Download Module3: Life of a Star

Module 3
Life of a Star
Ancient Cosmic Explosions
Activity Guide
ANCIENT COSMIC EXPLOSIONS - ACTIVITY GUIDE
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Introduction
In this project you will study LCOGT observations of supernova remnants to
measure how fast they are expanding and calculate how long ago the supernova
explosion occurred.
Materials
•
•
FITS file of a supernova remnant
A computer with ds9 image editing software installed
Background Science
Supernovae
Supernovae are the violent explosions of stars occurring at the end of their lives.
On average, one supernova goes off every 50 years or so in our Galaxy.
Supernovae release more energy in a single instant than the Sun will produce in its
whole lifetime! If the nearest massive star, Betelgeuse in the constellation Orion,
were to go supernova it would (for a short time) be brighter than the full moon.
There are two main types - Type Ia and II. Type II are the explosions of very
massive stars with mass greater than 8 times the mass of the Sun. Type Ia are the
explosions of stars similar in mass to the Sun, which have a binary companion and
become unstable.
In order these images show an artist’s impression of a Type II supernova, a Type Ia supernova and the
Spaghetti Nebula supernova remnant. Credit: ESO
Type II -These are caused by massive stars that 'live fast and die young', using up
all of their hydrogen and helium fuel in only a few million years — thousands of
times faster than the Sun burns its fuel. When the fuel supply is exhausted the star
must burn heavier and heavier elements until, finally, when it can do no more to
keep itself alive, the inner parts of the star collapse to form a neutron star or black
hole, and the outer parts are flung off in an explosion we call a supernova.
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Type Ia - These happen when a star similar in mass to the Sun reaches the end of
its life as a white dwarf star - a hot, dense core. If this hot core has a binary
companion star (two stars orbiting around a common centre of mass), the white
dwarf will pull matter from the companion star onto its surface, until it becomes
unstable and explodes as a supernova. Type Ia supernova can also be caused by
two white dwarfs merging to the same end.
Supernova Remnants
No matter whether it is a Type Ia or Type II supernova, the enormous explosions
from these stars ejects material into the surroundings at very high velocities,
sweeping up the surrounding interstellar gas into a shell or a giant bubble. This is
known as a supernova remnant. The ejected material and the swept-up
compressed gas are very hot. The shell (or bubble) shines at different wavelengths,
mainly in the X-ray, optical and radio.
Supernova remnants are studied at many different wavelengths from optical light to
X-rays. Different things are happening in different wavelengths; when we observe
in, say the X-ray, we are looking at the bits of the shell that are much hotter than
the bits shining in the optical.
In this activity we will concentrate on the optical emission that comes from the
interaction between the outward moving shell and the interstellar material that
surrounds the supernova. The material is compressed and heated to 10 thousand
degrees Kelvin. In the optical we can see the shocks caused by the expanding
material as it sweeps outwards at high velocities. Using the H-alpha filter we will
specifically see hydrogen gas.
Cassiopeia A
Cassiopiea A is the brightest radio object in the sky so it is very well studied (and
very beautiful)! It exploded about 300 years ago. It is around 11,000 light years
away and is about 8 arcmin across. It was a Type II Supernova i.e. it was formed
by the explosion of a massive star.
E0102 72:
E0102-72 is a supernova remnant located in a nearby dwarf galaxy called the
Small Magellanic Cloud.
Summary of Terms
symbol
description
value
KE
kinetic energy of shell
1044 J
density
density of surroundings
10-21 kg m-3
D
distance to the supernova
Find this value on the web
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Preparation
In this project you will choose one of the following supernova remnants to study
with the final goal of using observational data to calculate its expansion velocity and
its age.
1. Cassiopeia A (Cas A),
1. E0102-72
You can either use observations from the LCOGT data archive or make your own
observations. If you are using images from the LCOGT data archive visit:
http://lcogt.net/observations
Use the search bar to find images of the supernova remnant you have chosen. Find
an image taken using the red (R-band) or H-alpha filter. Once you have clicked on
an image the filter will be listed on the right-hand menu.
