Leif Svalgaard & Xudong Sun
Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305

Solar “activity” is usually defined by proxies constructed to somehow measure that component of the output of our variable Sun that is important for geo-space and conditions in the heliosphere. The longest-running direct proxies are, of course, the venerable Sunspot Number and the Number of Groups going back more than 400 years, and recently undergone a facelift, correcting inconsistencies and errors¹. Indirect proxies, going back more than 10,000 years, can be constructed from depositions of radionuclides such as ¹⁰Be (in ice cores) and ¹⁴C (in tree rings).

In 1947 the Canadian Arthur Covington discovered, using army surplus material, microwave emission from the Sun at 2800 Mhz or 10.7 cm wavelength (e.g. ref. 2). The emission can be measured every day regardless of weather and the F10.7 record of the flux extends unbroken (except on Sundays in the early years) from 1947 to the present. Observations in Japan agree closely with the Canadian values³ and it is generally accepted that the microwave flux is an excellent and objective measure of solar activity.

As we believe that solar activity has its origin in the Sun’s magnetic field, it is of interest to see how observations of the magnetic field agree with the suitably scaled F10.7 flux. This actually works both ways as the magnetic field is difficult to measure and the observing instruments are difficult to calibrate. Several series of magnetic data exist from different observatories and they do not agree very well⁴, as observers at times make perceived “improvements” of their instruments and also because the measured “flux” or “field” seems to depend on the spatial resolution of the instrument and on dubious “saturation” effects and zero-level issues.

Figure 1 | Upper green curve: MDI* LOS flux scaled to match the HMI LOS flux based on their overlap. Upper pink curve: HMI. Lower red curve: observed F10.7 flux reduced to 1 A.U. Blue curve: F10.7* computed from the magnetic flux of the composite record. All curves have 1-month resolution.

The two space-borne magnetographs, MDI on SoHO at L1 at more than 1 million km distance, and HMI on SDO in geosynchronous orbit much nearer the Earth⁵ measure the magnetic flux using the Zeeman effect in the spectral lines Fe Ⅰ 617.3 nm and Ni Ⅰ 675.8 nm, respectively. We use the latest versions of magnetic measurements from the two instruments (available at http://jsoc.stanford.edu/) to form a composite data set from 1996 to the present. The analysis proceeds as follows:

Step 1: Compute daily values of the unsigned magnetic flux from the 5-minute MDI Line-of-Sight (LOS) data averaged over the solar disk out to 0.99 of the radius and compute similar daily values from the 720-second HMI LOS data. The data values are expressed in units of 10²² Mx. If a pseudo field strength in Gauss is wanted, divide by the applicable area of the solar disk, 1.5×10²² cm².

Step 2: Compute monthly averages from the daily values. If there are fewer than 10 days with data in any month, the monthly value is interpolated and filled in from neighboring months.

Step 3: The MDI and HMI data overlap during 2010, May through 2011, April and we scale MDI to HMI (MDI* = 0.7429 MDI – 2.847) and form the composite data set as the average of HMI and the scaled MDI. The HMI and scaled MDI values are shown as the upper curves in Fig. 1.

Step 4: Get monthly averages of the F10.7 flux (at http://www.spaceweather.gc.ca/) reduced to 1 A.U. (without the URSI correction factor).

Step 5: There is a good, almost linear relationship between the monthly values of F10.7 and of our composite magnetic flux, M. For comparison purposes, we remove the slight non-linearity by fitting the relationship to a 4th degree polynomial, calculating the F10.7 flux as F10.7* = 0.0071136 M⁴ – 0.488305 M³ + 12.315337 M² – 125.4736 M + 510.854 sou (R² = 0.97) corresponding to a given magnetic flux. Part of M is due to noise as we do not apply any threshold on magnetic field. Our analysis is not affected, however, if the background is stable.

We plot the computed F10.7* flux derived for the magnetic flux and the observed F10.7 flux in Fig. 1. There is a remarkable agreement between the observed and calculated microwave fluxes, lending credence to the accuracy and physical significance of both. Repeating the analysis using the radial magnetic flux yields the same amazing agreement; in fact, even slightly better. Using the magnetic data from Wilcox Solar Observatory (WSO) yields a similar result, attesting to the stability of the measurements at Stanford. We have also used the result to detect changes in the calibration of the SOLIS series. We suggest that the F10.7 record can serve as an almost absolute reference scale for the solar magnetic field.

Figure 2 | Total unsigned magnetic LOS flux from HMI (blue curve) vs. F10.7 flux (pink curve). The green curve ​shows the HMI flux linearly scaled to the F10.7 flux.

The agreement between F10.7 and the unsigned magnetic flux extends even to daily values (Figure 2), albeit with an expected higher noise level. The scaling of HMI to F10.7 was done with a minimal linear relation HMI* = 8 HMI – 8 (R² = 0.79). This suggests that the microwave flux is controlled directly by the magnetic field without a complicated intermediate physical process.

References

[1] Clette, F., Svalgaard, L., Vaquero, J. M. & Cliver, E. W., 2014, SSRv, 186, 35
[2] Tapping, K. F. & Charrois, D. P., 1994, SoPh, 150, 305
[3] Svalgaard, L. & Hudson, H. S., 2010, ASP Conf. Ser., 428, 325
[4] Riley, P., Ben-Nun, M., Linker, J. A., et al., 2014, SoPh, 289, 769
[5] Liu, Y., Hoeksema, J. T., Scherrer, P. H., et al., 2012, SoPh, 279, 295