1. What is the Time Series of Sunspot Numbers Telling Us About Magnetic Flux Transport C.T. Russell1, L.K .Jian2, and J.G. Luhmann3 1. EPSS/UCLA, 2. GSFC, 3. SSL/UCB Session – Energetic Particles, Long-Term Solar Variability Noon, Thursday, July 12, 2018 Fourteenth Solar-Terrestrial Physics Symposium York University, Toronto, Canada

2. The Sun
The interior of the Sun contains a core where fusion produces 4He from 1H and releases energy.
This energy radiates upwards until it is more efficient to transport heat by convection.
The core and the radiation zone change slowly, but the convection zone can evolve much more rapidly.
The Sun also rotates, and as we have learned from Mercury, the Earth, Jupiter, Saturn, Uranus, and Neptune, the combination of convection and rotation can lead to the generation of a global magnetic field that extends into space and in the Sun’s case fills the heliosphere with a magnetic field that reverses about every 11 years.
From: Space Physics: An Introduction (Russell, Luhmann, and Strangeway). Available from Cambridge University Press.

3. Why is the Sun’s Magnetic Field Important to Us?
Also in Space Physics: An Introduction
With the onset of the Industrial Revolution, the Communication Revolution and the Computation Revolution, the civilization has become sensitive to space weather.

4. The Magnetic Sun and the Visible Sun
Yes, also from Space Physics: An Introduction
The convection transports magnetic flux to the surface of the Sun and the solar wind transports this flux to the Earth and throughout the heliosphere.
The photosphere often looks quiescent to us but high resolution images show the turbulent convection cells.
We have done a good job of monitoring the Sun from Earth, but not from the key vantage points from space such as:
The L5 Lagrangian point that complements the chronograph view from Earth.
Over the poles so that we can study the magnetic flux convection cycle.

5. The 22-year Magnetic Cycle of the Photosphere
Discussed in greater length in Space Physics: An Introduction
The magnetic flux brought to the surface moves to the poles in such a manner that the transported flux opposes the existing field polarity at the pole so that the old flux disappears and a new polarity is established.
Only one mission (Ulysses) has risen far enough above the ecliptic plane to sample the solar wind and magnetic field from the polar region, but it carried only a magnetometer and not a magnetograph. We need to be monitoring the Sun’s polar regions with magnetographs over both poles and the equator.

6. Understanding the Sun from What We Have!
Mankind became interested in blemishes in the purity of the solar surface well over 400 years ago.
Very good records exist of these sunspots for over 250 years.
The variation of sunspot area and number is quite puzzling. Both are quite periodic, but the periods vary.
Many observers have tried to use the time series to understand better the Sun’s interior and the solar dynamo.
In particular, does the Sun provide any clues as to what it is going to do? Can you use sunspot history to predict future space weather, statistically or definitively?
Let’s examine this question.

7. The Observed Sunspot Cycle Versus the “11”-year Period Clock
Dotted line: year period clock with an amplitude of 180
SILSO
We have 24 cycles of good sunspot observations and 5 cycles of solar wind data. What can we learn about the solar dynamo from these data? What predictive information is contained in the Sunspot Number time series?
We divide the time series into three segments with similar behavior.
A strong cycle develops a phase lead that is reduced in the following weaker cycles.
The next few cycles are weak and nestle inside the expected clocking cycles.
The phase lead can develop quickly followed by a low activity period in which the phase aligns with the ‘clock’.

8. The Anticorrelation of the Maximum SSN with Solar Cycle Duration
If we assume that the Sun produces the same amount of magnetic flux each solar cycle but the transport to the surface is slower in some cycles, then the maximum build-up of magnetic flux in the photosphere might be less during long solar cycles.
Sunspots only occur when the surface magnetic field is strong, so this low transport rate would control the SSN.
Since there is a general decrease in the maximum SSN with cycle duration, this observation is consistent with our expectation, but does not explain all of the SSN variation from cycle to cycle.