Just go to the webpage and type in the name of the supernova remnant you want,
click on the relevant thumbnail and select ‘FITS” from the right-hand options bar.
Be aware that the red filter may be listed as ‘Bessell-R’.
If you are taking you own observations, please note that these objects are very faint
and require long exposure times. The table below provides information on the
exposure time needed for each object and which filters to use.
A full guide to observing with LCOGT can be found online at:
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http://lcogt.net/files/OnSkyGuide.compressed.pdf
R-band (s)
H-alpha (s)
Cas A
120
120
E102-72
200
200
Instructions
1. Start ds9 and open the supernova remnant FITS file you have chosen to
work with.
2. Your image may appear black to begin with, try out different options in the
toolbars. You are looking for an image that shows as much detail as
possible of the supernova remnant.
This image of Cas A is shown demonstrating the following values:
scale > linear > 99%,
colour > cool
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You will now determine the diameter of the remnant by placing a circle over
the shell. This will tell you the angular size of the remnant.
2. Go to Region > Shape > Circle
3. Draw a circle over the supernova, marking out the shape of the shell. Aim
to be as exact as possible.
4. Go to Region > Get Information
5. A box will appear showing the centre co-ordinates of the circle.
6. Next, click on the box marked physical next to the Radius values. Select
WCS and choose the type of units you want - degrees. The example
below shows the radius = 0.0301 degrees.
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7. Note down your radius values below.
Radius in degrees =
___________________________________________________
Now that you know the diameter of your supernova remnant, you will calculate
the age of the supernova remnant and find out when the source star exploded.
Now that you have the radius, you will need to calculate the distance to your
supernova in metres.
8. Calculate the distance to your supernova in metres and not your result in
the table below. Remember that 1 light year = 9.5 × 1015 m.
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Name
Distance
(light years)
Distance
(metres)
Cas A
10,200
E102-72
190,000
9. The next step is to work out the radius of the supernova remnant in
metres by calculating the diameter (d) which is twice the radius. Do this
using the equation below:
d = D tan (θ)
D = distance to remnant in metres
d = diameter of remnant in metres
θ is the angle on the sky in degrees
10. Begin by calculating the angle on the sky for your supernova. This will be
your radius from step 7, but you will need to convert your radius from
degrees into radians: 360 deg = 2π rad or 1 deg = 0.0174 rad. Note your
result on the table below.
11. Next calculate the diameter of your supernova remnant and use this
value to calculate the radius: 0.5 x diameter. Note down your results in
the table below.
Θ degrees
Name
Diameter (m)
Radius (m)
Cas A
E102-72
12. Now that you have the radius, you can work out the volume of your
supernova remnant, a figure that will allow you to work out its mass.
Where V is volume and the R is the radius in metres. Use the equation:
V = (4/3) π R3
Enter your result into the table below.
In this table you will also find a value for density. Remember that density is a
measure of how much mass is in a given volume. For example, the density of
water is 1000 kg m-3, whereas the same volume of iron or lead will be much
heavier. Lead is 10 times denser than water.
During the initial collapse and rebound of the star's core when a supernova
occurs, the outer layers of the star's material are ejected, yet most of the gas in
a supernova remnant is not from the star but is collected afterward. As the
remnant expands, it sweeps up the surrounding interstellar medium, material
which builds up around the edge of the shockwave. The volume through which
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the remnant has expanded and the density of the interstellar medium can be
used to calculate the mass of the remnant.
In the space between the stars, the density of material is very low - there isn’t
much out there! In fact, the average density in space is about 1 x10-21 kg m-3!
This is the density value we will be using in the calculations for our supernova
remnant.
13. With a value for both density and volume you can calculate the mass of
your supernova remnant:
Mass = density x volume
Enter your result into the table below.
