A Mathematical Model for an Hourglass Magnetic Field

Abstract

Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's functions. We use this to derive an analytic form for an hourglass magnetic field pattern created by electrical currents that are concentrated near (but not confined within) the equatorial plane of a cylindrical coordinate system. Our solution is not characterized by a cusp at the equatorial plane, as in previous solutions based on a current sheet. The pattern we derive provides a very good fit to hourglass magnetic field patterns emerging from three-dimensional numerical simulations of core formation, and can in principle be used for source-fitting of observed magnetic hourglass patterns.

6 pages, 4 figures, to appear in ApJ (20 April 2013)

References in corpus (7)

• Magnetic Fields in the Formation of Sun-Like Stars
• Magnetic Fields and Rotations of Protostars
• Exploring Magnetic Field Structure in Star-Forming Cores with Polarization of Thermal Dust Emission
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• SOFIA observations of 30 Doradus: II -- Magnetic fields and large scale gas kinematics
• Distortion of Magnetic Fields in Barnard 335
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• Distortion of Magnetic Fields in BHR 71
• Fitting an Analytic Magnetic Field to a Prestellar Core
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• Distortion of Magnetic Fields in the Dense Core SL42 (CrA-E) in the Corona Australis Molecular Cloud Complex
• Star-forming environments in smoothed particle magnetohydrodynamics simulations I: Clump extraction and properties
• Hourglass Magnetic Field of a Protostellar System
• Hourglass Magnetic Field from a Survey of Current Density Profiles