Sunspots and the Solar Cycle
vcool
Student Number: 1337h4xX0r
November 30, 2009
Abstract
The study of sunspots is essential in our understanding of the Sun, and consequently of stars in general. These regions of low temperatures on the surface of our
Sun have fascinated astronomers since the dawn of mankind. Widely studied, it was
not until the early 20th century that strong magnetic fields were detected within
the Solar “blemishes”. Further studies with the first ever magnetograph concluded
that the Sun possesses a very strong global magnetic field. This discovery initiated a
paradigm shift, completely changing the way we look at stars today. We now know
that our Sun is not in perfect thermodynamic equilibrium, but is in fact a system
in constant activity evidenced by aforementioned sunspots, flares, prominences, and
coronal mass ejections. The old model of a hot ball of gas held in balance by a
delicate equilibrium of gravitation and pressure could no longer account for these
dramatic phenomena, forcing physicists to build a new stellar model, the so-called
magnetic dynamo model. In addition to helping us understand stars, the study of
sunspots may shed light on the effect of solar activity on humanity in general.
1
Introduction
The Sun has forever played a prominent role in almost every ancient culture in human
history. The fear that the Sun may not rise the next day demanded countless rituals and
festivities, some still followed today. Be it Aztecs with their Sun-god Huitzilopochtli, or
the Egyptians with Ra, or the Japanese with Amaterasu, it is evident that the Sun was
considered a god across the entire world. [5]
Being the center of so many cultures, it is only natural that the Sun has been meticulously observed for changes. Not surprisingly, there are numerous accounts that describe
structures similar to sunspots appearing on the solar disk. In 4th century BC, a Chinese
astronomer claimed to have seen a solar eclipse that started in the middle of the Sun. [4]
This could have not been a solar eclipse as it does not start from within the disk, but
rather from the edge. Hence there is a high probability the astronomer observed a large
sunspot. A legend from the Zambezi area in Africa provides another example of sunspot
observation. The legend states that the Moon consumed with jealousy would throw
patches of mud at the Sun. The Sun, however, being very cautious would never allow
the patches to hit it. Once every 10 years, however, the Sun would lose guard and get hit
by the thrown mud. [4] Apart from providing an example of sunspot observation, this
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legend is very interesting because it is known that the Sun possesses an 11 year sunspot
cycle, a number very close to that in the legend. Probably the first recorded sunspot
observation, however, was performed by the Babylonians, who wrote it down on tablets.
This would not be as interesting if the Babylonians haven’t also recorded weather. They
believed that weather followed a 12 year old cycle, a number dangerously close to the
actual period of sunspot appearance. [4]
In the 17th century, a more recent time frame, the sunspots were observed by 4
astronomers, Cristopher Scheiner from Germany, Galileo Galilei from Italy, Johann
Goldsmid fom Holland (also known as Fabricius) and Thomas Harriot from England. [1]
Who first discovered the sunspots remains a matter of debate among historians. It is
known, however, that Scheiner first thought it was a mechanical failure of his telescope.
He was soon convinced, however, that the spots were in fact situated on the Sun. Unfortunately, his superiors did not allow him to publish his observations. Scheiner thus sent
a series of anonymous letters Mark Wesler, a friend of Galileo Galilei. Wesler showed
the letters to Galileo, who quickly responded to Scheiner in three famous letters where
he stated that he was the first one to discover the sunpots and provided an account of
his own observations. It is not known whether Galileo actually observed them first, but
the letters succeeded in making Scheiner a mortal enemy of Galileo. Galileo only ended
up studying sunspots for two years, yet he was able to conclude that they could not be
planets (Scheiner’s initial hypothesis) due to the fact that they were changing size and
shape, and also that the Sun rotated around a fixed axis. Scheiner, in turn, spent almost
two decades observing the Sun at great detail. His work Rosa Ursina sive Sol largely
agreed with Galileo’s observations, and included very detailed diagrams of sunspots. [1]
Though the study of sunspots initally became popular, it took nearly 200 years for
another discovery connected to sunspots to surface. It is now known that there were very
few sunspots during the time period 1620 — 1725, commonly known as the Maunder
Minimum. [7] In 1843, Heinrich Schwabe, a German apothecary, announced a 10 year
periodicity in sunspots appearance. In his work Kosmos, Humboldt included Schwabe’s
tables and gave a more accurate estimate of an 11-year cycle. Another astronomer,
Rudolph Wolf, searched through all records and obtained a 11-year periodicity as well.
