Time-dependent models of magnetized pair plasmas

Abstract

A numerical code has been developed to study the time evolution of electron–positron plasmas. The code solves in a self-consistent manner kinetic equations describing the effects of Compton scattering, two-photon pair production, pair annihilation, cooling of pairs via Coulomb scattering, e–e bremsstrahlung, and synchrotron radiation. The kinetic equations are derived under the approximation of homogeneous and isotropic particle distributions following the discussion in Coppi & Blandford. Both stationary (equilibrium) and time-varying output radiation spectra have been computed. Good qualitative agreement with previous calculations is found, except where the differences are attributable to the improved treatment of the microphysics. These differences can be substantial. In magnetized plasmas, the self-absorption turnover frequency is found to vary weakly with the model input parameters. In particular, for mono-energetic injection at energy $$\gamma _ \text {inj}$$, the turnover frequency ν_t, is $$\sim3\times10^{13} U^{1/3}_{10 ^4} \gamma^{-1/3}_ \text {inj} \enspace \text {Hz}$$, where U is the smaller of either the magnetic or photon energy density (measured in units of 10⁴ erg cm⁻³). This may be relevant to the spectra of radio-quiet AGN. Also, the spectral index of the inverse Compton scattered radiation can differ significantly from the associated synchrotron radiation spectral index. (In fact, the equilibrium photon and pair distributions are often not well described by power laws.) Varying the energy and particle inputs to the pair plasma gives rise to many different types of spectral variability. The response of the plasma depends sensitively on both the current state of the plasma and the details of the changes in particle injection. Using time variability as a diagnostic (e.g., to determine the relevance of the models considered here) may thus prove difficult. A possible signature, however, is the response to a significant decrease in the injection of energetic pairs. If the initial Thomson optical depth is of order unity or more, the photon spectrum decays from the high-energy end downwards (lower frequencies lag higher frequencies). The decay of the continuum usually uncovers a prominent, long-lived annihilation feature.