Download STUDY OF UMBRA-PENUMBRA AREA RATIO OF SUNSPOTS

STUDY OF UMBRA-PENUMBRA AREA RATIO
OF SUNSPOTS
A Project Report By
Ragadeepika Pucha
Integrated MSc V year
Integrated Science Education and Research Center(ISERC)
Visva-Bharati, Santiniketan
Guided By
Prof. K.M. Hiremath
Indian Institute of Astrophysics, Bengaluru
August 2014 to April 2015
DECLARATION
I hereby declare that the project report titled, "Study of Umbra-Penumbra
Area Ratio of Sunspots" is submitted by me as a part of my final year dissertation work, that has been carried out at Indian Institute of Astrophysics,
under the guidance of Prof. K.M. Hiremath.
I further declare that I am the sole author of this report and this project
work or any part of it has not been previously submitted for any project,
degree or diploma in any university.
Date:
(Ragadeepika Pucha)
ACKNOWLEDGEMENTS
Firstly, I would like to thank my guru, His Holiness, Shri. Vijayendra
Saraswati Swami, for his constant blessings showering upon me. Then,
I thank my parents for their constant encouragement and their unfading
trust in me. I express my heartfelt gratitude to Prof. K.M. Hiremath,
who has agreed me as his project student and helped me in each step of
the way. His patience with me has led me to learn many things under his
guidance. I am very much greatful to the Director, Dr.P.Sreekumar, Indian Institute of Astrophysics, for giving me permission to do this project.
I am also very thankful for the Board of Graduate Studies, Indian Institute of Astrophysics, for arranging the accommodation during this project.
Last but not at all the least, I would take this oppurtunity to thank my
friends -Prasanna, Hemanth, Panini, Phanindra, Sashikumar, Parth, Lakshmi, Sowmya, Supriya, Athray, Anjana, Manasa, Jaya and Sankalp, who
encouraged me and inspired me throughout this term.
ABSTRACT
Sunspots are the most conspicuous aspects of the Sun. They
have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter
background. Sunspots cyclically appear and disappear with a
11-year periodicity and are associated with a strong magnetic field
(∼ 103 ) structure. Sunspots consist of a dark umbra, surrounded
by a lighter penumbra. Study of umbra-penumbra area ratio can
be used to give a rough idea as to how the convective energy of
the Sun is transported from the interior, as the sunspot’s thermal
structure is related to this convective medium.
Aim of this study is to develop a code to analyze the digitized
white-light images, obtained from the Kodaikanal Solar Observatory.
We developed such a code in IDL, that detects the edge of the solar
disk, computes its center and radius simultaneously and removes
the effect of limb darkening from the images. In addition, the code
detects the sunspots from the images, computes the whole spot area,
separates the umbra (with its area) from them and finally computes
the heliographic coordinates, and the required umbra-penumbra
area ratio of the sunspots. We compared all these estimated results
with results from other estimates (such as Debrecan sunspot data,
Greenwich Photoheliographic results, etc., ) and, we find that our
estimated results match with the results of other data.
Contents
1 THE SUN - AN INTRODUCTION
1.1 The Solar Interior . . . . . . . . . . . . .
1.1.1 Energy Generation . . . . . . . .
1.1.2 The Solar Model . . . . . . . . .
1.1.3 Energy Transport from the Core .
1.2 The Solar Atmosphere . . . . . . . . . .
1.2.1 The Photosphere . . . . . . . . .
1.2.2 The Chromosphere . . . . . . . .
1.2.3 The Corona . . . . . . . . . . . .
1.3 Solar Activity . . . . . . . . . . . . . . .
1.3.1 The Quiet Sun . . . . . . . . . .
1.3.2 The Active Sun . . . . . . . . . .
2 THE SUNSPOTS
2.1 The Structure of Sunspots . . . . .
2.1.1 Pores . . . . . . . . . . . . .
2.1.2 Penumbra . . . . . . . . . .
2.1.3 Umbra . . . . . . . . . . . .
2.2 Sunspots and the Solar Rotation . .
2.3 The Sunspot Cycle . . . . . . . . .
2.4 Sunspots and Solar Magnetic Field
2.5 Wilson Effect . . . . . . . . . . . .
2.6 Motivation of the Project . . . . . .
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3 DETECTION AND ESTIMATION OF HELIOGRAPHIC COORDINATES AND AREA OF SUNSPOTS FROM KODAIKANAL DIGITIZED DATA
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3.1 Detection of the Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Calculation of Center and Radius . . . . . . . . . . . . . . . . . . . . . 29
3.3 Removal of Limb Darkening . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Computation of Heliographic Coordinates . . . . . . . . . . . . . . . . 33
3.5 Detection of Sunspots . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.1 Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.2 Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 Opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.4 Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.5 Top-hat Transformation . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Separating the Umbra of a Sunspot . . . . . . . . . . . . . . . . . . . . 38
5
3.7
3.8
Computation of Average Heliographic Coordinates of Sunspots . . . . .
Computation of Area of Sunspots . . . . . . . . . . . . . . . . . . . . .
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4 RESULTS AND DISCUSSIONS
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4.1 Advantages and Disadvantages of the New Method . . . . . . . . . . . 48
4.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
Material Inside the Sun in Hydrostatic Equilibrium . . . . . .
A Theoretical Model of the Sun’s Interior : Luminosity Graph
A Theoretical Model of the Sun’s Interior : Mass Graph . . . .
A Theoretical Model of the Sun’s Interior : Temparature Graph
A Theoretical Model of the Sun’s Interior : Density Graph . .
Structure of the Solar Interior . . . . . . . . . . . . . . . . . .
The Photosphere . . . . . . . . . . . . . . . . . . . . . . . . .
The Chromosphere as seen during a Solar Eclipse . . . . . . .
The Corona during a Total Solar Eclipse . . . . . . . . . . . .
Granulation on the Sun . . . . . . . . . . . . . . . . . . . . .
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2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
The Sunspots . . . . . . . . . . . . . . . . . . . . . . . .
The Structure of Sunspots . . . . . . . . . . . . . . . . .
The Solar Rotation . . . . . . . . . . . . . . . . . . . . .
Sunspot Maximum and Sunspot Minimum . . . . . . . .
Variation of total number of Sunspots with respect to year
The Butterfly Diagram of Sunspots . . . . . . . . . . . .
Solar Magnetic Field Lines due to Differential Rotation .
The Wilson Effect . . . . . . . . . . . . . . . . . . . . . .
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3.1
3.2
3.3
3.4
White-light Image of the Sun from Kodaikanal Observatory . . . . . . .
Detected Edge of the Sun’s Image from the Kodaikanal Observatory . .
Limb Darkening Phenomenon . . . . . . . . . . . . . . . . . . . . . . .
An Example of Limb Darkening Removal from the Sun’s Image Obtained
from Kodaikanal Observatory . . . . . . . . . . . . . . . . . . . . . . .
Common Structuring Elements . . . . . . . . . . . . . . . . . . . . . .
An Irregular Shape Eroded by a Circular Structuring Element. . . . . .
An Irregular Shape Dilated by a Circular Structuring Element. . . . . .
An Example of the Detection . . . . . . . . . . . . . . . . . . . . . . . .
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3.5
3.6
3.7
3.8
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
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Scatter plot of Kodaikanal and Debracan Latitudes . . . . . . . . . . . .
Scatter plot of Kodaikanal and Debracan Longitude Differences from the
Central Meridian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scatter plot of Kodaikanal and Debracan Whole Spot Areas . . . . . . .
Scatter plot of Kodaikanal and Debracan Umbra Areas . . . . . . . . .
Scatter plot of Kodaikanal and Debracan Penumbra Areas . . . . . . . .
Scatter plot of Kodaikanal and Debracan Umbra-Penumbra Area Ratios
Variation of Whole Spot Area with Time . . . . . . . . . . . . . . . . .
Variation of Umbra-Penumbra Area Ratio with Time . . . . . . . . . .
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Chapter 1
THE SUN - AN INTRODUCTION
The Sun is a typical star. About a million times larger in volume than the Earth, the
Sun contains almost 99.9% of the mass of the solar system. It emits energy into space,
mostly in the form of electromagnetic radiation. The Sun’s spectrum is close to that of
an idealized black body with a temperature of about 5800 K and the maximum lying in
the visible region. Solar energy is very important for the life on the Earth to flourish. It
also controls the climate and seasons on Earth (Hiremath and Mandi, 2004; Hiremath,
2006; Hiremath et. al., 2015 ). We rely on the Sun for our survival. Hence, we need
to understand how the energy is generated in the Sun and to probe changes, if any, in
this production of energy. Even a slightest change can have enormous repercussions
to the life on Earth. Based on the radioactive calculations, it is known that the Sun
has completed almost half of its life span and is 4.57 × 109 years old (Stix, 2004 ).
Understanding physics of the Sun is also of great importance in the field of stellar
physics. The Sun is the closest star to us, being only 8 light minutes away, compared
with over 4 light years for the next nearest star. This offers a scope for the Sun to act
as a perfect laboratory for understanding more about stars. By studying the Sun, we
not only learn about the properties of a particular star, but also can study the details
of the physical processes that undoubtedly take place in more distant stars as well.
A crucial component of the Sun is its localized strong and continuously changing
magnetic field structure. This dominant magnetic field activity makes the Sun more
dynamic in nature. Majority of the solar activity phenomena such as sunspots, solar
flares and solar wind are related to this active magnetic field structure. Some essential
data about the Sun is given in Table 1.