In order to have some standardized measurement system, Wolf introduced the so-called
Zurich sunspot number equation
RZ = K(10g + f )
(1.0.1)
as a measure of sunspot activity. Here g is the number of sunspot groups, f is
the number of individual sunspots, and K is the personal reduction coefficient ranging
from 0 – 1, which describes how reliable the observer and his instruments are. Being
the direction of the Zurich Observatory, Wolf established a first of a kind program to
establish the daily value of RZ . Even today, Zurich remains to be the world center of
sunspot data. [1]
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2
Sunspot Analysis
2.1
Detection of Magnetic Fields
So far, however, the observations were purely numeric. The physical processes that
give rise to sunspots were not understood. It was not until the 1920s that a quantitative measurement of sunspots was conducted. Using the spectroheliograph invented by
George Hale, it was found that the temperature of sunspots was approximately 4000 K,
as compared to 6000 K of the surrounding plasma. More importantly, however, Hale
realised that sunspots must possess a strong magnetic field through the so-called Zeeman
effect. [1]
The Zeeman effect is a property of atoms placed in a magnetic field. The atoms,
acting like compasses, shift the energy levels of its electrons. If the atom is aligned in
the direction of the magnetic field, the electron’s energy increases. If, on the other hand,
the atom is aligned against the magnetic field, the electron’s energy decreases. Since
energy is directly related to emmision spectra, a conglomerate of many such atoms would
produce 3 split lines instead of 1 at a given wavelength. The split is proportional to the
strength of the magnetic field. For example, the shift in wavelength ∆λ of the outer two
lines is given by
∆λ = λ2 ∆v/c = 47λ2 B meters
(2.1.1)
Knowing this enabled Hale to measure the strengths of the magnetic field which are
about 3000 Gauss. [6]
2.2
Qualitative Analysis
Continuing his research in the following decade, Hale with his colleagues discovered a
pattern associated with the magnetic fields of sunspots. He noticed that sunspots tend
to form in groups with two to three larger sunspots and several smaller ones. The largest
sunspot is usually found on the western side while the next largest on the eastern side of
the group. They are called the “leader” and the “follower” spots. When Hale investigate
the magnetic polarity within groups, he came to the following conclusions: [1]
1. The leader spots in each hemisphere are generally all of one polarity, while the
follower spots are of the opposite polarity.
2. If one is to regard the leader and follower spots as bipoles, the orientation of these
bipoles is opposite in opposite hemispheres.
3. The magnetic axes of these dipoles are usually inclinced towards the equator, with
the leader spot being the closest.
4. Towards the end of a cycle, some spot groups appear at high altitudes with reversed
polarity orientation, while those with the normal polarity for the old cycle occur
close to the equator.
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5. Following the minimum between the cycles, the bipole polarities have all reversed
sign.
This pattern have come to be known as Hale’s periodicity laws. Later on, Babcock
and Babcock constructed a magnetograph, which enabled them to measure the much
weaker dipolar magnetic fields closer to the poles. It was noticed that this weak dipole
field would reverse sign at sunspot maximum. [2] Armed with this knowledge, and the
“butterfly” diagram (shown in Figure 1), Hale concluded that the Sun follows a 22-year
old magnetic cycle, and the 11-year sunspots cycles actually overlap by 2 – 3 years. [1]
DAILY SUNSPOT AREA AVERAGED OVER INDIVIDUAL SOLAR ROTATIONS
SUNSPOT AREA IN EQUAL AREA LATITUDE STRIPS (% OF STRIP AREA)
90N
> 0.0%
> 0.1%
> 1.0%
30N
EQ
30S
90S
1870
0.5
1880
1890
1900
1910
1920
1930
1940
DATE
1950
1960
1970
1980
1990
2000
2010
AVERAGE DAILY SUNSPOT AREA (% OF VISIBLE HEMISPHERE)
0.4
0.3
0.2
0.1
0.0
1870
12
1880
13
1890
14
1900
15
1910
1920
16
17
1930
1940
DATE
http://solarscience.msfc.nasa.gov/images/bfly.ps
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19
1950
1960
20
1970
21
1980
22
1990
23
2000
2010
HATHAWAY/NASA/MSFC 2009/11
Figure 1: The Butterfly Diagram, exhibiting the 11-year cycle. (Taken from
http://solarscience.msfc.nasa.gov/SunspotCycle.shtml)
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2.3
Morphology and Appearance
A typical sunspot resembles a dark patch of two regions. The first, the darkest and
coldest, is the “umbra”. It typically takes 40% of the total sunspot area. Its temperature
is generally 2000 K less than the surrounding photosphere. The annular region contained
between the umbra and the surrounding sun surface is called the “penumbra”. It is hotter
than the umbra with a temperature difference of only 400 K, and takes up the rest of
60% of the total sunspot area. Penumbras exhibit a filamentary structure, and resemble
warping, as if the matter is stretched in the direction of the sunspot nucleus. Generally
the magnetic field is almost exactly normal to the sunspot, however the inclination
increases as the sunspot becomes larger reaching an average value of 70 ◦ at the edge of
the sunspot. [2]
There are also great variations in sizes. The average sunspot is 10000 – 30000 km
in diameter, or approximately 3 times the Earth’s diameter (∼12000 km). The largest
sunspot ever recorded had a mean diameter of 130000 km, which is almost 10% of
the solar diameter. There also seems to be some correlation between the latitude and
size. Indeed, the size of the penumbra increases with height, while that of the umbra
decreases. [2]
An important question is – why do the sunpots appear so much darker? The total
flux at the surface of the Sun is given by the equation
Fsurf = σTe4
(2.3.1)
A decrease in temperature by 2000 K results in a drop of total flux by a factor of
(6000/4000)4 ' 5. While the blackbody radiation of a 4000 K hot object is still very
bright, when using dark filters in order to resolve the hotter photosphere, the spots
become dark. [3] It is perhaps natural to conclude that if sunspots are colder regions
of the gaseous photosphere, then they should manifest as depressions or “dents” on the
surface of the sun. In fact, in 1769 Alexander Wilson noticed that the width of the
penumbra on the disc-center side of the spot decreases more rapidly than the width on
the limbward side. He concluded that sunspots are depressions on the surface of the Sun
and the dark spots are the inner parts of the Sun. It is now known, however, that his
conclusion was erroneous and what is now called Wilson depression is a phenomenon of
a different kind discussed in the next section.
