The Efficiency of the Magnetic Acceleration in Relativistic Jets

Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze relativistic outflows by means of examining the momentum equation along the flow and in the transfield direction. We argue that the asymptotic Lorentz factor is γ_∞ ～ μ ? σ _M , and the asymptotic value of the Poynting-to-matter energy flux ratio—the so-called σ function—is given by σ_∞/(1 + σ_∞) ～ σ _M /μ, where σ _M is the Michel's magnetization parameter and μc ² the total energy-to-mass flux ratio. We discuss how these values depend on the conditions near the origin of the flow. By employing self-similar solutions we verify the above result, and show that a Poynting-dominated flow near the source reaches equipartition between Poynting and matter energy fluxes, or even becomes matter-dominated, depending on the value of σ _M /μ.