Relativistic centrifugal winds

Abstract

Centrifugal winds in the gravity- and pressure-free limit are investigated in the magnetohydrodynamic approximation. The critical condition at the magnetosonic point at infinity determines the angular momentum flow per unit flux tube β in terms of |$\Phi_\infty = (B_\text p \varpi^2)_\infty$| and the three integrals; α, the angular velocity of field line, |$\eta = \rho\kappa = \rho\upsilon_\text p/B_\text p$| the mass flux per unit flux tube and µ, the non-dimensional energy related to the flow, where Bp is the poloidal magnetic field. The flow variables such as the Lorentz factor γ are determined in terms of α, η and µ if |$\phi = \Phi_\infty/\Phi = (B_\text p\varpi^2)_\infty/(B_\text p\varpi^2)$| is specified as a function of axial distance ϖ together with Φ∞ and |$\sigma = (\gamma^2_\infty-1)^{3/2}=\alpha^2\Phi_\infty/4\pi\eta c^3$| decides the degree of relativity of the critical flow solution along each field line.