Non‐equilibrium effects in steady relativistic e + e −γ winds

We consider an ultrarelativistic wind consisting of electron–positron pairs and photons with the principal goal of finding the asymptotic Lorentz factor γ ∞ for zero baryon number. The wind is assumed to originate at radius r i where it has a Lorentz factor γ i and a temperature T i sufficiently high to maintain pair equilibrium. As r increases, T decreases and becomes less than the temperature corresponding to the electron mass m e , after which non‐equilibrium effects become important. The pairs, which carry only a small fraction of the total energy, may be accelerated by the photons until τ falls below ∼2 × 10 −5 γ 3/4 i . Radiative transfer calculations show that only at this point do the radiation flux and pressure start to deviate significantly from their blackbody values. The acceleration of the pairs increases γ by a factor ∼45 compared with its value at the photosphere; it is shown to approach γ ∞  ∼ 1.4× 10 3 ( r 6 i/10  cm) 1/4 γ {3/4} i T i /m e . The limit of zero baryon number is a good approximation when the mass injection rate M ˙ in the flow is below a critical value corresponding to ( E ˙/ M ˙ M ) c,0  ∼ 5 × 10 7 ( r 6 i/10  cm) T i / m e for fixed energy injection rate E ˙ E . For large baryon loading, ( E ˙/ M ˙ ≲  E ˙/ M ˙) c,M  ∼ 350( r i /10 6  cm) 1/4 γ 3/4 i T i /m e , the asymptotic Lorentz factor is γ ∞  ∼  E ˙/ M ˙. Surprisingly, increasing E ˙/ M ˙ from ( E ˙/ M ˙) c,M to ∞ only increases γ ∞ by a factor ∼( m p / m e ) 1/4 ≈6.5, less than an order of magnitude. As E ˙/ M ˙ increases, the fraction of the energy carried by pairs decreases, reaching ∼10 −5 γ 3/4 i as E ˙/ M ˙ to ∞.