The solar structure is sectioned into different regions depending on their different
properties and physical characteristics as given below:
1. Solar Interior
• The Core - Region of energy generation
• The Radiation Shell - Region of energy transport by radiation
• The Convection Shell - Region of energy transport by convection
2. Solar Atmosphere
• Photosphere - Region where visible photons are emitted
• Chromoshere - Second Layer of the atmosphere
1.1. The Solar Interior
9
• Corona - The super hot region where the solar wind originates
The boundaries between various regions are not quite sharp. The outermost layers
even extend into the interplanetary space, beyond the orbit of Earth. Each of these
layers are briefly explained in the following sections.
Table 1.1: Physical Parameters of the Sun
Mean Distance from the Earth
1 AU = 149, 597, 892 km
Maximum Distance from the Earth
1.521 × 108 km
Minimum Distance from the Earth
Light Travel Time to Earth
30’ 59.3”
Radius
696,000 km = 109 R⊕
Mass
1.9891 × 1030 kg = 3.33 × 105 M⊕
1410 kg m−3
Mean surface temperature
5800 K
Luminosity
3.9 × 1026 W
Spectral Class
1.1.1
8.32 minutes
Mean Angular Diameter
Mean density
1.1
1.471 × 108 km
G2V
Visual Apparent Magnitude
-26.7
Visual Absolute Magnitude
+4.8
Mean Synodic Rotation
27.2753 days
Mean Sidereal Rotation
25.380 days
The Solar Interior
Energy Generation
The Sun emits 3.9 × 1026 joules of energy per second. This huge amount of energy is
generated within the Sun’s core that extends from the center to upto 10 % of the solar
radius. The temperature in this region varies from around 15 million K near the center
to around 5 million K at the edge of the core. But, how is this tremendous energy
produced? There were many attempts to answer this question since as early as the
nineteenth century (Bhatnagar, 2005 ). The ideas from relativity and nuclear physics
finally led to its solution. The Einstein’s mass-energy equivalence relation: E = mc2
with m being quantity of mass in kg and c being the speed of light, 3 × 108 m/s holds quite an important role in this discovery. Since the velocity of light, c is a huge
number, even a small amount of matter can produce a vast amount of energy.
1.1. The Solar Interior
10
Two nuclear reaction cycles appeared to be the most promising in accounting for solar energy production (Bethe, 1938 ). They are - hydrogen fusion and carbon-nitrogen
cycle. The two factors which determine the most likely nuclear reactions are the
abundance of the reacting species and the reaction probability at the temperatures
prevailing in the solar core. The Sun’s low density indicates that it is made of very
light elements, mostly hydrogen and helium. Also, the strong coulomb repulsion between positively charged nuclei increases as the product of their nuclear charges, so
only the lightest elements will have the appreciable reaction probabilities. Hence,
in the Sun, the most efficient nuclear reaction is the hydrogen fusion, in which four
hydrogen nuclei fuse together to form one helium nucleus.
Hydrogen fusion in the Sun usually takes place in a sequence of steps called the
proton-proton chain. Each of these steps releases energy that heats up the Sun and
gives it its luminosity. This chain has been briefly explained below STEP-1 Two protons (H 1 ) combine to form a hydrogen isotope (H 2 ). Here, one of the
protons change into a neutron. One by-product of this conversion is a neutrino
(ν), which escapes from the Sun. The other by-product is a positron (e+ ), that
encounters an electron (e− ), annihilating both into gamma-ray photons. The
energy of these photons goes into sustaining the Sun’s internal heat.
2H 1 → H 2 + ν + e+
e+ + e− → γ
STEP-2 The H 2 nucleus produced in the above step collides with another proton, resulting in a helium isotope (He3 ), with two protons and one neutron. This reaction
releases another gamma-ray photon, whose energy also goes into sustaining the
internal heat of the Sun.
H 2 + H 1 → He3 + γ
STEP-3 The He3 nucleus produced collides with another such nucleus produced from
three other protons. Two protons and two neutrons from these nuclei rearrange
themselves into a different helium isotope (He4 ). The two remaining protons are
released. The energy of their motion contributes to the Sun’s internal heat.
2He3 → He4 + 2H 1
To summarize, six H 1 nuclei go into producing the two He3 nuclei, which in turn
rearrange to make one He4 nucleus. Since two of the original H 1 nuclei are returned
to their original state, the above three steps can be written into a single step:
4H 1 → He4 + ν + energy
This picture has been confirmed by detecting the by-products of this transmutation
- the neutrinos that stream outward from the Sun into space. Neutrinos hardly interact
with any matter, so they travel almost unimpeded through the Sun’s interior.
A small fraction (0.7%) of the initial mass of hydrogen is converted into energy,
every time this process takes place. That means, for every four hydrogen nuclei being
converted into a helium nucleus, 4.3 ×10−12 joules of energy is released. To produce
the Sun’s luminosity of 3.9 ×1026 joules per second, around 6 ×1011 kg of hydrogen is
converted into helium every second.
1.1. The Solar Interior
1.1.2
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The Solar Model
The conditions in the solar interior can be speculated by studying the temperature,
pressure and density profiles inside the Sun. It is known that the Sun is stable. The
Sun is not exploding or collapsing, nor is it significantly heating or cooling. The Sun
is said to be in both hydrostatic and thermal equilibrium. Our model should be such
that it is as stable as the real Sun.
To understand what is meant by hydrostatic equilibrium, imagine a slab of material
in the solar interior (Figure 1.1 ). In equilibrium, the slab on average will move neither
up nor down. Equilibrium is maintained by a balance among three forces that act on
this slab:
1. The downward pressure of the layers of solar material above the slab.
2. The upward pressure of the hot gases beneath the slab.
3. The slab’s weight, that is the downward gravitational pull it feels from the rest
of the Sun.
The pressure from below must balance both the slab’s weight and the pressure from
above. Hence, the pressure below the slab must be greater than that above the slab.
In other words, pressure has to increase with increasing depth.
Figure 1.1: Material Inside the Sun in Hydrostatic Equilibrium
Image Courtesy: www.public.asu.edu
Hydrostatic equilibrium also tells us about the density of the slab. At each depth,
the density of solar material must have a certain value and it must increase with
increasing depth. Furthermore, when you compress a gas, its temperature tends to
increase. Hence, the temperature must also increase as we move towards the Sun’s
center. While the temperature in the solar interior is different at different depths,
the temperature at each depth remains constant with time. This is called as thermal
equilibrium.
Using this knowledge as well as the data that the Sun’s surface temperature is 5800
K, its luminosity is 3.9 ×1026 W, and that the gas pressure and density at the surface
is assumed to be zero, a model of the Sun is constructed. The graphs given in Figure
1.2 to 1.5, explain this theoretical model of the Sun’s internal radial structure of mass,
density etc, quantitatively.
1.1. The Solar Interior
Figure 1.2: A Theoretical Model of the Sun’s Interior : Luminosity Graph
Image Courtesy: www.public.asu.edu
Figure 1.3: A Theoretical Model of the Sun’s Interior : Mass Graph
Image Courtesy: www.public.asu.edu
Figure 1.4: A Theoretical Model of the Sun’s Interior : Temparature Graph
Image Courtesy: www.public.asu.edu
Figure 1.5: A Theoretical Model of the Sun’s Interior : Density Graph
Image Courtesy: www.public.asu.edu
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1.1. The Solar Interior
1.1.3
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Energy Transport from the Core
The energy produced is transported outward from the core to the surface of the Sun.
Heat flows only when there is a temperature difference, that is from hotter to colder
regions. Thus, the temperature must steadily decrease from the core to the solar
surface. But, what mechanism of heat transfer occurs inside the Sun? There are three
methods of energy transport - conduction, convection and radiation. Conduction is
not an efficient means of energy transport in substances with low densities. Hence,
conduction is not possible inside stars like the Sun.
Inside the Sun, heat is transported by radiation in the first 70% of the solar radius,
thus giving the name radiation zone to this region. The photons liberated in the
thermonuclear processes at the core are high energy gamma rays. They bump with
electrons and atomic nuclei along their way resulting in lowering of their energy as they
diffuse outwards. The overall result is an outward migration of the photons towards
the cooler surface. The solar plasma in this region is comparatively transparent and
the photons can travel moderate distances before being scattered or absorbed.
Figure 1.6: Structure of the Solar Interior
Image Courtesy: Fundamentals of Solar Astronomy, A. Bhatnagar
In the last one third of the solar radius, the properties of the plasma change such
that the convection sets in. The temperature in this region is low enough for the atoms
to hang on to their electrons. This makes the gas opaque to the photons and hence,
the photons get absorbed. As the gas gets heated, it becomes less dense and rises
upward, whereas the cooler gas sinks downward. In this way, heat is transported via
convection cells, giving the name convection zone to this region.
The main aspects of the Sun’s internal structure is illustrated in Figure 1.6.
1.2. The Solar Atmosphere
1.2
1.2.1
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The Solar Atmosphere
The Photosphere
The photosphere is the lowest of the three main layers in the Sun’s atmosphere. It is
the layer from which the visible light emanates (“Sphere of light”). We can only see
about 400 km into the photosphere.
The spectrum of the solar photosphere is continuous, crossed by dark absorption
lines, known as Fraunhofer lines. They come from most of the chemical elements,
although some of the elements have many lines in the spectrum whereas some have
very few. The hydrogen Balmer lines are strong but few in number. This absorption
spectrum confirms that the temperature of the Sun’s photosphere falls with altitude.
