An Energetic Criterion for Astrophysical Winds and Jets

The dichotomy of astrophysical flows to appear either as collimated jets, or, uncollimated winds is discussed in the frame of ideal magnetohydrodynamics (MHD). In particular, we focus on the energetics of these outflows as an explanation of their appearance. In the simplest case where in the basic HD nonlinear and coupled partial differential equations, the physical variables of the radial distance and the latitude are separable, we analytically and explicitly show that there exists a universal integral of the system. This integral provides an energetic criterion, which may distinguish noncollimated astrophysical winds from well collimated jets.