Name
Volume
Density (kg m-3)
Cas A
1 x10-21
kg m-3
E102-72
1 x10-21
kg m-3
Mass
(kg)
14. The next step is to calculate the velocity of the material in your
supernova remnant. A typical supernova explosion will eject about 1044
Joules of energy into the surroundings. This is the value you will use for
kinetic energy. Use the following equation, where M is mass:
v = (2 K.E. /M)1/2
Velocity =___________________________________
15. The final step is to calculate the age of your supernova. You can do this
using the distance to your supernova remnant and its expansion velocity:
Time = distance / velocity
Distance is actually the size of the remnant (i.e. the distance the shell has
travelled since the explosion) and time is actually the age of the remnant. Your
result will be in seconds, convert it to years and note down your result below.
Note: this assumes that the exploding material has been travelling outwards at a
constant speed.
Age of your supernova remnant =________________________________
years
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Congratulations, you just calculated the age of a real supernova remnant!
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Ancient Cosmic Explosions
Answer Sheet
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Name
Radius (degrees)
Distance
(metres)
Cas A
E102-72
Name
Θ degrees
Diameter (m)
Radius (m)
Volume
Mass
(kg)
Velocity
Cas A
Kepler
E102-72
Name
Cas A
E102-72
Name
Age
Cas A
E102-72
Conclusion
1. Energy given off by XX watt light bulb in an hour =. Supernova gives off equivalent
energy of XX light bulbs in for one hour, or XX hours with one XX watt light bulb.
2. Mass of Sun =
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symbol
description
value
KE
kinetic energy of shell
1044 J
density
density of surroundings
10-21 kg m-3
D
distance to the supernova
Find this value on the web
ANCIENT COSMIC EXPLOSIONS - ACTIVITY GUIDE
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Star in a Box
Teacher’s Guide
STAR IN A BOX: ACTIVITY GUIDE
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Introduction
Have you ever wondered what happens to the different stars in the night sky as they get
older? This activity lets you explore the lifecycle of stars.
Star in a Box allows stars with different starting masses as they change during their lives.
Some stars live fast-paced, dramatic lives; others change very little for billions of years.
The webapp visualises the changes in mass, size, brightness and temperature for all these
different stages.
Objectives
•
•
•
Describe the relationship between a star's mass, its age, and its position on the
Hertzsprung-Russell diagram
Describe the relationship between a star's mass and its life span
Name the stages of a star's lifecycle, in order, for several masses of star
Materials
•
•
•
•
2x 1-metre ruler
Coloured paper (white, blue, orange, red, yellow)
Projector and Star in a Box PPT
Printed Axis Labels
Per student:
• Computer with Internet access
• Scissors
• Stellar Fact Sheet
• Star in a Box Student Worksheet (Beginner, Intermediate or Advanced)
Preparation
Before beginning the activity, clear a table or floor space and lay out your rulers at a 90°
angle, these will act as the Y-axis and X-axis for your H-R diagram. The Y-axis will
represent Luminosity relative to the Sun (L ), this will be shown logarithmically from
0.0001 to 1000000. The X-axis will show Temperature in Kelvin (K), the hottest
temperature should be at least 35,000K and the lowest around 2,000K.
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Create a model of the Sun for reference. Using yellow paper, draw a circle with a radius of
2.5cm and cut it out. Place this on the H-R diagram at 6,000 K and 1L
Instructions
1. Begin by introducing your students to the lifecycle of a star using the Star in a Box
powerpoint presentation. The presentation has been designed to suit a variety of
abilities. A rough guide to the levels:
○
○
○
Beginner: KS3
Intermediate: KS4
Advanced: KS5
2. Hand out the stellar fact sheets, one per student. Assign each student a star. For
beginners or younger students (KS3), stick to the Main Sequence stars. If you are
doing the activity with older students (A-level and above) or for the second time,
include the Other Stars.
3. Assign each of your students a star. Using the model Sun prepared earlier as a
reference for mass and colour, the students will each create a model of their star.
