EDUCATIONAL ACTIVITY
Calculation of Solar Activity
Authors:
Dr. Miquel Serra-Ricart. Astronomer of the Institute of Astrophysics of Canary Islands.
Mr. Juan Carlos Casado. Astrophotographer of tierrayestrellas.com, Barcelona.
Mr. Miguel Ángel Pío Jiménez. Astronomer of the Institute of Astrophysics of Canary Islands.
Dr. Vanessa Stroud. Astronomer Faulkes Telescope.
1 - Activity goals.
Tracking solar activity through continuous observation of the surface is an interesting project that
will allow to apply the scientific method.
The objectives to be achieved are:
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Apply a methodology for calculating an astrophysical parameter (Wolf index) from an
observable (digital images) as a technique for teaching applications, documentaries and
research. Apply knowledge of solar physics and basic statistics.
Understand and apply basic techniques of image analysis (counting active foci, orientation,
scale, ...).
Work cooperatively in a team, valuing individual contributions and expressing democratic
attitudes.
2 - Instrumentation
The activity will be made from digital images obtained by the Solar TAD (“Telescopio Abierto de
Divulgación”, ref 3-3) within the solar GLORIA Experiment or any other Telescope with images
from the photosphere, for example the project GONG (ref 3-2). Note that the time of image
acquisition is needed.
Connection to the Solar Experiment GLORIA is available on ref 3-3.
3 – Phenomenon
The Sun, due to its proximity, is the star that can be studied in more detail and in which theories
about stellar evolution and behavior can be tested.
3.1.- The Sun
The Sun is one of the 200,000 million stars that belong to the Milky Way, but for us it is the most
important one because it is only at an average distance of 150 million miles from Earth and is the
main supply of energy for our planet.
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With a diameter of 1,392,000 km - the Earth’s diameter is 12,756 km in the equator -, contains
98.6% of the entire mass of the Solar System.
The age of the Sun is estimated to be about 4,500 to 5,000 million years. It is going through the
intermediate stage of its life, in the so-called main sequence, thanks to a stable balance between
the thermonuclear reactions that occur in the interior of stars, which are used to convert hydrogen
into helium, and gravity, which tends to flatten them. Sun is expected to continue as it is for
another 5,000 million years. The Sun has several different layers, which can be divided into inner
and outer, relative to the surface or photosphere (see Figure 1).
Figure 1. The layers of the Sun. Scheme J.C. Casado.
Inner Layers
These are the layers that are not directly observable. The photosphere is about 300 km thick and
can be considered as the separation zone between the interior layers and the solar atmosphere.
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The core is the central region of the Sun and has a temperature of 15 million degrees. From here
comes the star’s power; every second 564 million tons of hydrogen are fused, through
thermonuclear reactions, to 560 million tons of helium. Hydrogen nuclei (protons) become helium
nuclei at a rate of four to one and the difference in mass (four million tons per second) is released
as energy, since the four protons are slightly heavier than helium nucleus formed.
The radiative zone. The energy generated in the core is first transported outwards across a layer
that surrounds it, as high energy radiation that is absorbed and re-emitted continuously.
The convective zone. The Sun has several layers above the radiative zone where the energy is
transferred to the surface or photosphere by convection phenomena. The result of these convective
flows can be seen as the Granulation in the photosphere. All the photosphere is covered by a celllike frame similar, by its geometry, a grain of rice. These cells are the top of each of the upward
(hotter) and downward (cooler) columns of the energy transport. The dimensions of this
granulation are considerable: each "grain" is about 800 km in diameter (see Figure 6b).
The Photosphere is the directly visible (with appropriate protection) solar surface which has an
approximate temperature of about 6,000° C. Different phonomena can be observed on it such as
sunspots which are useful to measure solar activity and will be discussed later. (Figure 2).
Figure 2. The photosphere of the Sun showing different sunspot groups taken on the 1st of
November 2003. Image J.C.Casado @ tierrayestrellas.com
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The Sun has an overall magnetic field with a mean intensity twice as strong as the one on Earth.
Although the local magnetic field intensity is much more stronger in the vicinity of the spots.
In general, it is thought that all the phenomena related to the solar activity are determined by
processes associated with the solar magnetic field.
The outer Layers
From the photosphere, photons can pass through these layers and disperse into space making these
areas observable.
The chromosphere is a reddish layer enveloping the photosphere, about 10,000 km thick. It
projects gas to very high temperatures creating protuberances (Figure 3) which are flares that are
blown into space at tremendous speeds and can reach several hundreds of thousands of kilometers
in altitude.