2.4
The Physics behind Sunspots
Sunspots are areas of strong magnetic fields. In the previous section it was noted that
colder regions of gas should “collapse” and cause depressions. This, however, does not
happen. It is now known that these strong magnetic fields in fact support the gas from
collapsing, while explaining the low temperature of sunspots. [2]
The magnetic field lines of the sun are “frozen” into the surface. That is to say that
if a given abstract field line erupts from the Sun’s surface at some coordinate, it will
remain there are the Sun evolves. Magnetic fields also constrain the motion of matter
within the field. Since the primary heat transfer method in the photosphere is through
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convection, a strong magnetic field will not allow convection to take place. Without
convection, the temperature in the region quickly falls and our sunspot is created.
This does not, however, explain why sunspots approaching the limb appear to be depressions. This happens because of lower gas temperature and hence lower gas pressure,
the gas is more translucent than the surrounding photosphere. We are simply seeing
deeper in the sunspot area than the surrounding photosphere, and thus it appears as if
there is an actual depression on the Sun’s surface. [2]
The actual magnetic structure of sunspots is rather difficult to model. The two most
widespread ideas is the monolith and the cluters models. In both of the models a sunspot
is a complicated flux tube having several subparts. In the monolith model, however, in
the layer beneath the surface of the sun the flux tubes that compose the overall sunspot
fux tube are all coherent and aligned. The cluster model imagines the subsurface flux
tubes to be entangled and full of knots. Either model has it’s faults, and none can fully
describe the origin of sunspots. [2]
3
Magnetic Dynamo Theory
In the preceding sections it becomes evident that just about every major feature of
sunspots is connected to its magnetic field. In addition, the 22-year magnetic solar cycle
hints towards an importance of the global solar magnetic field. It is not clear how to
describe the Sun, but one model has the most success so far - the Magnetic Dynamo
model.
The model was proposed in 1961 by Horace Babcock. As mentioned earlier, the solar
magnetic field lines are “frozen” into the surface of the Sun. The differential motion of
the sun then drags along these field lines, with the regions close the equator moving
faster. As shown in Figure 2, this rotation converts a poloidal field of the sun, into a
toroidal field. Due to turbulence in the convective zone, the lines are twisted creating
high intesnity structures called magnetic ropes. Magnetic pressure pushes out the ropes
onto the surface of the sun, exposing them to outer space. These ropes then form the
sunspots. As the rotation continues, the toroidal field is converted back into a poloidal
field, and the solar polarity is reversed. [3]
While this model is able to describe the polarity reversal, it does not explain other
active phenomena such as flares. It also does not account for the Maunder Minimum,
which is regarded by some as a much larger cycle. [3]
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Figure 2: The Magnetic Dynamo model, shown in steps. (Taken from Carrol & Ostlie)
4
Conclusion
It is clear that the study of sunspots is extremely important in our understanding of
the Sun. Sunspots first hinted at the presence of a global solar magnetic field, and
completely changed the way we look at our Sun today. However, our Sun is not unique
in this aspect. Sunspots, or as their deep space sisters are called, starspots, have been
shown to exist on other stars, sometimes exhibiting a much higher level of activity.
The study of sunspots and stellar activity is very topical today, since we are currently
experiencing a minimum and we are overdue for the start of a new cycle. It is not well
understood why the solar activity is still at a minimum right now. Perhaps it is linked
to the bigger Maunder Minimum, and we are currently about to enter such a minimum.
Time will show.
References
[1] Peter R. Wilson, Solar and Stellar Activity Cycles, Cambridge University Press,
Cambridge, United Kingdom, 1994
[2] John H. Thomas and Nigel O. Weiss, Sunspots and Starspots, Cambridge University
Press, Cambridge, United Kingdom, 2008
[3] Bradley W. Carrol and Dale A. Ostlie, An Introduction to Modern Astrophysics,
Second Edition, Addison-Wesley, San Francisco, CA, 2007
[4] Judit Brody, The Enigma of Sunspots: A story of discovery and scientific revolution,
Floris Books, Poland, 2002
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[5] Arvind Bhatnagar and William Livingston, Fundamentals of Solar Astronomy, World
Scientific Publishing, Singapore, 2005
[6] Kenneth R. Lang, The Sun from Space, Springer-Verlag, Berlin, 2000
[7] Willie Wei-Hock Soon and Steven H. Yaskell, The Maunder Minimum and the Variable Sun-Earth Connection, World Scientific Publishing, Singapore, 2003
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