Figure 1.7: The Photosphere
Image Courtesy: SOHO, NASA
The photosphere can be seen only upto a certain depth. This is due to its hydrogen atoms that sometimes acquire an extra electron, becoming negative hydrogen
ions. This extra electron is only loosely attached and can be dislodged if it absorbs
a photon of any visible wavelength. Hence, negative hydrogen ions are very efficient
light absorbers, and there are enough of these light-absorbing ions in the photosphere
to make it quite opaque. Due to this effect, the photosphere’s spectrum is close to that
of an ideal blackbody. Figure 1.7 shows a typical white light image of the photosphere,
taken by SOHO on 28/10/2003 06:24 UT.
1.2.2
The Chromosphere
Just above the photosphere is a spiky layer about 10,000 km thick, and only about
1.5% of the solar radius. This layer cannot be seen with the naked eye except during
a solar eclipse, during which it glows colorfully pinkish (Figure 1.8 ). It is called as
the chromosphere (“Sphere of Color”). The chromospheric gas is at a temperature of
approximately 10,000 K, and is slightly hotter than the photosphere below it.
1.2. The Solar Atmosphere
15
Figure 1.8: The Chromosphere as seen during a Solar Eclipse
Image Courtesy: www.astronomynotes.com
Unlike the photosphere, which has an absorption spectrum, the chromosphere has
a spectrum that is dominated by emission lines. These emission lines appear to flash
into view at the beginning and at the end of totality, so the visible spectrum of the
chromosphere is known as the flash spectrum. One of the strongest lines in the chromosphere’s spectrum is the Hα line at 656.3 nm. The spectrum also contains emission
lines of singly ionized calcium, and lines due to ionized helium and ionized metals.
Analysis of this emission spectrum shows that the temperature increases with increasing height. The top of the chromosphere has a temperature of nearly 25,000 K.
By using a special filter that is transparent to light only at the wavelength of Hα ,
astronomers can make the chromosphere visible.
1.2.3
The Corona
Above the chromosphere, there is a ghostly white halo called the corona (Figure 1.9 ),
that extends tens of millions of kilometers into space. The corona is continually expanding into interplanetary space. It is only seen during total solar eclipses, when first
the photosphere and then the chromosphere are completely hidden from view.
Like the chromosphere below it, the corona also has an emission line spectrum. The
emission lines are caused by atoms in highly ionized states. For example, a prominent
green line at 530.3 nm is caused by highly ionized iron atoms, each of which has been
stripped off 13 of its 26 electrons. For achieving this state, temperatures in corona
must reach ∼ 2 million kelvin or even higher.
The density of corona is very low, compared to the photosphere. This explains why
it is so dim as compared to the photosphere. In general, the higher the temperature
of a gas, the brighter it glows. But because there are so few atoms in the corona, the
net amount of light that it emits is very feeble compared with the light from the much
cooler, but also much denser photosphere. Special telescopes called coronographs block
out the solar photosphere so that the corona can be easily studied.
1.3. Solar Activity
16
Figure 1.9: The Corona during a Total Solar Eclipse
Image Courtesy: www.public.asu.edu
1.3
Solar Activity
A host of activity phenomena that vary on different spatial and temporal scales are
superimposed on the basic structure of the Sun. Description of the physical nature of
these phenomena and understanding of their origins is aided by their division into two
classes: quiet and active solar activity phenomena.
1.3.1
The Quiet Sun
In the quiescent model, the sun is viewed as a static, spherically symmetric ball of
hot gas; that is, solar properties change with radius only. In each layer, there are
some phenomena like granules, supergranules, spicules and solar wind, that occur
continuously and show very slow variations. These are the aspects of the quiet Sun.
Granules and Supergranules
The photosphere is not perfectly smooth, but it has kind of a blotchy pattern, called
granulation. Typically, granules are 700 to 1000 km in diameter. Granules appear
as bright spots surrounded by narrow darker regions. The difference in brightness
between the center and the edge of a granulation corresponds to a temperature drop
of about 300 K.
Granulation is caused by convection of gas in the photosphere. Granules are
columns of hotter gas arising from below the photosphere. As the rising gas reaches the
photosphere, it spreads out and sinks down again. The darker intergranular regions
are the cooler gases sinking back (Figure 1.10 ). This phenomenon is further proof
that the upper part of the photosphere must be cooler than the lower part.
Granules form, disappear, and reform in cycles lasting only for a few minutes. They
may persist for about 8 minutes. At any single time, about 4 million granules cover
the solar surface.
Superimposed on the pattern of granulation are even larger convection cells called
supergranules. A typical supergranule is about 35,000 km in diameter, large enough to
enclose several hundred granules. Similar to granules, gases rise upward in the middle
1.3. Solar Activity
17
Figure 1.10: Granulation on the Sun
Image Courtesy: www.spaceplasma.com
of a supergranule, move horizontally outward towards its edge, and descend back into
the Sun. A given supergranule lasts about a day. Another important point to note is
that the magnetic fields are concentrated at the supergranule boundaries.
Spicules
The chromosphere contains numerous vertical jet-like structures called spicules. These
are spikes of rising gas, which rise thousands of kilometers in height. These features
occur at the edges of supergranule cells. A typical spicule lasts just 15 minutes or so.
It rises at a rate of about 20 km/s, reaches a certain height, and then collapses and
fades away. Approximately 300,000 spicules exist at any one time, covering about 1%
of the solar surface.
Solar Wind and Corona Holes
The Sun’s gravitational force keeps most of the gases of the photosphere, chromosphere
and corona from escaping. But, due to the very high temperature of corona, the atoms
and ions move at very high speeds. As a result, some of the coronal gas escapes. This
outflow of gas is called the solar wind. The solar wind is composed almost entirely of
electrons and nuclei of hydrogen and helium. About 0.1% of the solar wind is made of
ions of more massive atoms, such as silicon, sulphur, calcium, chromium, nickel, iron,
and argon. The corona is not uniform in temperature and density. Some of the areas
in the corona appear dark as they are almost devoid of gas. These areas are called
coronal holes. These holes are thought to be the main corridors for the particles of the
solar wind to escape from the Sun.
1.3. Solar Activity
1.3.2
18
The Active Sun
In contrast, active phenomena refer to the processes that occur in localized regions of
the solar atmosphere and within finite time intervals. Such features lead to sudden
violent changes in the solar atmosphere and they constitute the active Sun. The time
scales for such solar activity can be classified as slow, intermediate, or fast, and have
magnitudes from many years down to seconds. The phenomena like sunspots, plages,
faculae, prominences and flares are the aspects of the active Sun.
Sunspots
Sunspots are dark regions in the photosphere. Sometimes sunspots appear in isolation,
but are frequently found in groups. Although sunspots vary greatly in size, typical
ones measure a few tens of thousands of kilometers across. Sunspots last between a
few hours and a few months. A sunspot is a region in the photosphere where the
temperature is relatively low, making it appear darker than its surroundings. Another
important feature of sunspots is that they are regions of high magnetic field(∼ 103
G) through the photosphere and majority of them are bipolar. Sunspots are further
explored in the next chapter.
Plages and Faculae
In an image produced with the Hα filter, bright clouds are visible in the chromosphere
around the region of sunspots. These regions are termed as plages. They appear in
places with higher than average magnetic fields.
Plages sometimes emit light at many wavelengths and can be seen in the whitelight image of the Sun. These plages are called faculae. Faculae are best seen near the
limb of the Sun where the photosphere is not so bright.
Filaments and Prominences
In the Hα images, dark streaks known as filaments can also be seen. They are relatively
cool and the dense parts of the chromosphere are pulled along with the magnetic field
lines as they arch to high altitudes.
These filaments appear as bright columns of gas when viewed from the side. In
such cases, they are termed as prominences. They can extend for tens of thousands of
kilometers above the photosphere. Some prominences last for only a few hours, while
others persist upto many months.
Solar Flares and Coronal Mass Ejections
Abrupt eruptive events occur on the Sun, known as solar flares. They are frequent
near complex sunspot groups. Within only a few minutes, temperatures in a compact
region may soar to 5 × 106 K and vast amount of particles and radiation are blasted
out into space. These eruptions can cause disturbances that spread outward in the
solar atmosphere. The energy of the solar flare comes from the intense magnetic field
around a sunspot group.
CME’s are explosive events that are related to large-scale alterations in the Sun’s
magnetic field. They are much more heavy and violent than the solar flares.
Chapter 2
THE SUNSPOTS
Sunspots are among the most conspicuous aspects of solar activity on the Sun. They
are the regions which appear darker than the surrounding photosphere. But, if a
sunspot is isolated from the Sun, it will be as bright as the moon. The earliest
reference to a sunspot dates back to fourth century B.C., but they were interpreted
as transit of either Mercury or Venus. This was due to the widespread belief in the
‘perfection’ of the Sun (Bray and Loughhead, 1964 ). This view changed when Galileo
observed sunspots with his telescope in the year 1611. He concluded, once and for
all, the suggestion that spots might really be small planets revolving around the Sun,
pointing out that this hypothesis was incompatible with the observed changes in their
size and shape. Later, the law of 11-year periodicity of the sunspots was discovered
by Schwabe.
Sunspots are associated with strong magnetic field (∼ 103 G) structures. They vary
in time, magnitude and location. The life-time of sunspots vary from a few hours to
several days. Their size may range from a few thousand square kilometers to several
millionths of the solar disk, some of them even larger than the Earth itself (Figure
2.1 ).