4. Ask the students to collect a piece of paper. They must choose the correct colour
for their star based on temperature (e.g. Betelgeuse should be red)
Spectral Class
Temperature
Colour
O
30,000 - 60,000 K
Blue
B
10,000 - 30,000 K
Blue-white
A
7,500 - 10,000 K
White
F
6,000 - 7,500 K
Yellow-white
G
5,000 - 6,000 K
Yellow
K
3,500 - 5,000 K
Orange
M
< 3,500 K
Red
5. They will need to draw a circle of the correct size relative to the Sun model and the
other stars on the Stellar Fact sheet. Note that even the largest star will be no
bigger than the size of an A4 sheet.
6. Assign any remaining stars to the students so that you end up with circles
representing all stars on the sheet.
7. Next, ask the students to place their star on the H-R diagram one at a time.
8. Once all of the stars have been plotted, gather the class around the H-R diagram.
Does your plot look like the H-R diagrams you looked at earlier (during the Star in a
Box presentation)? Do you see the Main Sequence, red giants, white dwarfs etc?
Ask your students the following questions:
○ What is the approximate temperature of the Sun?
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○
○
○
What colour would a star with the following surface temperature be: 18000K,
2000K, 10000K
What factor affects the colour of a star?
What factor affects the luminosity of a star?
9. Ask the students to go back to their seats and ensure each student has access to a
computer with Internet access.
10. Hand out the Star in a Box Student Worksheets (one per student) and ask them to
log on to http://lcogt.net/siab/ and complete their worksheet. This will take approx.
30 minutes.
11. When the students have finished the online activity, gather them around the H-R
diagram again. Ask them to answer the following questions:
○ Most of the stars on the H-R Diagram are classified as which type of star?
○ What type of star has a high temperature but a low luminosity?
○ What type of star has a high temperature and a high luminosity?
○ What type of star has a low temperature but a high luminosity?
○ What type of star has a low temperature and a low luminosity?
○ Is the surface temperature of a white dwarf higher or lower than a red
supergiant?
○ What property of a star uniquely determines where it will be on the Main
Sequence?
○ If you increase the temperature of a star and leave it’s size the same, which
way would it move on the H-R diagram?
○ How do we know a star is larger than the Sun from it’s position on the H-R
diagram?
○ What do we know about stars directly below the Sun on the H-R Diagram?
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Star in a Box
Teacher’s Answer Sheet
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Answers
8.
What is the approximate temperature of the Sun? 6000 K
What colour would a star with the following surface temperature be: 18000K (Blue),
2000K (Red), 10000K (Blue-White)
What factor affects the colour of a star? (Temperature)
What factor affects the luminosity of a star? (Size and Temperature)
11.
Most of the stars on the H-R Diagram are classified as which type of star? (Main
Sequence)
What type of star has a high temperature but a low luminosity? (White Dwarfs)
What type of star has a high temperature and a high luminosity? (Blue Giants)
What type of star has a low temperature but a high luminosity? (Red Giants)
What type of star has a low temperature and a low luminosity? (Red Dwarfs)
Is the surface temperature of a white dwarf higher or lower than a red supergiant
(higher)
What property of a star uniquely determines where it will be on the Main Sequence?
(Mass)
If you increase the temperature of a star and leave it’s size the same, which way would
it move on the H-R diagram? (Left)
How do we know a star is larger than the Sun from it’s position on the H-R diagram? (It
sits higher)
What do we know about stars directly below the Sun on the H-R Diagram? (They are
smaller)
STAR IN A BOX: ACTIVITY GUIDE
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Exploring the Sunspot Cycle
Teacher’s Guide
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Introduction
For over 300 years, activity on the surface of our star has been monitored continuously. In
this project you will plot and anaylse historical sunspot data to find out if any patterns
emerge when sunspot numbers are plotted over time. Does the number of sunspots
change in a regular cycle? Can we predict how many sunspots there will be at a point in
the future? Do sunspot cycles have a faster rise or decay time?
Materials:
•
•
Computer with internet access
Excel spreadsheet software or equivalent
Learning Objectives
•
•
•
•
Realise that the number and intensity of sunspots on the surface of the Sun waxes
and wanes in an approximate 11-year cycle.
Practise working with a spreadsheet programme.
