On the stability of electron–positron pair equilibria and the X-ray variability of active galactic nuclei

We perform a detailed linear stability analysis of pair equilibria in homogeneous, static two-temperature plasma clouds. We consider the case in which electrons and positrons are heated in Coulomb interactions with hot protons, and are cooled by bremsstrahlung, annihilation and Compton scattering. The treatment is kept analytical, except for a numerical evaluation of the eigenvalues of the stability matrix. Including energy conservation for both pairs and protons has a stabilizing effect on the equilibria causing the unstable region in parameter space to decrease by a factor of 2. The pair equilibria are unstable only when the compactness of the plasma cloud, $$l, (= {L\sigma}_\text{T}/{Rm}_\text{e}{c}^{3})$$ is in the limited range from 10 to 25, and the proton optical depth, $$\tau _\text{p}(={n}_\text{p}{\sigma}_\text{T} R),$$ is less than 2. This pair instability is therefore not likely to be the major cause for the observed X-ray time variability in active galactic nuclei.