Figure 2.1: The Sunspots
Image Courtesy: www.uni.edu
2.1. The Structure of Sunspots
2.1
20
The Structure of Sunspots
Sunspots consist of a dark central core, called the umbra, and a surrounding less dark
region known as the penumbra. Some of the spots do not show penumbrae. These are
called as pores. It is well known that Wien’s law relates the color of a blackbody to
its temperature. Using this law, the temperature of umbra is known to be typically
4300 K and that of the penumbra to be about 5000 K. The Stefan-Boltzmann law
states that the energy flux from a blackbody is proportional to the fourth power of its
temperature. This can be used to compare the radiative flux intensity of umbra and
penumbra to the photosphere.
Radiative f lux f rom umbra
Radiative f lux f rom photosphere
4300K 4
= ( 5800K
) ' 0.3
Radiative f lux f rom penumbra
Radiative f lux f rom photosphere
5000K 4
= ( 5800K
) ' 0.5
Hence, the umbra emits only 30% as much light as an equally large patch of undisturbed photosphere and similarly the penumbra emits 50% as much light.
2.1.1
Pores
Pores are the simplest form of sunspots, devoid of any penumbral structure. Majority
of the pores do not develop beyond this stage. The pores have magnetic fields (∼ 2000
G), the strength of which is comparable to that of a small spot. In most cases, pores
have a tendency to occur in the area near the leading (western) spot, rather than near
the following (eastern) spot. The occurrence of pores is not restricted to the vicinity
of spot groups. They may sometime appear alone or in small clusters, far away from
spot groups.
Majority of the pores have diameters in the range of 2-5 arc-seconds. If the size of
a pore is more than 7 arc-seconds, it has a tendency to develop into small spots having
at least some penumbral structure. The brightness of pores is less than the intergranular surrounding region, though it is greater than the umbra of larger sunspots.
Pores have much longer lifetimes than the photospheric granules, and they often remain
unchanged for many hours.
The growth of a new pore occurs through the gradual disappearance of surrounding
granules. This may be interpreted as due to opening up or lifting of magnetic flux tubes
from beneath the surface. Similarly, the dissolution of pores,that fail to develop into
a spot takes place by individual granules pushing into the dark area of pores and then
gradually covering the whole pore.
2.1.2
Penumbra
Sunspots begin their lives as pores. If they do not decay, they transform into spots
with penumbra. The structure of penumbra consists of a pattern of narrow bright
filaments on a darker background. These bright fibril structures run outwards from
the umbra to the photosphere. Although there is always a sharp distinction between
the penumbra and umbra of a spot, the penumbra often contains projections from the
umbra or sometimes, even isolated areas of umbral material.
In addition to penumbral filaments and dark umbral material, most spot penumbrae
contain bright features of various shapes, whose brightness may exceed that of the
2.2. Sunspots and the Solar Rotation
21
neighboring photosphere. These bright regions may occur anywhere in the penumbra
and are often found at the border of the umbra, of an umbral projection or of an isolated
umbral area. The outer penumbral-photospheric boundary ends abruptly with a sharp
but jagged boundary.
In the year 1909, it was found that the solar gases show a predominantly radial
outflow in the penumbrae at the photospheric level. Such a flow appears to be parallel
to the surface and is directed outwards from the umbra-penumbra boundary towards
the surrounding photosphere. This mass motion is known as the Evershed effect (Bhatnagar, 2005 ), named after its discoverer.
2.1.3
Umbra
Umbra is the dark region of the sunspots. There exists a bright granular structure
in the umbrae. The umbral granules are smaller than the photospheric granules.
Their lifetimes are still not determined (Bray and Loughhead, 1964 ). The presence
of granulation in the umbrae of sunspots shows that the basic convective processes
responsible for the photospheric granulation also operate in sunspots, although it was
believed that a sunspot magnetic field would suppress the convection.
Umbrae of most sunspots is complicated by the presence of light-bridges. They
show a great diversity in shape, size and brightness. Most of the light-bridges span an
umbra and may cover an appreciable part of it. They are only 1 arc-second in width,
extending into the umbral region. Light-bridges play a crucial role in the final stages
of sunspot evolution. The appearance of a light-bridge can be a sign of an impending
division or final dissolution of a spot. Sometimes, an irregular spot is transformed into
several smaller spots, as a result of divisions made by light-bridges.
The pores, umbra and penumbra of sunspots are shown explicitly in Figure 2.2.
Figure 2.2: The Structure of Sunspots
Image Courtesy: www.enchantedlearning.com
2.2
Sunspots and the Solar Rotation
By observing the motion of sunspots across the solar disk, it can be said that the Sun
rotates about its axis. The sunspots move from east to west across the disk. It was
Galileo who studied this movement and came up with the conclusion that the rotation
2.3. The Sunspot Cycle
22
period of the Sun is roughly one month. Later, Richard Carrington demonstrated that
the Sun does not rotate like a rigid body. The equator of the Sun rotates more rapidly
than the polar regions. This phenomenon is known as the differential rotation. It was
found that the time period of rotation is around 25.8 days at the equator, 28.0 days
at latitude 40o , and 36.4 days at latitude 80o . This phenomenon is attributed to the
fact that the Sun is a huge ball of gas. In addition to this, the inclination of the Sun’s
axis to the ecliptic plane was found to be i = 7.25o . The solar rotation can be better
understood by studying the Figure 2.3.
Figure 2.3: The Solar Rotation
Image Courtesy: www.mtk.nao.ac.jp
2.3
The Sunspot Cycle
The number of sunspots visible on the Sun is not constant. This number actually
varies periodically with a period of about 11 years. A period of exceptionally many
sunspots is a sunspot maximum. Conversely, the Sun is almost devoid of sunspots at
a sunspot minimum. In Figure 2.4, the left figure illustrates sunspot activity during
2.3. The Sunspot Cycle
23
the period of sunspot maximum, whereas the right figure shows the sunspot activity
during the period of sunspot minimum. Figure 2.5 shows the variation of number of
sunspots with time, showing the sunspot cycles quite clearly.
Figure 2.4: Sunspot Maximum and Sunspot Minimum
Image Courtesy: www.scieducar.com
Figure 2.5: Variation of total number of Sunspots with respect to year
Image Courtesy: www.astronomy.nmsu.edu
Figure 2.6: The Butterfly Diagram of Sunspots
Image Courtesy: www.astronomy.nmsu.edu
The locations of sunspots also vary with the same 11-year cycle. It was Richard
Carrington who made this discovery. He observed that the average latitude of sunspots
decreases steadily from the beginning to the end of each cycle. Majority of spots occur
between the equator and the latitude zone of ±40o . At the onset of each cycle, the
spots appear at high latitudes and slowly move closer to the equator until the end of
the cycle. The graph of latitude vs year is given in Figure 2.6, and for obvious reasons
known as the butterfly diagram.
2.4. Sunspots and Solar Magnetic Field
2.4
24
Sunspots and Solar Magnetic Field
When the light coming from the sunspots is passed into the spectroscope, it is found
that many spectral lines are split into several closely spaced lines. This splitting of
lines is called the Zeeman effect, which suggests that a spectral line splits when the
atoms are subjected to intense magnetic fields. The extent of splitting depends on the
strength of the magnetic field. In sunspots, the strength of observed magnetic field
range from 100 to nearly 4000 gauss. Magnetic field is present in the sunspot region
as well as the surrounding region, that persists even after the spot disappears.
Sunspots are the locations of concentrated magnetic field with very little magnetic
field in the surrounding regions. Due to the intense magnetic field, convection currents
are almost inhibited in these regions. As a result, the hot plasma from the interior is
not able to reach the surface and hence the gas in these locations is relatively cool and
hence glows less brightly.
Sunspots generally appear in groups. As the group moves with the Sun’s rotation,
the sunspots in front are called the “preceding members” of the group, while the ones
lagging behind are referred to as the “following members”. The line joining the preceding and the following spots of a bipolar group at the beginning of solar cycle is almost
parallel to the solar equator. But with time, as the cycle progresses, the tilt of this
line with the equator increases. This tilt of sunspots with the equator is known as the
Joy’s Law. At any time, the preceding and following members have opposite polarities.
Recent investigations (Hiremath, 2007 ) suggest that majority of the sunspots occur
as bipolar. Also, all the preceding members in a particular hemisphere have the same
polarity as that of its hemisphere. Another interesting phenomenon is that the Sun’s
polarity pattern completely reverses itself in 11 years - the same period as the solar
sunspot cycle. Thus, the Sun’s magnetic pattern repeats itself only after two sunspot
cycles, hence this phenomenon is referred to as the 22-year solar cycle. Figure 2.7
shows the variation of magnetic field lines in the Sun due to the differential rotation
of the solar plasma.
Figure 2.7: Solar Magnetic Field Lines due to Differential Rotation
Image Courtesy: www.scientificgamer.com
The picture of magnetic field in sunspots can be expressed as follows (Bhatnagar,
2005 ) 1. The magnetic field is generally symmetrical around the axis of the spot in the
2.5. Wilson Effect
25
umbra.
2. The maximum value of the field is at the center of the umbra, and the lines
of force are perpendicular to the solar surface. The darkest position in a spot
corresponds to the highest field strength.
3. Away from the umbral center, the strength of the field decreases and the lines of
force near the penumbral boundary are inclined to the vertical.
4. All sunspots have detectable magnetic fields and the strength increases with spot
size.
The magentic field strength decreases across a spot from a maximum near the
center of the umbra to a small value beyond the outer boundary of the penumbra. An
approximate empirical relation can be given for the magnetic field at a radial distance
r from the spot center -
B = Bm (1 −
r2
b2 )
where B is the strength of magnetic field at a radial distance r from the spot center
Bm is the maximum field strength
and b is the radius of the spot
2.5
Wilson Effect
Due to the rotation of the Sun, the sunspots appear to travel across the Sun from east
to west. During its disk passage, appearance of the sunspot changes from elongated
shape near the eastern limb, to become round near the disk center, and again changing
to elongated near the western limb. This is because of the projection effects, as the
Sun is a spherical body which is projected onto a plane in the images.
