Adam James Finley
University of Exeter – AWESoMeStars ERC Project

Assets used for this project:

• Python
• SHTOOLS, for the spherical harmonic tools: link
  • the subsequent python dependencies
• PLUTO MHD code, to generate the PFSS models: link
• VisIt, for 3D visualisations: link
• Matplotlib, for 2D visualisations: link
• Data from both the Michelson Doppler Imager and the Helioseismic and Magnetic Imager, onboard the SOlar and Heliospheric Observatory and the Solar Dynamics Observatory, respectively.

Introduction
As shown previously, the Solar magnetic field can be decomposed into its spherical harmonic components (see work in Ref. 1). The lowest order components (l=1, 2, 3) represent the large-scale magnetic field, which has been shown to be the most significant in producing an efficient braking torque, for a given mass loss, in a stellar wind^{2, 3}. The Sun’s magnetic field has been recorded for many decades, with surface magnetograms available from both ground based (Wilcox Solar Observatory, Global Oscillation Network Group) and spacecraft (SOlar and Heliospheric Observatory, Solar Dynamics Observatory) observatories.

The Solar magnetic field has now been continuously observed by space-borne instruments (SOHO/MDI and SDO/HMI) for 22 years, the length of the magnetic solar cycle. We choose to use these data to observe how the lowest order component fluctuate over decadal timescales.

Method
To visually explore the data, the spherical harmonics are evaluated using SHTOOLS and stored in tabulated data files, for each available synoptic magnetogram (spanning 1996.6-2017.9). For each l=1, 2, 3 component, including all m’s, a Potential Field Source Surface model (Source Surface Radius of 2.5 Solar Radii) is computed. This is done for every magnetogram using the PLUTO code (just for ease) and then is visualized in VisIt. The outputs are recorded and formatted into a video file.

Results

The evolution of the dipole, quadrupole and octupole components of the global magnetic field during the last 22 years. Top Left: Synoptic magnetograms from both MDI and HMI in a time series from 1996.6-2017.9, the color represents the radial magnetic field with the color scale covering -50G to 50G. Top Right: The decomposed components from the spherical harmonic analysis, from top to bottom, dipole, quadrupole and octupole, with increasing m from left to right (the leftmost panels represent the axisymmetric components). Bottom Row: PFSS reconstructions of the dipole, quadrupole, and octupole components alone, each including all values of m for their given l. The source surface is set to 2.5 solar radii and the surface colorscales cover -5G to 5G.

Conclusion
Here we present a visualization spanning over 200 magnetograms from SOHO/MDI and SDO/HMI, which transforms each into three PFSS models for the dipole, quadrupole and octupole components of the Solar magnetic field. This video, in essence, highlights the results of Section 3 in Ref. 1, and although this does not show anything new, it is an interesting way to view the wealth of solar data available.

Points of Interest:

• The dipole’s tilt and strength during the cycle.
• The coherence of the axisymmetric dipole and octupole.
• The relative strength of each mode during the cycle.

The ability to accurately characterize the strength of the lowest order components for stars other than the Sun is a challenging topic, for which techniques such as Zeeman Doppler Imaging play a crucial role. It remains unknown how magnetic variability impacts our understanding of the rotational-evolution of sun-like stars. Future work will therefore use this analysis to evaluate the variability of the spin-down torque on the Sun (using results from MHD modelling).

References

[1] DeRosa, M.L., Brun, A.S., & Hoeksema, J.T. 2012, ApJ, 757, 96
[2] Finley, A.J., & Matt, S.P. 2017, ApJ, 845, 46
[3] Finley, A.J., & Matt, S.P. 2017, submitted