The magnetic field vector of the Sun-as-a-star

• Published in: Monthly notices of the Royal Astronomical Society Vol. 459; no. 2; pp. 1533 - 1542
• Main Author: Vidotto, A. A.
• Format: Journal Article
• Language: English
• Published: London Oxford University Press 21.06.2016
• Subjects: Comparative analysis; Decomposition; Fields (mathematics); Magnetic fields; Mathematical analysis; Simulation; Solar magnetic field; Spherical harmonics; Star & galaxy formation; Vectors (mathematics); methods: analytical; stars: magnetic fields; Sun: magnetic fields; Sun: surface magnetism
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stw758

Direct comparison between stellar and solar magnetic maps is hampered by their dramatic differences in resolution. Here, we present a method to filter out the small-scale component of vector fields, in such a way that comparison between solar and stellar (large-scale) magnetic field vector maps can be directly made. Our approach extends the technique widely used to decompose the radial component of the solar magnetic field to the azimuthal and meridional components as well. For that, we self-consistently decompose the three-components of the vector field using spherical harmonics of different l degrees. By retaining the low l degrees in the decomposition, we are able to calculate the large-scale magnetic field vector. Using a synoptic map of the solar vector field at Carrington Rotation CR2109, we derive the solar magnetic field vector at a similar resolution level as that from stellar magnetic images. We demonstrate that the large-scale field of the Sun is not purely radial, as often assumed – at CR2109, 83 per cent of the magnetic energy is in the radial component, while 10 per cent is in the azimuthal and 7 per cent is in the meridional components. By separating the vector field into poloidal and toroidal components, we show that the solar magnetic energy at CR2109 is mainly (>90 per cent) poloidal. Our description is entirely consistent with the description adopted in several stellar studies. Our formalism can also be used to confront synoptic maps synthesized in numerical simulations of dynamo and magnetic flux transport studies to those derived from stellar observations.