Figure 2.8: The Wilson Effect
Image Courtesy: www.forum.2astro.dk
2.6. Motivation of the Project
26
It is observed that the width of the penumbra on the side of a spot away from the
limb decreases at a greater rate than the penumbra close to the limb side (Bray and
Loughhead, 1964 ). This phenomenon is termed as the Wilson effect. This has been
clearly shown in the Figure 2.8.
2.6
Motivation of the Project
Our Sun is a star. Understanding of the processes on the Sun brings us a little closer to
understanding all other stars. Sunspots are an important part of the Sun that affect the
energy flowing in the Sun. Nearly after 400 yeard after the discovery of sunspots, the
genesis of sunspots and the physics of the solar cycle is still not completely understood
(Hiremath, 2010a; 2010b; 2008; 2006 ). The knowledge of their origin and duration is
very crucial for understanding the solar irradiation, that changes from one solar cycle
to another. Recent evidences show that the solar cycle and the activity phenomena
play an important role in affecting the Earth’s climate and its environment. Sunspot
activities spew highly energetic particles into the space. They are also associated with
solar flares and coronal mass ejections. These catastrophic solar events may lead to
breaking down of our communication links by frying the satellites and communication
systems. The high energetic particles released from the Sun may also pose dangers to
any astronauts in space. All these disastrous events can be minimized if the origin of
sunspots are understood and are properly predicted.
In addiction to the phenomenon of solar dominant differential rotation (∼ 2 km/sec),
there is also a large scale weak (∼ a f ew m/sec) plasma flow from the equator towards
the poles along the meridian of the Sun. Such a large scale flow is called the meridional flow, that is used to input in the so-called solar dynamo models which apparently
explain some solar cycle activity phenomena. Hence, accurate estimate of steady and
time-dependent meridional flow velocity is necessary. For accurate estimation of either the solar rotation or meridional flow velocity, accurate estimation of heliographic
coordinates is quite important.
The Kodaikanal Solar Observatory has a large amount of solar data from as early
as 1901. If this data is properly analyzed, many physical phenomena of the Sun that
are not understood can be solved. Already existing information from the Greenwich
data were calculated manually, without any error bars. Hence, they may include bias
in the measurements of heliographic coordinates and area of the sunspots. To avoid
this, a proper method has to be developed, which minimizes the human errors. Aim
of this project is to develop an algorithm, using the Kodaikanal Observatory whitelight images data, to detect the sunspots and to calculate their positions on the Sun
as well as their area as accurately as possible with error bars. To knowledge of this
author, this is the first time such an unbiased estimate of sunspots area and positional
measurements is undertaken.
Chapter 3
DETECTION AND ESTIMATION
OF HELIOGRAPHIC
COORDINATES AND AREA OF
SUNSPOTS FROM KODAIKANAL
DIGITIZED DATA
The images used for analysis in this project were taken in the Kodiakanal Solar Observatory, established in 1899. Over 100 years of white light images were taken on
photographic plates. It is very cumbersome to extract useful information from these
plates. Hence, all these images were digitized. The CCD used for this purpose was
a 4k × 4k format CCD-camera based digitizer unit. The resulting images were calibrated for relative plate density and aligned in such a way that the solar north is in
the upward direction. An example of a white-light image of the Sun is given in Figure
3.1. The black cross-wire in the center of the image represents the east-west direction
of the sky.
Figure 3.1: White-light Image of the Sun from Kodaikanal Observatory
3.1. Detection of the Edge
28
As mentioned in the previous chapter (Section 2.6 ), aim of this project is to extract
sunspots from the Sun’s images and to calculate their heliographic coordinates and
their area as accurately as possible. Important steps of this analysis are as given
below:
1. Detection of the edge of the Sun.
2. Calculation of center and radius of the Sun.
3. Limb darkening removal from the image.
4. Computation of heliographic coordinates for all the pixels in the image.
5. Detection of sunspots.
6. Separation of umbra from sunspots.
7. Calculation of average heliographic coordiantes (with error bars) of sunspots.
8. Calculation of area (with error bars) of the sunspots as well as the umbrae.
Each of these steps is explained in detail in the following sections.
3.1
Detection of the Edge
In order to estimate the heliographic coordinates of the sunspots, it is important to
calculate the center and radius of the solar disc. It is necessary to detect the edge
of the disc for this calculation. Edge detection uses the concept of sudden gradient
change near the edges. The Sobel Operator is used for edge detection for each of the
images. The Sobel operator is explained below.
Sobel Operator The sobel operator, also called as a sobel filter performs a two-dimensional spatial
gradient measurement on the image. Thus, high spatial frequencies of the images are
emphasized, that are the edges. Normally, it is used to find the approximate absolute
magnitude of the gradient at each point in a grayscale image.
The sobel filter consists of two 3 × 3 filters, that are to be convoluted on the image.
They are -
3.2. Calculation of Center and Radius
29
These kernels are applied separately along each direction to produce separate measurements of the gradient component in each direction. These can then be combined
to find absolute magnitude of the gradient at each point. It Gx and Gy are the gradient
components along x and y directions respectively, then the magnitude of the gradient
is given by p
|G| = (Gx )2 + (Gy )2 .
The angle of orientation of the edge, relative to the pixel grid is given by G
θ = tan−1 ( Gxy ).
Figure 3.2: Detected Edge of the Sun’s Image from the Kodaikanal Observatory
Since intensity function of a digital image is known only at discrete points, the
derivatives of this function cannot be defined unless it is assumed that there is an
underlying continuous intensity function which has been sampled at the image points.
This means, derivatives of any particular point are functions of the intensity values of
all image points. Figure 3.2 shows the detected edge of the Sun by the sobel filter.
3.2
Calculation of Center and Radius
Having detected the edge of the Sun, the next major step is to calculate the coordinates
of the center of the Sun’s image as well as the radius of the solar disc in each image.
These parameters are very important for the estimation of heliographic coordinates
of the sunspots. The parameters are estimated by fitting a circle using the points
detected at the edge by the sobel filter. Least-square fitting produces the best fit and
one can determine all the three parameters (radius and two coordinates of the center)
simultaneously and uniquely. Procedure for obtaining these coordinates is as follows.
Let xi and yi be the x- and y-coordinates of the detected pixels, respectively, where
i varies from 1 to N, given N is the total number of pixels detected. Let x and y be
the mean of the respective xi and yi coordinates.
3.2. Calculation of Center and Radius
30
That is,
Σxi
N
x=
,
and
y=
.
Σyi
N
Firstly, we convert the (xi , yi ) coordinates into a new system of (ui , vi ) with u i = xi − x ,
and
vi = yi − y .
Let (uc , vc ) be the center of the circle and let R be its radius in this new coordinate
system. Let α = R2 .
Distance of any point (ui , vi ) from the center is =
p
(ui − uc )2 + (vi − vc )2 .
to the least square fit, best fit is obtained when the function S =
P According
2
[g(ui , vi )] is minimized, where g(ui , vi ) = (ui − uc )2 + (vi − vc )2 − α. Hence, the
i
partial derivatives of this functions with respect to α, uc and vc should all be zero.
Condition 1 X
∂g
∂S
=2×
g[ui , vi ]
= 0,
∂α
∂α
i
⇒ −2 ×
⇒
ui 2 +
⇒
P
⇒
X
P
i
P
i
uc 2 +
i
It is known that
i
P
i
P
vi 2 +
i
X
g[ui , vi ] = 0 ,
i
[(ui − uc )2 + (vi − vc )2 − α] = 0 ,
i
ui 2 +
P
(3.1)
P
i
P
P
P
vc 2 − 2[ ui uc + vi vc ] = α ,
i
vi 2 + N [uc 2 + vc 2 ] − 2[uc
i
X
ui + vc
i
X
i
vi ] = N α .
(3.2)
i
P
P
ui = (xi − x) = N x − N x = 0. Similarly,
vi = 0. Putting
i
this in equation (3.2), we get X
X
ui 2 +
vi 2 + N [uc 2 + vc 2 ] = N α .
i
i
i
(3.3)
3.2. Calculation of Center and Radius
31
Condition 2 X
∂S
∂g
=2×
g[ui , vi ]
= 0,
∂uc
∂u
c
i
⇒
P
i
(3.4)
(ui − uc )g(ui , vi ) = 0 .
On Expansion ⇒
-
P
ui 3 +
i
P
i
ui vi 2 − 2uc
P
i
ui 2 − 2vc
P
i
ui vi − uc
P
N αuc = 0 .
i
ui 2 − uc
P
i
vi 2 − N uc 3 − N uc vc 2 +
Substituting the value of N α from equation (3.3), the following equation is obtained
uc
X
ui 2 + vc
X
i
i
1X 3 X
ui +
ui vi 2 ] .
ui vi = [
2 i
i
(3.5)
Condition 3 X
∂g
∂S
=2×
g[ui , vi ]
= 0.
∂vc
∂vc
i
(3.6)
Proceeding the same way as in condition 2, the following equation is obtained uc
X
ui vi + vc
X
i
i
1X 3 X
vi 2 + = [
vi +
vi ui 2 ] .
2 i
i
(3.7)
Solving simultaneous equations (3.5) and (3.7), the values of uc and vc are obtained.
Then from equation (3.3) α = R2 = (uc 2 + vc 2 ) +
and
√
1 X 2 X 2
[
ui +
vi ] ,
N i
i
(3.8)
r
1
[Σui 2 + Σvi 2 ] .
