Transonic canards and stellar wind

Parker's classical stellar wind solution [20] describing steady spherically symmetric outflow from the surface of a star is revisited. Viscous dissipation is retained. The resulting system of equations has slow-fast structure and is amenable to analysis using geometric singular perturbation theory. This technique leads to a reinterpretation of the sonic point as a folded saddle and the identification of shock solutions as canard trajectories in space [22]. The results shed light on the location of the shock and its sensitivity to the system parameters. The related spherically symmetric stellar accretion solution of Bondi [4] is described by the same theory.