Starting from a nonequilibrium configuration we analyze the role of the direct and the inverse binary and triple interactions in reaching thermal equilibrium in a homogeneous isotropic pair plasma. We focus on energies in the range 0.1-10 MeV. We numerically integrate the relativistic Boltzmann equation with the exact QED collisional integrals taking into account all binary and triple interactions. We show that first, when a detailed balance is reached for all binary interactions on a time scale t(k) < or approximately 10(-14) sec, photons and electron-positron pairs establish kinetic equilibrium. Subsequently, when triple interactions satisfy the detailed balance on a time scale t(eq) < or approximately 10(-12) sec, the plasma reaches thermal equilibrium. It is shown that neglecting the inverse triple interactions prevents reaching thermal equilibrium. Our results obtained in the theoretical physics domain also find application in astrophysics and cosmology.

In the recent Letter [1] we considered the approach of nonequilibrium pair plasma towards thermal equilibrium state adopting a kinetic treatment and solving numerically the relativistic Boltzmann equations. It was shown that plasma in the energy range 0.1-10 MeV first reaches kinetic equilibrium, on a timescale t k 10 −14 sec, with detailed balance between binary interactions such as Compton, Bhabha and Møller scattering, and pair production and annihilation. Later the electron-positron-photon plasma approaches thermal equilibrium on a timescale t th 10 −12 sec, with detailed balance for all direct and inverse reactions. In the present paper we systematically present details of the computational scheme used in [1], as well as generalize our treatment, considering proton loading of the pair plasma. When proton loading is large, protons thermalize first by proton-proton scattering, and then with the electron-positron-photon plasma by proton-electron scattering. In the opposite case of small proton loading proton-electron scattering dominates over proton-proton one. Thus in all cases the plasma, even with proton admixture, reaches thermal equilibrium configuration on a timescale t th 10 −11 sec. We show that it is crucial to account for not only binary but also triple direct and inverse interactions between electrons, positrons, photons and protons. Several explicit examples are given and the corresponding timescales for reaching kinetic and thermal equilibria are determined.

We consider a stationary, spherically outflowing wind consisting of electron-positron pairs and photons. We do not assume thermal equilibrium and include the two-body processes that occur in such a wind, Møller and Bhaba scattering of pairs, Compton scattering, two-photon pair annihilation, and two-photon pair production, together with their radiative three-body variants: bremsstrahlung, double Compton scattering, and three-photon pair annihilation, with their inverse processes. In the concrete example described here, the wind injection source is a hot, bare, strange star. Such stars are thought to be powerful sources of pairs created by the Coulomb barrier at the quark surface. We present a new, finite difference scheme for solving the relativistic kinetic Boltzmann equations for pairs and photons. Using this method, we study the kinetics of the wind particles and the emerging emission for total luminosities of L ¼ 10 34 10 42 ergs s À1 (the upper limit being set, at the moment, by computational limitations). We find the rates of particle number and energy outflows, outflow velocities, number densities, energy spectra, and other parameters for both photons and pairs as functions of the distance. We find that for L > 2 ; 10 35 ergs s À1 , photons dominate the emerging emission. For all values of L the number rate of emerging pairs is bounded:Ṅ e PṄ max e ' 10 43 s À1 . As L increases from $10 34 to 10 42 ergs s À1 , the mean energy of emergent photons decreases from $400-500 to 40 keV, as the spectrum changes in shape from that of a wide annihilation line to nearly a blackbody spectrum with a high-energy (>100 keV) tail. These results are pertinent to the deduction of the outside appearance of hot bare strange stars, which might help discern them from neutron stars.