Use real scientific data and scientific method to investigate a hypothesis and present
your findings.
Practise communication skill when presenting your results to the group.
Background Information
i. The Sun
The Solar System is made up of the Sun and everything that orbits around it: the
Earth, the planets, asteroids and comets. The Sun makes up 99.9% of all the mass
in our Solar System. The Earth orbits around 150 million kilometres from the Sun,
although due to the elliptical shape of Earth’s orbit this distance varies throughout
the year.
The Sun is an average star - there are many other stars which are much hotter or
much cooler, and intrinsically much brighter or fainter. However, since it is by far the
closest star to the Earth, it looks bigger and brighter in our sky than any other star.
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With a diameter of about 1.4 million kilometers (860,000 miles) it would take 109
Earths strung together to be as long as the diameter of the Sun.
The Sun is mostly made up of hydrogen (about 92.1% of the number of atoms,
75% of the mass). Helium can also be found in the Sun (7.8% of the number of
atoms and 25% of the mass). The other 0.1% is made up of heavier elements,
mainly carbon, nitrogen, oxygen, neon, magnesium, silicon and iron. The Sun is
neither a solid nor a gas but is actually plasma (see below). This plasma is tenuous
and gaseous near the surface, but gets denser down towards the Sun's fusion
core.
ii. Plasma
Plasma is one of the four fundamental states of matter (the others being solid,
liquid, and gas). When air or gas is ionized, plasma forms with similar conductive
properties to that of metals. Plasma is the most abundant form of matter in the
Universe, because most stars are in plasma state.
iii.. Layers of the Sun
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The Sun can be divided into six layers. From the center out, the layers of the Sun
are as follows: the solar interior composed of the core (which occupies the
innermost quarter or so of the Sun's radius), the radiative zone, and the the
convective zone, then there is the visible surface known as the photosphere, the
chromosphere, and finally the outermost layer, the corona.
The energy produced through fusion in the Sun's core powers the Sun and
produces all of the heat and light that we receive here on Earth. The process by
which energy escapes from the Sun is very complex. Since we can't see inside the
Sun, most of what astronomers know about this subject comes from combining
theoretical models of the Sun's interior with observational facts such as the Sun's
mass, surface temperature and luminosity which is the total amount of energy
output from the surface.
a. Core
All of the energy from the Sun that we detect as light and heat originates from
nuclear reactions deep inside the Sun's high-temperature "core." This core extends
about one quarter of the way from the center of Sun where the temperature is
around 15.7 million kelvin (K) its surface, which is only 6000 K.
b. Radiative Zone
Above this core, we can think of the Sun's interior as being like two nested
spherical shells that surround the core. In the innermost shell, right above the core,
energy is carried outwards by radiation. This "radiative zone" extends about three
quarters of the way to the surface. The radiation does not travel directly outwards in this part of the Sun's interior, the plasma density is very high, and the radiation
gets bounced around countless numbers of times, following a zig-zag path outward.
It takes several hundred thousand years for radiation to make its way from the core
to the top of the radiative zone. In the outermost of the two shells, where the
temperature drops below 2 million K the plasma in the Sun's interior is too cool and
opaque to allow radiation to pass. Instead, huge convection currents form and large
bubbles of hot plasma move up towards the surface (similar to a boiling pot of
water that is heated at the bottom by a stove). Compared to the amount of time it
takes to get through the radiative zone, energy is transported very quickly through
the outer convective zone.
c. Convective Zone
The convective zone is the final 30 percent of the sun's radius, dominated by
convection currents that carry the energy outward to the surface. These convection
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currents are rising movements of hot gas next to falling movements of cool gas –
imagine watching herbs in a simmering pot of water. The convection currents carry
photons outward to the surface faster than the radiative transfer that occurs in the
core and radiative zone. With so many interactions occurring between photons and
gas molecules in the radiative and convection zones, it takes a photon
approximately 100,000 to 200,000 years to reach the surface.
