Liu, Yang¹; Griñón-Marín, Ana B.^1,2,3 Hoeksema, J. T.¹, Norton, Aimee A.¹, Sun, Xudong⁴

1 W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085, USA
2 Institute of Theoretical Astrophysics, University of Oslo, NO-0315 Oslo, Norway
3 Rosseland Centre for Solar Physics, University of Oslo, NO-0315 Oslo, Norway
4 Institute for Astronomy, University of Hawaii at Mānoa, 96768, Pukalani, HI, USA

The East-West component of the magnetic field (B_φ or B_p), as observed in solar magnetograms containing weak field regions, is found to change its sign when the regions cross the central meridian^[1]. This can be seen in both SDO/HMI and SOLIS/VSM full disk vector magnetograms; and furthermore, the signs of the horinzotal field in the HMI and VSM data are opposite in weak field regions (see Figure 1). A mismatch between the calibrated line-of-sight and transverse fields is the reason for this hemispheric bias problem. Here mismatch means one of the fields is either overestimated or underestimated. For HMI data, the transverse field is overestimated. This mismatch is caused ultimately by a filling factor that is not precisely determined when unresolved structures are present^[2]. In a nominal magnetogram, about 24% pixels with decent magnetic signals may have a wrong sign in Bp.

Figure 1| Example of disagreement in the orientation of B_θ and B_φ magnetic field vector components of an active region in the southern hemisphere, which passed the central meridian on 19 November 2015. Upper panels show radial (B_r), meridional (B_θ) and zonal (B_φ) field from SDO/HMI and lower panels from SOLIS/VSM. Meridional (middle) and zonal (right) components depict opposite orientation. Red/blue represents positive/negative polarities scaled between ±50 G (From Ref. [1]).

Recently, an updated inversion procedure for HMI observations has been developed^[3], and it is able to derive the filling factor with reasonable accuracy. The new data show that the hemispheric bias problem has been mitigated substantially. Figure 2 shows the percentage of pixels in a weak-field region that had B_p < 0 for the 5-day period. The percentage for the original data shows significant hemispheric bias that changes from 84.8% in the East hemisphere to 3.2% to the West (red dots). In contrast, it is 44.3% in the East hemisphere and 33.9% in the West for the new data (black dots). The updated VFISV mitigates the hemispheric bias significantly.

Figure 2| The percentage of pixels with B_p<0 in a weak-field region for a period of 5 days when the region rotates from the East to the West hemispheres. Black (red) dots refer to the data from the updated (original) VFISV. The error bars refer to a confidence interval at a 99% confidence level. Only the pixels with field strengths greater than 300 Mx cm^-2, 3 sigma of the data are included.

Vector magnetic fields on the spheric coordinates, B_r, B_t, and B_p, are contributed from the observed line-of-sight and transverse fields. Thus, B_r is impacted by this mismatch, as well. Shown in Figure 3 is the average of δB_r, |B_r^old| – |B_r^new|, the difference of B_r between the new and original data, over 15 days. The average is done for the data from November 15 to 30, 2015 with a cadence of 3 hours. If B_r^new is ground truth, B_r^old is generally overestimated, and this overestimation increases toward the limb. δB_r is slightly higher in the east hemisphere than in the western hemisphere, indicating that B_r^old may also have a hemispheric bias.

Figure 3| Average of δB_r over 15 days. Only the pixels with B > 300.0 Mx cm^-2 are included for averaging.

Processing HMI data with the new VFISV is computationally expensive. For a nominal full disk data, it takes about 5 times as much time as using the original module for inverting all the pixels. It can be reduced substantially when only selected pixels are processed with the new code. The processing time reduces to about 1.6 times of the original code when only the pixels with polarization greater than 0.25% is processed, which includes most pixels in magnetic features on the disk.

References:

[1] Pevtsov, A. A., Liu, Y., Virtanen, I., et al. 2021, JSWSC, 11, 14
[2] Liu, Y., Griñón-Marín, A.B., Hoeksema, J.T., et al. 2022, Solar Phys, 297, 17
[3] Griñón-Marín, A.B., Pastor Yabar, A, Liu, Y., et al. 2021, ApJ, 923, 84