron-proton interactions, but little has been done to handle the redistribution of the particles as a result of their Coulomb interaction with themselves. The most detailed analysis thus far for finding the exact electron distribution appears to have been done within the framework of nonthermal models, where the electron distribution is approximated as a thermal one at low energy with a nonthermal tail at higher energy. Recent attention, however, has been focused on thermal models. Our goal here is to use a Fokker-Planck approach in order to develop a fully self-consistent theory for the interaction of arbitrarily distributed particles and radiation to arrive at an accurate representation of the high-energy plasma in these sources. We derive Fokker-Planck coefficients for an arbitrary electron distribution and correct an earlier expression for the diffusion coefficient used by previous authors. We conduct several tests representative of two dominant segments of parameter space. For high source compactness of the total radiation field, l ~ 10², we find that although the electron distribution deviates substantially from a Maxwellian, the resulting photon spectra are insensitive to the shape of the exact electron distribution, in accordance with some earlier results. For low source compactness, l ~ few, and an optical depth 0.2, however, we find that both the electron distribution and the photon spectra differ strongly from what they would be in the case of a Maxwellian distribution. In addition, for all values of compactness, we find that different electron distributions lead to different positron number densities and proton equilibrium temperatures. This means that the ratio of radiation pressure to proton pressure is strongly dependent on the lepton distribution, which might lead to different configurations of hydrostatic equilibrium. This, in turn, may change the compactness, optical depth, and heating and cooling rates and therefore lead to an additional change in the spectrum. An important result of our analysis is the derivation of useful, approximate analytical forms for the electron distribution in the case of strongly non-Maxwellian plasmas.