OBTAINING POTENTIAL FIELD SOLUTIONS WITH SPHERICAL HARMONICS AND FINITE DIFFERENCES

Journal Article · Tue May 10 04:00:00 EDT 2011 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/732/2/102· OSTI ID:21576846

Toth, Gabor; Van der Holst, Bart; Zhenguang, Huang ^[1]

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1. Center for Space Environment Modeling, University of Michigan, Ann Arbor, MI 48109 (United States)

Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current- and divergence-free magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: (1) remeshing the magnetogram onto a grid with uniform resolution in latitude and limiting the highest order of the spherical harmonics to the anti-alias limit; (2) using an iterative finite difference algorithm to solve for the potential field. The naive and the improved numerical solutions are compared for actual magnetograms and the differences are found to be rather dramatic. We made our new Finite Difference Iterative Potential-field Solver (FDIPS) a publicly available code so that other researchers can also use it as an alternative to the spherical harmonics approach.

• OSTI ID: 21576846
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 732; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ALGORITHMS
CALCULATION METHODS
FUNCTIONS
ITERATIVE METHODS
MAGNETIC FIELDS
MAGNETISM
MAIN SEQUENCE STARS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
SPHERICAL HARMONICS
STARS
SUN
SURFACES