d. Photosphere
The Sun's visible surface the photosphere is about 5,800 K. Most of the energy we
receive from the Sun is the visible light emitted from the photosphere. The
photosphere is one of the coolest regions of the Sun, so only a small fraction
(0.1%) of the gas is in the plasma state. The photosphere is the densest part of the
solar atmosphere, but is still tenuous compared to Earth's atmosphere, just 0.01%
of the mass density of air at sea level).
e. Chromosphere
Just above the photosphere is a thin layer called the chromosphere. The name
chromosphere is derived from the word chromos, the Greek word for color. It can
be detected in red hydrogen-alpha light meaning that it appears bright red.
f. Corona
Above the surface is a region of hot plasma called the corona. The corona is about
2 million K, much hotter than the visible surface, and it is even hotter in a flare. Why
the atmosphere gets so hot has been a mystery for decades; SOHO's observations
are helping to solve this mystery.
iv. Sunspots
Sunspots are regions of the solar surface which are cooler than their surrounding,
they appear as dark spots on the surface of the Sun. Temperatures in the dark
centers of sunspots drop to about 3700 K compared to 5700 K for the surrounding
photosphere. They typically last for several days, although very large ones may
exist for several weeks.
Sunspots are magnetic regions on the Sun with magnetic field strengths thousands
of times stronger than the Earth's magnetic field. They usually appear in groups
with two sets of spots; one set will have positive or north magnetic field, while the
other set will have negative or south magnetic field. The field is strongest in the
darker parts of the sunspots - the umbra. The field is weaker and more horizontal in
the lighter part - the penumbra.
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v. Sunspot Cycle
In 1610, shortly after viewing the sun with his new telescope, Galileo Galilei made
the first European observations of Sunspots. Continuous daily observations were
started at the Zurich Observatory in 1849 and earlier observations have been used
to extend the records back to 1610. The ‘sunspot number’ is calculated by first
counting the number of sunspot groups and then the number of individual sunspots.
The "sunspot number" is then given by the sum of the number of individual
sunspots and ten times the number of groups. Since most sunspot groups have, on
average, about ten spots, this formula for counting sunspots gives reliable numbers
even when the observing conditions are less than ideal and small spots are hard to
see. Monthly averages (updated monthly) of the sunspot numbers show that the
number of sunspots visible on the sun waxes and wanes with an approximate 11year cycle.
There are actually at least two "official" sunspot numbers reported. The
International Sunspot Number is compiled by the Solar Influences Data Analysis
Center in Belgium, which we will work with in this activity, and the NOAA sunspot
number compiled by the US National Oceanic and Atmospheric Administration.
Detailed observations of sunspots have been obtained by the Royal Greenwich
Observatory (UK) since 1874. These observations include information on the sizes
and positions of sunspots as well as their numbers. These data show that sunspots
do not appear at random over the surface of the sun but are concentrated in two
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latitude bands on either side of the equator. A butterfly diagram showing the
positions of the spots for each rotation of the sun since May 1874 shows that these
bands first form at mid-latitudes, widen, and then move toward the equator as each
cycle progresses.
vi. Coronal Mass Ejection
The outer solar atmosphere, known as the corona, is structured by strong magnetic
fields. Where these fields are closed, often above sunspot groups, the confined
solar atmosphere can suddenly and violently release bubbles of gas and magnetic
fields called coronal mass ejections (CME). A large CME can contain a billion tons
of matter that can be accelerated to several million miles per hour in a spectacular
explosion. Solar material streams out through the interplanetary medium, impacting
any planet or spacecraft in its path. CMEs are sometimes associated with flares but
can occur independently.
vii. SOHO
SOHO stands for Solar and Heliospheric Observatory and is a satellite that studies
the Sun 24 hours a day, 365 days a year without interruptions. The spacecraft has
12 scientific instruments collecting information about the Sun ranging from activity
in the Sun's corona to vibrations deep in the Sun's interior.
The Sun is the only star close enough to have real and dramatic effects on our life
here on Earth, we certainly expect and hope that improving our observations and
our understanding of this beautiful, awesome object will in the course of time bring
about beneficial applications. While it's never possible to tell where the quest for
knowledge will lead, at this time the area where we have the greatest expectation
of useful fallout is in the "space weather" arena.
