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Equation of the field lines of an axisymmetric multipole with a source surface

Gregory, S. G. (2011) Equation of the field lines of an axisymmetric multipole with a source surface. American Journal of Physics, 79 (5). pp. 461-469. ISSN 0002-9505.

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Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ℓ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential.

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Additional Information:© 2011 American Association of Physics Teachers. Received 6 April 2010; accepted 21 December 2010. This work was supported by the Science and Technology Facilities Council Grant No. ST/G006261/1. The author thanks the two referees for constructive comments, and Professor C.G. Gray (University of Guelph) for insightful comments and a detailed reading of the manuscript.
Funding AgencyGrant Number
Science and Technology Facilities Council (STFC)ST/G006261/1
Subject Keywords:Laplace equations, magnetic stars, physics education, polarimeters, stellar atmospheres, stellar magnetism
Issue or Number:5
Classification Code:PACS: 41.00.00
Record Number:CaltechAUTHORS:20110506-153202559
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23594
Deposited By: Tony Diaz
Deposited On:06 May 2011 23:03
Last Modified:03 Oct 2019 02:48

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