Transonic canards and stellar wind

Paul Carter, Edgar Knobloch, Martin Wechselberger

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1006-1033
Number of pages28
Issue number3
StatePublished - Jan 25 2017
Externally publishedYes

Bibliographical note

Funding 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).

Publisher Copyright:
© 2017 IOP Publishing Ltd & London Mathematical Society.


  • canard
  • geometric singular perturbation theory
  • stellar wind
  • transonic flows
  • viscous gas flow


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