Preparation
Before beginning this activity familiarise yourself with the terms and concepts
covered in the Background Science. Fill out the Sun Trek worksheet to ensure your
understanding of the structure and activity of the Sun.
Instructions
1. Download a table of historical sunspot numbers from http://sidc.oma.be/.
Click on the link for "Sunspot" > "Data" and select " Monthly mean total
sunspot number”. Ensure that you select the CSV file.
2. Import the sunspot data into your spreadsheet programme.
Note: If you are not familiar with using a spreadsheet programme, be sure to
take the time to go through a tutorial before beginning this activity.
3. You will now analyse the sunspot data to test the following hypothesis:
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What patterns emerge when sunspot numbers are plotted over time?
4. Create a graph of your data with time in years along the x-axis and number
of sunspots along the y-axis.
5. To plot sunspot numbers per month, delete all columns except for B and C,
these are the date and number of sunspots per month consecutively. The
date is shown as the Julian Day Number (JDN), this is the continuous count
of days since the beginning of the Julian Period and is used often by
astronomers. A scattergraph will allow you to visualize both the monthly
sunspot numbers (column D) and the monthly smoothed sunspot numbers
(column F).
6. You may want to select a smaller sample size of around 55 years, rather
than plotting all the data. The final graph should look similar to the example
below.
7. Complete the Sunspot Cycles Worksheet.
Looking at sunspot cycle onset and decay times (advanced)
In this part of the activity you will be using statistical analysis to investigate any
difference between the onset and decay time of each Solar Cycle.
1. Go back to the original sunspot data. From the spreadsheet data, identify the
beginning, end and maximum of each cycle. Make a table of these values.
2. Use the spreadsheet functions to calculate the onset time and decay time for
each cycle. Also, calculate the difference between onset time and decay
time for each cycle, and the average and standard deviation for all solar
cycles.
3. Compare the results. Is there a difference between onset time and decay
time? Is the difference statistically significant?
You will be using a "paired t-test" for this calculation. The t-test tells you how
confident you can be that your results are not simply due to random chance.
4. Begin by formulating (and note down) your “null hypothesis” -- essentially the
opposite of what you want to prove*.
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5. Select the appropriate statistical test for the data. In this case, the onset time
and decay time are paired valued, since each one is describing a different
feature of the same solar cycle. The test to use in this case is a ‘paired ttest’.
6. The result of the t-test will tell us, under certain assumptions, the probability
that the null hypothesis is true. By convention, the probability is referred to
as a “p value” and is given as an inequality. For example, if p < 0.01 means
we are 99% certain that our desired hypothesis is true.
7. Use the following link to run a paired t-test on your data:
www.physics.csbsju.edu/stats/t-test.html
8. Select “Student's t-test via copy and paste”. On the next page enter your
pairs of onset and decay times for each solar cycle. When this is finished
click “Calculate now” at the top of the page to get your results.
9. Indicate the p-value with your results displayed and discuss your value with
other members of the class.
* In this case, the null hypothesis may be that there is no different between onset
time and decay time.
Additionally you may ask students to test the rate of rise and decay (includes both
time and magnitude) – is there a correlation between the magnitude of sunspot
activity and the difference in onset vs decay rate?
Conclusion
Ask the students to present their results in a minute and explain what they found.
This data from this activity may be used to complete a follow-up activity “Correlation
of Coronal Mass Ejections with the Solar Sunspot Cycle”.
Evaluation
The students’ answers to the Sunspot Cycle Worksheet can be used as a basis for
evaluating their understanding of the subject. The following questions can be used
to evaluate students knowledge of the topic in future.
1. What is the solar cycle? 2. What is the average time between the high points (periods of maximum
sunspot activity)? 3. What is the average time between the low points (periods of minimum
sunspot activity)?
