Parker's classical stellar wind solution  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 . 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  is described by the same theory.
Bibliographical noteFunding Information:
PC would like to thank Nat Trask for helpful discussions. This work was supported in part by the National Science Foundation under grants DMS-1148284 (PC) and DMS-1317596 (EK), and by the Australian Research Council Future Fellowship grant FT120100309 (MW).
- geometric singular perturbation theory
- stellar wind
- transonic flows
- viscous gas flow