Steady mildly relativistic thermal plasmas: processes and properties

The physical properties of a finite, thermal plasma in pair balance are investigated as a function of the three dimensionless parameters: (i) the temperature |θ (≡ kT/mc²|⁠, where m is the electron mass), (ii) the ‘proton optical depth’ |τ_ p (≡ n_ p σ _ T R)| and (iii) the proton density np or radius R. At a dimensionless luminosity |l (≡ Lσ_ T/Rmc³ = 3 L₄₃/R₁₄) 1| Comptonization of bremsstrahlung and double Compton photons dominates the cooling. A determination of the steady pair density in such a Wien equilibrium plasma (WEP) shows the existence of the two pair density branches previously found for optically thin plasmas. Photon–photon absorption modifies the pair annihilation line into a Wien tail. The |τ_ p-θ| parameter space is divided into 11 regions, each characterized by some combination of dominant processes. Pair effects cause part of |τ_ p-θ| space to contain three possible states, two of which are pair dominated. For |τ_ p| greater than 102−105 (depending on np) the plasma cloud is necessarily in LTE. In |l-θ| space pair annihilations cannot balance pair productions at |θ > θₘax ≈ 24| when l = ≫ and at |l > lWE| when l≫ 1 (and |θ 0.4|⁠), where |lWE≈ 4(2π)1/2θ 5/2 exp (1/θ)| is the luminosity of a pair-dominated WEP. At |θ 0.1| the requirement of pair balance can provide a stronger constraint on the luminosity than the pair-free Eddington limit |l_ E ≈ 10⁴ R_ s/R| where Rs is the Schwarzschild radius of the confining mass. At intermediate temperatures, |1/3 θ 3|⁠, steady thermal plasmas are possible only for luminosities smaller than LE by a factor 500 (Rs/R). The presence of magnetic fields would strengthen these luminosity limits. Objects observed at MeV energies are discussed with the emphasis on pair effects.