(3.9)
N
From this equation, the value of radius, R of the solar disc is estimated. The
next step is converting (uc , vc ) into the original coordinate system, that is obtained by
adding the respective mean values
R=
α=
(uc 2 + vc 2 ) +
xc = uc + x ,
and
yc = vc + y .
Hence, using this method, the coordinates of the center of the image (xc , yc ) and
the radius of the solar disc, R, is computed for each image.
3.3. Removal of Limb Darkening
3.3
32
Removal of Limb Darkening
When the Sun is observed, the center of the image appears more brighter than the
limb. This is because at the center, the light comes from the deeper hotter layers
of the Sun. Towards the limb, light from the cooler upper layers is observed. As a
result, a gradual decrease of intensity from the center to the limb is observed. Such a
phenomenon is known as the limb darkening. It is very crucial to remove this effect
before any further analysis of the Sun’s image is done. To remove limb darkening, the
following procedure is adopted on each of the images.
Figure 3.3: Limb Darkening Phenomenon
For each of the images, concentric circles are drawn from the center to the edge,
each of whose radius increases by one unit. The median of intensities in each of the
concentric circles correspond to the radius of that circle. Hence, a fixed intensity value
for each radius is obtained. A polynomial of degree 3 fits very well for these intensities.
The intensity-radius graph for the same is given in Figure 3.3.
(a) Original Image
(b) Processed Image
Figure 3.4: An Example of Limb Darkening Removal from the Sun’s Image Obtained
from Kodaikanal Observatory
3.4. Computation of Heliographic Coordinates
33
If r is the radius of a particular pixel, I is it’s intensity and I(r) is it’s intensity
profile according to the fit, then its corrected value is Icorrected =
I
.
I(r)
By applying this formula for all pixels in the digitized image, a uniformly bright
image is obtained, which suggests that the limb darkening is removed. An original
image, along with its limb darkening removed image is illustrated in Figure 3.4.
3.4
Computation of Heliographic Coordinates
The next major step is finding heliographic coordinates, θ and L, for each pixel in every
image frame. The heliographic latitude, θ, is measured from 0o to +90o from the solar
equator to the north pole and from 0o to −90o to the south pole. The heliographic
longitude, L, is measured as the angle between the solar meridian and the Carrington’s
zero meridian towards west, from 0o to 360o . Distance l of a pixel from the central
meridian is different from the heliographic longitude. It is measured from 0o to ±90o
and is taken positive towards the west.
As a result of the solar rotation and the revolution of Earth around the Sun, the
orientation of the solar axis, the positions of the solar equator and its zero meridian
change daily. The solar equator is inclined at an angle of i = 7.25o to the ecliptic, i.e.,
the plane of orbit of the Earth. Hence, the heliographic latitude Bo of the center of
the solar disk varies between +7.25o and −7.25o . Also, the polar angle P between the
solar axis and the north-south direction in the sky changes between ±26.37o , where
(+) is the solar axis inclined towards east and (-) is an inclination towards the west.
Another important term is Lo , which is the heliographic coordinate of the apparent
center of the Sun, which falls periodically from 360o to 0o . The points at which Lo = 0o
is taken as the beginning of a new synodic solar rotation.
Daily computation of Bo , Lo and P is necessary for the estimation of heliographic
coordinates.
, where JD is the Julian Date of observation and T is the numLet T = JD−2415020
36525
ber of Julian centuries since epoch 1900 Jan 0.5.
The geometric mean latitude L’, mean anomaly g and right ascension Ω of the
ascending node of the Sun are L0 = 279o .69668 + 36000o .76892T + 0o .0003025T 2 ,
g = 358o .47583 + 35999o .04975T − 0o .00015T 2 − 0o .0000033T 2 ,
and
Ω = 259o .18 − 1934o .142T .
The true longitude λJ , of the Sun is given by λJ = L 0 + C ,
3.4. Computation of Heliographic Coordinates
34
where C is called the equation of the center and is defined as
C = (1o .91946 − 0o .004789T − 0o .000014T 2 )sin(g) + (0o .020094 − 0o .0001T )sin(2g) +
0o .000293sin(3g) .
The apparent longitude of the Sun, λa consists of the true longitude, λJ and
corrections for aberration and nutation λa = λJ − 0o .00569 − 0o .00479sin(Ω) .
The actual physical ephemeris computations begin with φ=
360
(JD
25.38
− 2398220) .
The inclination of the equator of the Sun relative to the ecliptic plane is I = 7.25o
and the longitude of the ascending node of the solar equator, K is
K = 74o .3646 + 1o .395833T .
X and Y are defined such that tan(X) = −cos(λ0 )tan()
and
tan(Y ) = −cos(λJ − K)tan(I).
where is the obliquity of the ecliptic and λ0 is the Sun’s apparent longitude corrected for nutation.
The mean obliquity o is determined from o = 23o .452295 − 0o .0130125T − 0o .00000164T 2 + 0o .000000503T 3 ,
and with the correction of nutation as,
= o + 0o .00256 cos(Ω) .
Finally, polar angle P, Bo and Lo can be computed as follows.
P=X+Y ,
Bo = sin−1 [sin(λJ − K)sin(I)] ,
Lo = tan−1 [
sin(Ω−λJ )cos(I)
]
−cos(Ω−λJ )
+M ,
where M = 360o − φ.
φ must be reduced to the range 0o − 360o by subtracting integral multiples of 360o .
The solar radius as viewed from the Earth changes daily due to the revolution of
Earth around the Sun. Hence, the resolution of the pixels changes daily as well.
3.4. Computation of Heliographic Coordinates
35
n = JD - 2451545.0 ,
g = 357o .528 + 00 .9856003 n .
Here, n is the number of days from J2000.0 and g is the mean anomaly, as measured
from epoch J2000.0. Reduce g into the of range 0o to 360o by adding multiples of 360o .
Distance of the Sun from Earth, R0 , in AU isR0 = 1.00014 − 0.01671cos(g) − 0.00014cos(2g)
The Semi-diameter of the Sun, Rad in arc-seconds is Rad = ( 0.2666
)o × 360000
R0
Mathematical determination of the heliographic coordinates is based on the polar
coordinates (r, θ0 ). This means, before computation of heliographic coordinates, the
observed Sun’s image in cartesian coordinates is transformed to polar coordinates. The
angular distance ρ of any pixel from the center of the solar disc is then determined
from the equation
sin(ρ) =
r
R
,
where R is the radius of the solar disc as described in section 3.2, using circle fit. To
calculate the heliographic latitude θ and longitude l from the central meridian, of any
pixel, the following equations are used:
sin(θ) = cos(ρ)sin(Bo ) + sin(ρ)cos(Bo )sin(θ0 ) ,
sin(l) =
cos(θ0 )sin(ρ)
cos(θ)
.
The heliographic longitude is obtained by adding the value of Lo to the the longitudinal difference l of the pixel from the central meridian.
L = Lo + l
For more accurate results, correction for distortion of the Sun’s image is considered.
Telescope objective lens with a short focal length can contribute to distortion of the
projected image. This distortion is corrected by using the following empirical relations.
T =
Ro = 29.5953 cos[ cos
,
Rad
15
−1 (−0.00629T )
3
ρ0 = Ro ×
r
R
+ 240] ,
,
and
0
sin(ρ )
ρ = sin−1 ( sin(R
) − ρ0 .
o)
This ρ is then taken as the corrected angular distance and then the heliographic
coordinates are computed as mentioned above.
3.5. Detection of Sunspots
3.5
36
Detection of Sunspots
The main techniques used in this project for the detection of sunspots are from the
field of mathematical morphology, which is a non-linear image processing technique
developed by Matheron (1975) and Serra (1982). This method uses shape and structure
of digital images to analyze the features present in the image. All the operations
of mathematical morphology can be broken down into two basic operators: erosion
and dilation, which use a structuring element to probe the image. The shape of the
structuring element may be anything, but the most common choices are crosses, circles
and squares as given in Figure 3.5. The white dots represent the origin of the respective
structuring elements.
Figure 3.5: Common Structuring Elements
Image Courtesy: Phd Thesis, Watson F.T., 2012
Each of the operators is explained briefly below.
3.5.1
Erosion
The result of an image, X, eroded by a structuring element B, consists of all the point
h, for which the translation of B by h fits inside X. This is represented as below.
X B = {h|Bh ⊆ X}.
Figure 3.6: An Irregular Shape Eroded by a Circular Structuring Element.
The shape with the thick line is the result of erosion.
Image Courtesy: Phd Thesis, Watson F.T., 2012
3.5. Detection of Sunspots
37
Erosion has the effect of shrinking bright regions in the input image, so the eroded
image is a subset of the input image (Figure 3.6 ). The erosion results in a darker
image and darker objects become bigger.
3.5.2
Dilation
If B has a center at origin, then the dilation of X by B can be thought as the locus of
the points covered by B, when the center of B moves inside X. This is expressed as:
X ⊕ B = {h|Bh ∩ X 6= φ}.
The dilation has an expanding effect filling in the small dark holes in the images.
This method leads to a brighter image, reducing, at the same time, the size of dark
objects (Figure 3.7 ).
Figure 3.7: An Irregular Shape Dilated by a Circular Structuring Element.
The shape with the thick line is the result of dilation.
Image Courtesy: Phd Thesis, Watson F.T., 2012
3.5.3
Opening
Opening of an input image, X, by a structuring element B, is defined as an erosion
followed by a dilation. It is expressed as follows.
