Coronal magnetic field evolution over cycle 24

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: chifu@mps.mpg.de
² Institute of Astrophysics and Geophysics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Received: 22 March 2020
Accepted: 27 December 2021

Abstract

Context. The photospheric magnetic field vector is continuously derived from measurements, while reconstruction of the three-dimensional (3D) coronal magnetic field requires modelling with photospheric measurements as a boundary condition. For decades, the cycle variation of the magnetic field in the photosphere has been investigated. Until now, there has been no study of the evolution of the coronal magnetic flux in the corona or of the evolution of solar cycle magnetic free energy.

Aims. The aim of this paper is to analyze the temporal variation of the magnetic field and free magnetic energy in the solar corona for solar cycle 24 and the behavior of the magnetic field in the two hemispheres. We want to investigate whether or not we can obtain better estimates of the magnetic field at Earth using the nonlinear force-free field extrapolation method.

Methods. To model the magnetic field over cycle 24 we apply the nonlinear force-free field (NLFFF) optimization method to the entire set of the synoptic vector magnetic maps derived from observations made using the Heliospheric and Magnetic Imager (HMI) on board Solar Dynamic Observatory (SDO).

Results. From our results, we find that during solar cycle 24, the maximum of the Sun’s dynamics is different than the sunspot number (SSN) maximum peak. The major contribution to the total unsigned flux is provided by the flux coming from the magnetic field structures other than sunspots (MSOS) within latitudes of −30° and +30°. The magnetic flux variation during solar cycle 24 shows a different evolution in the corona than in the photosphere. We find a correlation value of 0.8 between the derived magnetic energy from our model and the flare energy index derived from observations. On average, cycle 24 had a higher number of sunspots in the northern hemisphere (NH) but stronger flux in the southern hemisphere (SH) which could more effectively reach the higher layers of the atmosphere. The coupling between the hemispheres increases with height. The strongest asymmetries in the unsigned magnetic flux are between the two SSN peaks.