Figure 3. Image of the chromosphere obtained with a telescope fitted with a hydrogen-alpha filter.
At the edge of the disk, various protuberances can be observed. Image J.C.Casado @
tierrayestrellas.com
Both the chromosphere and protuberances can be observed directly during the totality phase of a
Solar eclipse. Under normal conditions, it is necessary to use devices or filters to be observed.
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Corona. Above the chromosphere is the corona, a kind of aura with a structure that follows the
lines of force of the solar magnetic field. It is composed of gases with temperatures of more than 1
million degrees, but with a very low density and therefore generates little heat and light. Its
boundaries are imprecise, to the point that Earth can be considered to be immersed in its outermost
regions where, in addition to gases, include abundant dust particles. The solar corona is visible with
the naked eye during the totality phase of a total solar eclipse (Figure 4).
Figure 4. Solar corona photographed during the total solar eclipse of July 11, 2010 from Easter
Island. Photos and processing J.C. Casado and M. Serra-Ricart @ tierrayestrellas.com
3.2.- The solar activity.
Solar activity is manifested in the three observable layers of the Sun: the photosphere, the
chromosphere and corona. This activity spreads to Earth in the form of radiation and particles
(called solar wind).
The photosphere is the visible layer which is most easily observable. The most characteristic
manifestation of solar activity are the sunspots that appear on the Sun's surface. Although sunspots
had already been detected with the naked eye several centuries before our era, these were not
understood and systematically recorded as such until the invention of the astronomical telescope
(1610). Early observers soon perceived that they were not immutable, but had a duration and a
variable size.
The German naturalist Heinrich Schwabe discovered in 1843 that the spots appeared to have a
period of about 10 years. This was confirmed in 1855 by Rudolph Wolf who found a periodicity of
11 years, known as the solar undecenal cycle.
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In 1859 the Englishman Richard Carrington discovered that the Sun had a differential rotation, and
that it spins faster in equator than at the poles. He also found that the average latitude of the spots
varies with time; at the beginning of the activity cycle the spots appear around the latitudes of 30°
and, as the cycle progresses, they started to increasingly form closer to the equator, being located
at the maximum near 10° latitude. Actually the solar cycle length is twice of this cycle (about 22
years) since every 11 years the solar magnetic poles are reversed and therefore it takes 22 years for
the Sun to return to its original configuration. All cycles are not the same since their duration and
intensity vary. The shortest registered single cycle lasted 7 years and the longest 17. There have
been also exceptions to the cycle, as once detected by E.W. Maunder in 1893, which showed that
for 70 years, between 1645 and 1715, sunspots virtually disappeared (in his honor this is called the
"Maunder Minimum"). Studies suggest the existence of other Maunder minimum-like events
previous to this one. Geological investigations show that the undecenal solar cycle existed millions
of years ago which suggests it is a permanent solar phenomenon, although there are many
indications that its intensity can vary widely.
Solar activity cycles are numbered from the maximum of 1761. Currently (2013) we are in the
cycle No. 24 and expecting it to peak in mid-2013 (Figure 5).
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Figure 5. Numbered cycles of solar activity since its establishment. The coloured data indicate
observational coverage.
Also certain variable stars (type BY Draconis and RS Canum Venaticorum) appear to show a solar
like activity but at a much larger scale.
4 – Methodology
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4.1.-Methods to observe the photosphere
Solar observation requires some security measures that must be taken into account. Therefore we
only indicate the safest observation methods (see ref7).
Solar Filters. These filters must be placed in the aperture of the telescope specially designed for
this purpose. There are available as metallized flexible sheets which can be adapted to different
sizes, or as a glass with a mount for different diameters. In general this is preferred method.
The filters that are placed directly in the eyepiece should be disposed after use since they could be
dangerous due to the risk of being damaged by the concentration of solar heat.
Projection. Refractor telescopes are preferred for this method. It projects the solar image (no filter)
on a white surface perpendicular to the optical axis of the telescope. It is advised to create a dark
environment around the projection screen to increase the image contrast, making the structures
better to observe. This method allows the image to be observed simultaneously by several people.
Helioscope (Herschel prism). Recommended for refractor telescope. It consists of an optical prism
which is placed in the focuser, diverting 95% of the incident light. It is also necessary to use an
absorbent filter (density 3).
Other methods. There are other alternatives, such as using reflecting telescopes with primary
mirror without aluminizing (or both mirrors, also the secondary). This requires a dense filter into
the eyepiece holder, but without the risk of breakage. This telescope will be unusable for other
astronomical observations.