9. Correlation of Maximum SSN with Ratios of Declining Phase Duration to Rising Phase Duration (Td/Tr)
If transport of flux were variable and the magnetic flux available were fixed, then a more rapid transport of flux to the surface would produce a shorter rising phase and a larger maximum SSN.
If the rate of return of flux to the interior did not increase or if it lessened, Td/Tr would become larger.
The correlation of Td/Tr and the maximum SSN is good, consistent with a variable flux transport rate. However, there are clearly other factors governing activity.
The thick line here is the best-fit correlation. The two thin lines are parallel but offset to represent subsets of higher and lower activity that appear to have a similar trend line to that of the full set.

10. Predictive Power of Td/Tr
If we examine Td/Tr, we find that cycles 4 [square] and 11 (circle) had high ratios. They presumably brought much flux to the photosphere in a short period, producing high SSN.
The following cycles 5 and 12 had a delayed start and low activity.
The next cycles 6 as well as 13 and 14 also had low activity.
The low maximum sunspot number of cycle 24 was not predicted by this ratio.
The three trend lines suggest that the Sun has three different operational states: low, medium and high field strengths.

11. The Independence of Two Hemispheres
Here the rising phase was short for the north and long for the south pole. The highest line shows the maximum of the two.
One hemisphere can be dominant and/or have quite different rise and fall times than the other hemisphere. Thus we should be careful to average north and south behavior and not favor one over the other. The midpoint is probably the best choice.
The independence of the north and south photospheres can be understood from this overly simplified diagram of a rapidly rotating fluid with a large non-convecting core.

12. How Do We Treat the Two Almost Independent Cycles?19 18 22 17 21 23 20 13 12 24 14 15 16
This shows the smoothed sunspot area for north and south separately.
Take the absolute maximum? Average? Midpoint?
Clearly the sun does not communicate well between the two poles, but also clearly the two hemispheres are correlated.
However, we wish to use all solar cycles, and have taken the midpoint between double maxima in our study.

13. The Sunspot Numbers Used in the Study

14. Let Us Repeat Our Correlations for MidPoint
We still see a weak inverse correlation between the duration of rising phase and the maximum SSN.
However, if you plot the rate of sunspots per year, you get a nearly perfect correlation. There is a base level of 55 sunspots each solar cycle and then a cycle-dependent rising rate for about a fixed duration.

15. Variation of the Solar Wind during the Sunspot Cycle
The SSN is a measure of the number of regions of strong magnetic field in the photosphere.
The strength of the IMF varies during a solar cycle and is weaker during weak solar cycles.
The solar wind density does not seem to have a variation controlled by the phase of the sunspot count, but it has changed significantly on occasion. This drop in density has persisted into solar cycle 24, but has now recovered some.
The only correlation of the solar wind speed with the solar cycle is with the phase of the SSN variation. After the peak SSN, there is often a period of fast solar wind flow.

16. Summary
The transport of magnetic flux in the Sun is quite variable and is not necessarily north-south symmetric.
The best predictor of the maximum sunspot number is the rate of rise of a new cycle.
The duration of solar cycles is variable, causing the solar cycle phase to change relative to a fixed clock.
The Sun often returns to the phase of the constant clock with a drop in activity, allowing us to anticipate low activity.
The solar wind density occasionally undergoes significant decreases and maintained that decrease over more than one complete solar cycle.
Using the mid peak time as the end of the rising phase would have predicted a weak cycle 24. Cycle 24 is weak and we would expect cycle 25 to be weak also.

17. Recommendations
We understand too little about the magnetic flux transport between the dynamo and the solar surface.
We need to continue to study solar dynamo models.
We need to monitor the solar field over a wider range of longitudes.
The polar regions of the Sun should play an important role in the transport of the magnetic flux.
We need to understand this transport better.
We need to observe the Sun’s magnetic field from high inclination orbiters and do so for several solar cycles.