SIMBAD references

Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow, we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder. Therefore, the ratio of the Poynting to particle energy flux, generically referred to as σ, decreases inversely proportional to distance from a large value (typically ≳10⁴) near the light cylinder to σ≃1 at a transition distance R_trans. Beyond this distance, the inertial effects of the outflowing plasma become important, and the magnetic field geometry must deviate from the almost monopolar form it attains between R_lc and R_trans. We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis, ensuring that the magnetic field pressure in the equatorial region will fall off faster than 1/R² (R being the cylindrical radius). This leads both to a value σ=σ_s≪1 at the nebular reverse shock at distance R_s (R_s≫R_trans) and to a component of the flow perpendicular to the equatorial component, as required by observation. The presence of the strong shock at R=R_s allows for the efficient conversion of kinetic energy into radiation. We speculate that the Crab pulsar is unique in requiring σ_s≃3x10^–3 because of its small translational velocity, which allows for the shock distance R_s to grow to values ≫R_trans.