4.2.- Photospheric structures
By observing the photosphere we can see a series of details and characteristics formations (Figure
6a):
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Figure 6a. Details mentioned in the text: Solar limb darkening, granulation, spots and faculae.
Photo J.C.Casado © tierrayestrellas.com
Solar limb darkening. The center of the sun appears brighter than the edges. This phenomenon is
caused by the absorption of part of the light by the solar atmosphere.
Granulation. As mentioned, the photosphere is formed by cells that make the surface appears
rough (Figure. 6b). These "grains" are convective currents produced in lower layers with a duration
of a few minutes.
Figure 6b. Solar granulation. Image from the Solar Swedish Tower (ORM, IAC).
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Spots. There are darker areas in the photosphere due to their lower temperature (about 2000° less)
and are tracers of the Sun’s magnetic activity. Typically a sunspot consists of a dark central region
called umbra, surrounded by a lighter area or penumbra which consists of light and dark
filaments depart radially from the umbra. The average diameter of the penumbra is usually about
two and a half times that of the shadow, but in highly developed groups it can represent up to 80%
of the total area of the spot. If the spot is small and has no penumbra, it is called a pore.
Faculae. They can be seen near the limb as areas brighter than the rest of the solar surface. They
are associated with the spots and have a duration greater than these; they usually appear before the
spot and disappear after them. These can be observed both during the maxima and minima of the
solar cycles and are a good indicator of electromagnetic activity since they result in spots most of
the time.
4.3. - Heliographic coordinates
The rotation axis of the Sun and Earth are tilted relative to the plane of the ecliptic by about 7º and
23° respectively. The combination of both inclinations causes throughout the year a deviation in the
solar axis with respect to the North-South direction and an inclination of the equator with respect to
the line of sight (Figure 7).
Figure 7. Orientation of the solar disk throughout the year.
To determine the correct orientation of the solar disc three parameters or heliographic coordinates
must be known (These heliographic coordinates can be calculated for a specific date and time in the
website in ref 8 see Figure 8).
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Figure 8. Heliographic coordinates (in red). N and S
are the poles of the ecliptic. SNP is the north pole of the
Sun.
P . The position angle of the Northern end of the axis of rotation measured from the North point of
the disk, positive to the East and negative to west. P varies between +/- 26.3°.
B0. The heliographic latitude of the center point of the solar disk. This is due to the inclination of
the ecliptic with respect to the solar equatorial plane. Ranges from +/- 7.23°.
L0. Heliographic length of the center point of the disc. The length value is determined by a fixed
length with a variation of 13.2° /day. The initial meridian is defined as the meridian which passed
through the ascending node of the solar equator on June 1, 1854 at 12:00 UTC, being calculated to
the present date assuming a uniform sidereal rotation of 25.38 days (period of synodic rotation or
Carrington rotation of 27.2753 days).
To calculate the coordinates of a spot or a detail, measure its position on the apparent disk and
subsequently make the necessary corrections according to heliographic coordinates at the time of
observation (you can use templates to perform this task -variations of 1 ° in heliographic latitude-,
downloadable from: ftp://howard.astro.ucla.edu/pub/obs/stonyhurst_disks ).
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4.3.2.- The Wolf Number Calculation. http://goo.gl/aBnxw
5 - References
ref 1 - SOHO Observatory ( http://sohowww.nascom.nasa.gov )
ref 2 - GONG Telescopes Network ( http://gong.nso.edu/ )
ref 3 - Images of the Sun (photosphere) from internet.
1.- From the Space (SOHO satellite)
http://sohowww.nascom.nasa.gov/data/realtime/hmi_igr/1024/latest.jpg
2.- From a network of ground Telescopes (GONG)
http://gong2.nso.edu/dailyimages/
3.- Images of the Sun (photosphere) through a robotic Solar telescope - TAD - (Teide
Observatory, IAC) from the GLORIA project http://users.gloria-project.eu (Solar
Experiment )
ref 4 - Images of Great Celestial Shows http://www.tierrayestrellas.com
ref 5 - Solar Influences Data Analysis Center -SIDC-, Royal Observatory of Belgium
http://sidc.oma.be/index.php3
ref 6 - Space Weather Prediction Center -SWPC- , USA http://www.swpc.noaa.gov/
ref 7 - Solar safe observation http://www.cascaeducation.ca/files/solar_observing.html
ref 8 - Heliographic coordinates http://www.astrosurf.com/obsolar/ephemeris.html
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