X ◦ B = {Bh |Bh ⊆ X}
This operation acts as a smoothening filter on the image. Overall effect is the
deletion of small bright regions, smaller than the structuring element, while preserving
the rest of the image.
3.5.4
Closing
Closing of a image is defined as a dilation, followed by an erosion. The result is the
deletion of darker points smaller than the structuring element and preserving the rest
of the image.
3.6. Separating the Umbra of a Sunspot
3.5.5
38
Top-hat Transformation
Top-hat transformation consists of subtracting the opening image from the original
image. With opening, all the small bright objects of the image are erased and in the
next step, by subtracting this image from the original image, only the bright objects
are obtained.
top_hat(X, B) = X − (X ◦ B).
The above concepts are used to detect the sunspots from the images of the Kodaikanal Observatory. After the limb darkening is removed, the image is inverted by
taking the reciprocal of intensities at each point. This transformation results in the
sunspots appearing brighter on a darker background. This makes it easy to extract
sunspots from the image. Next, a top-hat transformation is applied. The structuring
element used in this case is a disk of radius 50 units. A certain intensity threshold,
obtained from taking mean of values from several sunspots is applied. As a result,
a frame consisting of the bright sunspot regions and a few artifacts is obtained. A
morphological opening with a circle of radius 3 pixels is applied leading to the removal
of the small noise elements. Some more noise still persists in the resulting image. This
cannot be removed without affecting the sunspots. Thus, all the regions are labeled
and sunspot regions are selected manually. After applying mask filter over these labelled regions that makes the intensity of all the selected regions equal to unity, they
are multiplied with the original image to obtain only the sunspot regions in the image.
3.6
Separating the Umbra of a Sunspot
To obtain more information on the formation and evolution of sunspots, it is useful to
have separate information on the darkest region of the sunspot, the umbra. Automated
umbra detection has been examined in the past with examples such as the inflection
point method of Steinegger et al.(1997), the cumulative histogram method of Pettauer
and Brandt (1997), the fuzzy-logic approach of Fonte and Fernandes (2009) and the
morphological method of Zharkov et al. (2005). In this project, a simple thresholding
method is used.
(a) A Typical Sunspot
(b) Extracted Sunspot
(c) Separated Umbra
Figure 3.8: An Example of the Detection
After the sunspot regions are detected using the techniques of mathematical morphology, each region is normalized by dividing the intensities of sunspot’s pixels with
3.7. Computation of Average Heliographic Coordinates of Sunspots
39
its maximum value. A threshold that is unique for each of these regions is then applied.
The threshold is 15 % more than the minimum value in each region. This threshold
is taken from observing several sunspots and considering the mean of all the values.
These processes are repeated for each of the images to obtain the umbrae separated
from all the sunspots.
An example of extracted sunspot and the separated umbra is given in the Figure
3.8.
3.7
Computation of Average Heliographic Coordinates
of Sunspots
After the whole spot and umbra have been detected, accurate calculation of their
position on the Sun is quite important. For this purpose, the heliographic coordinates
detected for each pixel are used. Computation of average heliographic coordinates for
the sunspots is based on the weighted mean of the coordinates of the pixels constituting
the spot. The formulas used are given below.
P
θn ×In
nP
θspot =
In
,
n
P
lspot =
ln ×In
nP
In
,
n
where θn is the latitude, ln is the longitude from the central meridian and In is the
intensity of the nth pixel and n varies over all the pixels of the sunspot. The errors,
δθ and δl in these heliographic coordinates are computed as follows.
δθ =
√σθ
N
,
δl =
√σl
N
.
Here, σθ and σl denote standard deviation of latitude and londitude difference
values of the sunspot pixels, and N is the total number of pixels in the given spot.
Using the above mentioned formulae, the heliographic coordinates and their errors for
each sunspot in every image is successfully estimated.
3.8
Computation of Area of Sunspots
The most important part and the ultimate aim of this project is the calculation of
umbra area to penumbra area ratio. For this purpose, the whole spot area and the
umbral area are calculated separately. In general, area is the product of number of
pixels and area of each pixel. If one knows the size of a pixel. then area of pixel is
square of the pixel size. Pixel size is computed as follows.
pixel_size =
Radius of Sun in arcseconds
Radius of Sun in pixels
=
Rad
R
3.8. Computation of Area of Sunspots
40
where Rad is calculated in section 3.4 and R is given by equation (3.9) in section 3.2.
The number of pixels in the whole spot and umbra is then estimated and multiplied
by area of the pixel. This area is then expressed in millionth of area of solar hemisphere,
which is the standard unit for measuring the area of sunspots.
The Sun is a sphere, but it is flattened on the image. This leads to some projection
effects at the edge of the Sun. Owing to the spherical shape of ths Sun, the area of
sunspots appear less than the true area. This effect is also called as the foreshortening
in area. This projection effect near the limb is corrected as follows.
Area, A0 of sunspot = N o. of pixels × P ixel area,
Corrected Area (A) =
A0
cos(δ)
where cos(δ) = sin(Bo )sin(B) + cos(Bo )cos(B)cos(l), where all the terms have their
usual meanings as proposed in section 3.4.
The errors in the area of whole sunspot and umbra are determined by moving
the boundary inwards and outwards by one pixel, since we are confident in locating
the boundaries to within one pixel of their true location. The penumbra area is then
calculated by subtracting the umbra area from the whole spot area and the required
umbra-penumbra ratio is then obtained.
Chapter 4
RESULTS AND DISCUSSIONS
For this project, the white-light images of the year 2011, obtained from Kodaikanal
Observatory are analyzed. The whole procedure is performed using the techniques
specified in the last chapter. After the complete analysis, two files - one containing the
radius values for each day and another containing the latitude, longitude and umbra
area to penumbra area ratio for each sunspot - are obtained. A typical table of daily
center and radius values for the images of January, 2011 is given in Table 4.1.
Table 4.1: Estimated Center and Radius Values
Year Month Date and Time X-Center Y-Center Radius (No. of Pixels)
2011
1
1.340278
2048
2048
1522.84
2011
1
2.362500
2048
2048
1519.16
2011
1
4.340278
2048
2048
1523.65
2011
1
5.315972
2048
2048
1523.06
2011
1
5.345139
2048
2048
1526.33
2011
1
6.331250
2048
2048
1521.75
2011
1
7.322917
2048
2048
1522.77
2011
1
8.347222
2048
2048
1524.53
2011
1
9.383333
2048
2048
1524.16
2011
1
10.427083
2048
2048
1523.38
2011
1
11.333333
2048
2048
1525.38
2011
1
12.438889
2048
2048
1526.99
2011
1
13.395833
2048
2048
1524.86
2011
1
16.625000
2048
2048
1523.68
2011
1
17.333334
2048
2048
1523.06
42
Year Month Date and Time X-Center Y-Center Radius (No. of Pixels)
2011
1
18.322916
2048
2048
1522.81
2011
1
18.447916
2048
2048
1523.94
2011
1
19.329861
2048
2048
1522.96
2011
1
20.336805
2048
2048
1522.85
2011
1
21.340279
2048
2048
1523.38
2011
1
22.324306
2048
2048
1521.30
2011
1
23.326389
2048
2048
1522.54
2011
1
24.326389
2048
2048
1519.10
2011
1
25.364584
2048
2048
1521.62
2011
1
26.322916
2048
2048
1521.07
2011
1
27.597221
2048
2048
1521.92
2011
1
28.345139
2048
2048
1522.67
2011
1
29.378471
2048
2048
1522.31
2011
1
30.338194
2048
2048
1520.16
2011
1
31.340973
2048
2048
1519.98
In Table 4.2, a part of the final result file for February 2011 is given. For each
detected sunspot, the date and time of observation, the heliographic coordinates with
the respective error bars, the corrected whole spot area, the umbra area, the penumbra area and the umbra-penumbra area ratio with the corresponding error bars are
presented.
In order to validate our detected method of sunspots and computation of their area
and heliographic coordinates, the different parameters of the sunspots are compared
with the estimated parameters obtained from different studies. One such comparison
is with the results of Debracan Sunspot observations. This comparison is done for a
data set of one year. Typical scatter plots of heliographic coordinates (Figures 4.1 and
4.2 ), area (Figures 4.3, 4.4 and 4.5 ) and of umbra-penumbra area ratio (Figure 4.6 )
are presented. The variation of whole spot area and umbra-penumbra area ratio over
the year is also plotted and compared with the Debracan data. Figures 4.7 and 4.8
illustrates these plots.
