X-winds in Action
Mike J. Cai, Hsien Shang, Hsiao-Hsuan Lin, Frank H. Shu

TL;DR
This paper develops a variational approach to solve the complex Grad-Shafranov equation governing X-winds from young stars, providing analytic solutions useful for various astrophysical applications.
Contribution
It introduces a variational principle to efficiently solve the PDE governing X-winds, simplifying the problem by adopting the cold limit and ignoring magnetic threading effects.
Findings
Derived analytic forms for X-wind solutions
Tabulated coefficients for practical use
Enhanced understanding of wind launching mechanisms
Abstract
The interaction of accretion disks with the magnetospheres of young stars can produce X-winds and funnel flows. With the assumption of axial symmetry and steady state flow, the problem can be formulated in terms of quantities that are conserved along streamlines, such as the Bernoulli integral (BI), plus a partial differential equation (PDE), called the Grad-Shafranov equation (GSE), that governs the distribution of streamlines in the meridional plane. The GSE plus BI yields a PDE of mixed type, elliptic before critical surfaces where the flow speed equals certain characteristic wave speeds are crossed and hyperbolic afterward. The computational difficulties are exacerbated by the locations of the critical surfaces not being known in advance. To overcome these obstacles, we consider a variational principle by which the GSE can be attacked by extremizing an action integral, with all…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
