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  Inferring magnetic helicity spectrum in spherical domains: Method and example applications

Prabhu, A. P., Singh, N. K., Käpylä, M. J., & Lagg, A. (2021). Inferring magnetic helicity spectrum in spherical domains: Method and example applications. Astronomy and Astrophysics, 654: A3. doi:10.1051/0004-6361/202141101.

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Prabhu, A. P.1, Author
Singh, N. K., Author
Käpylä, Maarit J.1, 2, Author              
Lagg, A.2, Author              
1Max Planck Research Group in Solar and Stellar Magnetic Activity, Max Planck Institute for Solar System Research, Max Planck Society, ou_2265638              
2Department Sun and Heliosphere, Max Planck Institute for Solar System Research, Max Planck Society, ou_1832289              


Free keywords: Sun: magnetic fields / magnetohydrodynamics (MHD) / dynamo / turbulence
 Abstract: Context. Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. Aims. The magnetic helicity spectrum provides important information about the α effect. Here we demonstrate a formalism in spherical geometry to infer magnetic helicity spectra directly from observations of the magnetic field, taking into account the sign change of magnetic helicity across the Sun’s equator. Methods. Using an angular correlation function of the magnetic field, we develop a method to infer spectra for magnetic energy and helicity. The retrieval of the latter relies on a fundamental definition of helicity in terms of linkage of magnetic flux. We apply the two-scale approach, previously used in Cartesian geometry, to spherical geometry for systems where a sign reversal of helicity is expected across the equator on both small and large scales. Results. We test the method by applying it to an analytical model of a fully helical field, and to magneto-hydrodynamic simulations of a turbulent dynamo. The helicity spectra computed from the vector potential available in the models are in excellent agreement with the spectra computed solely from the magnetic field using our method. In a next test, we use our method to obtain the helicity spectrum from a synoptic magnetic field map corresponding to a Carrington rotation. We observe clear signs of a bihelical spectrum of magnetic helicity, which is in complete accordance to the previously reported spectra in literature from the same map. Conclusions. Our formalism makes it possible to infer magnetic helicity in spherical geometry, without the necessity of computing the magnetic vector potential. It has many applications in solar and stellar observations, but can also be used to analyse global magnetoconvection models of stars and to compare them with observations.


Language(s): eng - English
 Dates: 2021
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1051/0004-6361/202141101
 Degree: -



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Title: Astronomy and Astrophysics
  Other : Astron. Astrophys.
Source Genre: Journal
Publ. Info: Les Ulis Cedex A France : EDP Sciences
Pages: - Volume / Issue: 654 Sequence Number: A3 Start / End Page: - Identifier: ISSN: 1432-0746
ISSN: 0004-6361
CoNE: https://pure.mpg.de/cone/journals/resource/954922828219_1