2
2
2
2
2
2
2
2
2
2
2
2
2
2011
2011
2011
2011
2011
2011
2011
2011
2011
2011
2011
2011
2011
12.329861
12.329861
12.329861
11.333333
10.331250
10.331250
9.357639
8.324306
4.649305
4.649305
3.326389
2.440972
2.440972
Year Month Date and Time
δB
l
δl
WA
57.380
0.014 42.368
19.272
0.015 -26.321 0.010 25.199
-19.399 0.011 -26.641 0.012 34.884
-19.651 0.011 -21.519 0.012 40.469
-3.805
-20.591 0.008 -18.231 0.020 31.826
-20.234 0.011
5.432
5.032
3.450
4.690
5.641
δW A
6.800
5.492
6.013
6.543
6.904
5.382
5.661
0.021 35.037 10.026
0.010 34.042
0.012 30.020
0.011 15.201
0.010 24.599
0.011 -33.471 0.015 19.413
0.012
-4.470
-6.566
6.213
-6.092
-20.734 0.009 -24.280 0.017 26.736
19.947
15.616
-17.985 0.013
-18.673 0.010
-20.252 0.011
-20.409 0.012
-23.081 0.011 -13.103 0.012 30.338
B
δU A
PA
7.123
2.769 20.474
2.497
3.989 22.233
2.558 19.142
6.886
8.407
9.066
9.435
3.009 16.792
2.833 25.818
2.729 31.033
10.567 4.009 31.801
9.593
7.594
1.592
2.263
0.953
1.615
2.160
δP A
1.009
0.466
1.134
0.953
1.046
UA
PA
3.791
2.659
3.283
2.534
2.915
2.824
2.123
0.000
0.132
0.084
0.199
0.122
0.082
A
δ UP A
0.501
0.351
0.304
0.332
0.431
0.397
0.066
0.074
0.056
0.100
0.123
0.075
1.819 -0.047
0.000 35.037 10.026 0.000
12.526 3.538
0.000
17.096 3.839 16.946
9.546
8.078
12.006 3.075 12.593
15.509 3.480 14.829
UA
Table 4.2: Estimated Heliographic Coordinates, Whole Spot Area and Umbra-Penumbra Area Ratio of Sunspots
43
44
Figure 4.1: Scatter plot of Kodaikanal and Debracan Latitudes
Figure 4.2: Scatter plot of Kodaikanal and Debracan Longitude Differences from the
Central Meridian
45
Figure 4.3: Scatter plot of Kodaikanal and Debracan Whole Spot Areas
Figure 4.4: Scatter plot of Kodaikanal and Debracan Umbra Areas
46
Figure 4.5: Scatter plot of Kodaikanal and Debracan Penumbra Areas
Figure 4.6: Scatter plot of Kodaikanal and Debracan Umbra-Penumbra Area Ratios
One can notice from the scatter plots that there is almost a perfect correlation
the Kodaikanal and Debracan results, hence validating our method of detection of
47
sunspots. The χ2 denoted on the plots is calculated by normalizing the values and
error bars, as the number of data points is too large and the error bars are too small.
Figure 4.7: Variation of Whole Spot Area with Time
Figure 4.8: Variation of Umbra-Penumbra Area Ratio with Time
From the variation plots, it is known that both the Kodaikanal and Debracan
results follow a similar trend and the Debracan results are well within the our error
bars.
4.1. Advantages and Disadvantages of the New Method
4.1
48
Advantages and Disadvantages of the New Method
The devised method to detect sunspots and to estimate their parameters from the
digitized images of Kodaikanal Observatory is quite efficient. It automatically detects
the edge of the solar disc, computes its radius and center simultaneously and uniquely,
removes limb-darkening and computes heliographic coordinates - all in one go. It also
detects the sunspots and estimates the required parameters, whose results perfectly
match with those of already existing results, such as the Debracan sunspot results. Our
method also computes the error bars in all the estimates, making the computation more
accurate. It is a semi-automatic code, thus reducing the errors introduced by human
bias.
One most important disadvantage of this code is that it is not fully automatic.
It needs a minute human interaction for detection of sunspots. This is because the
images are not fully clear. There are always some artifacts and noise pertaining in
the images, even after processing. Another feature is that it uses a certain intensity
threshold for umbra detection, which is not particularly unique. This may result in
some errors in the future.
4.2
Conclusion
A semi-automatic algorithm is successfully developed to analyze the Kodaikanal solar
white light images. The algorithm includes computation of the radius and center of the
solar disc simultaneously and uniquely. Our developed algorithm further detects the
sunspots with a little manual help and estimates the average latitude and longitude
of each of the detected sunspots. It further separates the umbra from each sunspot
and computes the area of both the whole spot and umbra. The results obtained
are compared with the existing Debracan data and it is found that the heliographic
coordinates of sunspots and their areas, estimated by our method are almost similar to
the Debracan results. Hence, this validates our methodology of detection of sunspots
and estimation of area and their heliographic coordinates.
Bibliography
[1] B. Ravindra, T.G. Priya., et.al. 2013, ’Digitized archieve of the Kodaikanal images: Representative results of solar cycle variation from Sunspot area determination’, A & A 500, A19(2013).
[2] Jagdev Singh, B. Ravindra, 2012, ’Twin Telescope observations of the Sun at
Kodaikanal Observatory’, Bull, Astr.Soc.India (2012).
[3] C. Denker, A. Johannesson., et.al. 1998, ’Synoptic Hα Full-Disk Observations of
the Sun from the Big Bear Solar Observatory’, Solar Physics 184: 87-102.
[4] H.R. Neilson, J.B. Lester, 2013, ’Spherically symmetric model stellar atmospheres and limb darkening’, A & A 556, A86(2013).
[5] W.T.Thompson, 2006, ’Coordinate systems for solar image data’, A & A 449,
791-803 (2006).
[6] S. Zharkov, V. Zharkova, S. Ipson, A. Benkhalil, 2005, ’Technique for Automated Recognition of Sunspots on Full-disk Solar Images’, EURASIP Journal in
Applied Signal Processing 2005:15, 2573-2584.
[7] J.J. Curto, M. Blanca, E. Martinez, 2008, ’Automatic Sunspots Detection on
Full-Disk Solar Images using Mathematical Morphology’, Solar Physics (2008)
250: 411-429.
[8] Suruchi Goel, Shibu K. Mathew, 2014, ’Automated Detection, Characterization, and Tracking of Sunspots from SoHO/MDI Continuum Images’, Solar
Physics(2014) 289: 1413-1431.
[9] Lajos Gyori, ’Automation of Area Measurement of Sunspots’, Solar Physics 180:
109-130, 1998.
[10] K.M. Hiremath, M.Hedge, ’Rotation Rates of Coronal Holes and their probable
anchoring depths’, 2013, The Astronomy Journal, 763:137.
[11] U. Grossmann-Doerth, W. Schmidt, 1981, ’The Brightness Distribution in
Sunspot Penumbrae’, Astron. Astophys. 95, 366-372(1981).
[12] Peter Meadows, 2002, ’The Measurement of Sunspot Area’, British Astronomical
Association.
[13] D.H.Ballard, ’Generalizing the Hough Transform to Detect Arbitrary Shapes’,
Pattern Recognition Vol. 13, No. 2, pp. 111 122, 1981.
49
Bibliography
50
[14] F.Watson, L.Fletcher, S.Dalla, S. Marshall, ’Modelling the Longitudinal Asymmetry in Sunspot Emergence: The Role of the Wilson Depression’, Solar Phys
(2009) 260: 5-19.
[15] T.Baranyi, ’Comparison of Debrecen and Mount Wilson/Kodaikanal sunspot
group tilt angles and the Joy’s law’, MNRAS 447, 1857-1865 (2015).
[16] T.Baranyi, A. Ludmany, L. Gyori, H.E. Coffey, ’Comparison of Three Sunspot
Area Databases’, ESA SP-448, December 1999.
[17] K.R. Sivaraman, ’An Overview of the Results from Synoptic Observations at
Kodaikanal’, ASP Conference Series, Vol. 140, 1998.
[18] T. Pettauer, P.N. Brandt, ’On Novel Methods to Determine Areas of Sunspots
from Photoheliograms’, Solar Physics 175: 197-203, 1997.
[19] H. Cakmak, ’A Digital Method to Calculate the True Areas of Sunspot Groups’,
Astrophysics, 2014.
[20] Lan Yu, Linhua Deng, Song Feng, ’Automated Sunspot Detection Using Morphological Reconstruction and Adaptive Region Growing Techniques’, Proceedings
of the 33rd Chinese Control Conference, July 28-30, 2014.
[21] L. Balmaceda, S.K.Solanki, N.Krivova, ’A cross-calibrated sunspot areas time
series since 1874’, Mem. S.A.It.Vol.76, 929, 2005.
[22] Cidalia C. Fonte, Joao Fernandes, ’Application of Fuzzy Sets to the Determination of Sunspot Areas’, Solar Physics (2009) 260: 21-41.
[23] I.Poljancic, R. Brajsa, D. Hrzina, H. Wohl, A. Hanslmeier, W. Potzi, T. Baranyi,
A. Ozguc, J. Singh, V. Ruzdjak, ’Differences in Heliographic Positions and Rotational Velocities of Sunspot Groups from Various Observatories’, Cent. Eur.
Astrophys. Bull. 35 (2011) 1, 59-70.
[24] Robert Howard, Peter A. Gilman, Pamela I. Gilman, ’Rotation of the Sun Measured from Mount Wilson White-light Images’, The Astrophysical Journal, 283:
373-384, 1984 August 1.
[25] K. R. Sivaraman, S.S. Gupta, ’Measurement of Kodaikanal White-light images A comparison of 35 years of Kodaikanal and Mount Wilson Sunspot Data’, Solar
Physics 146: 27-47, 1993.
[26] The Universe, Roger A. Freedman, Robert M. Geller, William J. Kaufmann III,
Book.
[27] Exploration of the Universe, Abell, Book.
[28] Astonomy, J. Pasachoff, Book.
[29] Astrophysics for Physicists, A.R.Choudary, Book.
[30] The Sunpots, R.J. Bray, R.E. Loughhead, Book.
[31] The Quiet Sun, E.G. Gibson, Book.
Bibliography
51
[32] The Sun - An Introduction, Michael Stix, Book.
[33] Solar Astronomy, A. Bhatnagar, Book.
[34] Solar Astronomy Handbook, R. Beck, H. Hilbrecht, K. Reinsch, P. Volker, Book.
[35] www.wikipedia.com, web
[36] www.petermeadows.com, web
[37] Greenwich Photoheliographic Results
[38] Debracan Sunspot Catalogues, fenyi.solarobs.unideb.hu, web