# 106. The vector magnetic field of the Sun-as-a-star during activity cycle 24

Contributed by Aline Vidotto. Posted on July 29, 2018

Aline Vidotto1, Lisa Lehmann2, Moira Jardine2, & Alexei Pevtsov3
1. Trinity College Dublin, Ireland;
2. University of St Andrews, Scotland;
3. National Solar Observatory, USA

The direct comparison between stellar and solar magnetic maps are hampered by their dramatic differences in resolution. This striking difference is easily seen when we decompose solar/stellar surface fields in spherical harmonics of different degree $\ell$ ($\ell=1$ represents a dipole, $\ell=2$ a quadrupole, $\ell=3$ an octupole, etc). In high-resolution solar synoptic maps, $\ell_\mathrm{max}=192$[1], while in stellar synoptic maps, $\ell_\mathrm{max}= 5 - 10$[2]. This demonstrates that stellar magnetic field maps reconstructed with the Zeeman Doppler Imaging (ZDI) technique can only capture the large-scale structure of stellar magnetic fields[2].

Figure 1| Full-resolution (left) and filtered/large-scale (right) HMI synoptic vector magnetic field map of the Sun. From top to bottom: radial, meridional (north-south; positive from north to south) and azimuthal (east-west; positive from east to west) magnetic field components. The right panels show typical resolution to stellar magnetic field maps reconstructed with the Zeeman Doppler Imaging technique (e.g., Ref [2]).

To transform high-resolution solar vector synoptic maps into maps with similar resolution as those derived in stellar studies, we filter out the spherical harmonics with high degrees in solar maps[3,4,5]. This way, the comparison between large-scale solar and stellar magnetic field vector maps can be directly made. The left panels of Figure 1 show the HMI vector synoptic map of the Sun for Carrington Rotation (CR) 2150 (near maximum of activity) in its full resolution (3600×1440 pixels2). The right panels show the same vector synoptic map reconstructed with $\ell_\mathrm{max}= 5$ (i.e., magnetic fields with degrees of 6 or larger have been filtered out).

Figure 2| Large-scale magnetic field reconstructed from high-resolution solar vector synoptic maps, obtained by restricting the spherical harmonics reconstruction up to a degree $\ell_\mathrm{max}= 5$, which is typical in stellar studies. From top to bottom: radial, meridional and azimuthal components. The first and third column of maps show the field configuration of the Sun when it is nearly in sunspot minima (CR2097 and CR2202, respectively) and the middle column corresponds to when the Sun is near sunspot maximum (CR2150).

We do the same for all available HMI maps from January 2010 to April 2018. Figure 2 shows the large-scale magnetic field vector of the Sun for three different CRs: CR2097, CR2150 and CR2202. These CRs were chosen as to represent minimum, maximum and minimum in sunspot number, respectively. Figure 2 shows that the polarities of the radial and meridional fields are different in the two consecutive minima, indicating a field reversal between CR2097 and CR2202. There is no reversal yet in the azimuthal component. A closer analysis shows that the azimuthal component is mainly from the toroidal part of the field, which does not reverse polarity throughout the 11-yr activity (sunspot) cycle. Because of this, the azimuthal field remains with roughly two polarity bands through the activity cycle: a positive (negative) azimuthal band in the southern (northern) hemisphere.

Figure 3| Time-latitude diagrams of the observed (left) and large-scale (right) magnetic field of the Sun for $\ell_\mathrm{max}= 5$. The y-axis is shown as sine(latitude) and latitude in the left and right panels, respectively. The wiggles seen in high latitudes are likely due to the inclination of the solar rotation axis with respect to the ecliptic. Note the field reverses polarity in Br and Bθ components (top two rows), but not yet in Bϕ (bottom row), which is expected to reverse sign at the beginning of next sunspot cycle.

Using the HMI maps, we average each component of the magnetic field over longitudinal bands and stack them to obtain a temporal evolution. The left panels in Figure 3 show time-latitude diagrams for the full resolution HMI maps and the right panels show only the large-scale ($\ell_\mathrm{max}= 5$) magnetic field of the Sun. We clearly see that the radial and meridional components reverse polarities in the observed, full-resolution, field (left) and in the large-scale components (right), but the azimuthal component remains mainly negative (positive) in the northern (southern) hemisphere. It is interesting to note also from the bottom left panel that, within the same hemisphere, the polarity of the azimuthal component is opposite in the active regions (which can be seen at low latitudes) and at higher latitudes.

By comparing the large-scale field of the Sun over cycle 24 with the stellar ZDI data, we also showed in Ref. [4] that the large-scale solar magnetic properties fit smoothly with observational trends of stellar magnetism reconstructed with ZDI.

The results of this study including most figures presented here have been published in Vidotto et al., 2018, MNRAS.

### References

[1] DeRosa, M., et al, 2012, ApJ, 757, 96
[2] Donati, J.-F., & Landstreet, J. D., 2009, ARA&A, 47, 333
[3] Vidotto, A. 2016, MNRAS, 459, 1533
[4] Vidotto, A., et al. 2018, MNRAS, in press arXiv:1807.06334, https://doi.org/10.1093/mnras/sty1926
[5] Lehmann, L. T., et al. 2018, MNRAS, 478, 4390