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EP: Fachverband Extraterrestrische Physik
EP 14: Astrophysics: Stellar Astrophysics
EP 14.6: Talk
Friday, March 24, 2023, 12:30–12:45, HSZ/0004
An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models — •Jens Kleimann1 and Christian Röken2, 3 — 1Theoretische Physik IV, Ruhr-Universität Bochum, Germany — 2Department of Geometry and Topology, Faculty of Science, University of Granada, Spain — 3Lichtenberg Group for History and Philosophy of Physics, Institut für Philosophie, Universität Bonn, Germany
Rotationally symmetric bodies with parabolic cross sections are frequently used to model astrophysical objects such as magnetospheres immersed in interplanetary or interstellar plasma flows. We discuss a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. Prescribing this flow, we derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics, obtaining explicit expressions for an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. Our solution procedure employs Euler potentials and Cauchy's integral formalism based on the flow's stream function and isochrones. Furthermore, a novel renormalization procedure allows us to generate more general analytic expressions modeling the deformations experienced by arbitrary scalar or vector-valued fields embedded in the flow as they are advected towards and then past the parabolic obstacle. Finally, both the velocity field and the magnetic field embedded therein are generalized from incompressible to mildly compressible flow.