Electron-Positron Pair Equilibria in Relativistic Plasmas

The physical properties of a thermal plasma of size R in the temperature range θ (≡ kT/mc2, where m is the electron mass) = ⅓-100 are studied assuming pair equilibrium and thermal balance. The radiation field is obtained by multiplying the spectral emissivities by the photon escape time. The effect of scatterings is approximately allowed for by treating them as coherent. All important pair and photon producing processes in a plasma with a Thomson scattering optical depth τT of order unity or less are included. The spectral emissivities and the cooling rates for bremsstrahlung and pair annihilation are discussed. The photon-photon, photon-particle, and particle-particle pair production rates, and the pair annihilation rate as well as the opacities are calculated. Simple approximate expressions are given for several rates. The equilibrium ratio z of the pair density n+ to the proton density n+ is given by the roots to the pair equilibrium equation (a polynomial in z). For a given τN ≡ Nre2R -1, there exists a temperature θc beyond which the pair annihilation rate cannot balance the pair production rate and there are no pair equilibria. For θ c there are a high-z pair equilibrium branch (z ≪1) with τT of order unity, where photon-photon pair production dominates, and an optically thin low-z pair equilibrium branch (z ≪ τN-1), where particle-particle pair production dominates. The temperature θc has a maximum value θmax ≍ 25 for τN 10-4 and decreases monotonically for larger τN. Several aspects of the obtained pair equilibria, such as parameter space dependence, cooling rates, optical depths, stability, and confinement are briefly discussed. Optically thick (τT > 1) pair equilibria are considered qualitatively. The approach of the solution curves in the z-θ plane to complete thermodynamic equilibrium is expected to occur at a temperature θmin ≍1/10 - 1/3 V1o-I The physical significance of θmin and θmax is discussed. A pair equilibrium plasma is kept at θmin (for τT > > 1) or at θmax (for τT -3) over a wide range of heating rates. It is, however, emphasized that realistic semirelativistic plasmas may be neither in pair equilibrium nor in thermal balance.