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4. When will the next sunspot minimum occur? 5. When will the next two solar maxima occur? 6. Where will we be in the sunspot cycle when you graduate from high school? 7. What makes sunspot activity unpredictable?
Additional information
Source: http://www.spaceweathercenter.org/resources/05/solarscapes/Act2s.pdf
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Exploring the Sunspot Cycle
Student Worksheet
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Name:_________________________
Date:__________________________
Print out your graph. Number each sunspot maximum directly about the line on
your graph. You will now work in groups to discuss the patterns found on your
graphs. Record your ideas and answer the following questions and explain your
reasoning. Be prepared to share your ideas with the class.
1.
Compare what you now know about sunspots and their variation to what
you knew when you started this activity.
2.
What patterns emerge when sunspot numbers are plotted over a period
of time?
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3.
What is the average time between points of maximum sunspot activity?
4.
Predict the years for the next two sunspot maxima.
5.
Predict the years for the next two sunspot minima.
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6.
Predict how many sunspots there will be for your 30th birthday.
7.
Plot two new graphs, one showing sunspot activity over 5 years and one
over 100 years. What additional patterns do you see when you observe a short
time period compared to a longer period?
8.
Why is it important to plot data over longer time periods before drawing
conclusions?
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Coronal Mass Ejections and
the Sunspot Cycle
Teacher’s Guide
EXPLORING THE SUNSPOT CYCLE: TEACHER’S GUIDE
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Introduction
Using real observational data and scientific investigation, in this activity students will aim to
determine whether there is a correlation between coronal mass ejection activity and the
solar sunspot cycle, using historical data.
Materials:
•
•
Computer with internet access
Excel spreadsheet software or equivalent
Learning Objectives
•
•
•
Become familiar with another solar phenomena: coronal mass ejections.
Use real scientific data and scientific method to investigate a hypothesis and present
your findings.
Practise communication skill when presenting your results to the group.
Background Information
i. Sunspots
Sunspots are regions of the solar surface which are cooler than their surrounding,
they appear as dark spots on the surface of the Sun. Temperatures in the dark
centers of sunspots drop to about 3700 K compared to 5700 K for the surrounding
photosphere. They typically last for several days, although very large ones may
exist for several weeks.
Sunspots are magnetic regions on the Sun with magnetic field strengths thousands
of times stronger than the Earth's magnetic field. They usually appear in groups
with two sets of spots; one set will have positive or north magnetic field, while the
other set will have negative or south magnetic field. The field is strongest in the
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darker parts of the sunspots - the umbra. The field is weaker and more horizontal in
the lighter part - the penumbra.
ii. Sunspot Cycle
In 1610, shortly after viewing the sun with his new telescope, Galileo Galilei made
the first European observations of Sunspots. Continuous daily observations were
started at the Zurich Observatory in 1849 and earlier observations have been used
to extend the records back to 1610. The ‘sunspot number’ is calculated by first
counting the number of sunspot groups and then the number of individual sunspots.
The "sunspot number" is then given by the sum of the number of individual
sunspots and ten times the number of groups. Since most sunspot groups have, on
average, about ten spots, this formula for counting sunspots gives reliable numbers
even when the observing conditions are less than ideal and small spots are hard to
see. Monthly averages (updated monthly) of the sunspot numbers show that the
number of sunspots visible on the sun waxes and wanes with an approximate 11year cycle.
There are actually at least two "official" sunspot numbers reported. The
International Sunspot Number is compiled by the Solar Influences Data Analysis
Center in Belgium, which we will work with in this activity, and the NOAA sunspot
number compiled by the US National Oceanic and Atmospheric Administration.
Detailed observations of sunspots have been obtained by the Royal Greenwich
Observatory (UK) since 1874. These observations include information on the sizes
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and positions of sunspots as well as their numbers. These data show that sunspots
do not appear at random over the surface of the sun but are concentrated in two
latitude bands on either side of the equator. A butterfly diagram showing the
positions of the spots for each rotation of the sun since May 1874 shows that these
bands first form at mid-latitudes, widen, and then move toward the equator as each
cycle progresses.
iii. Coronal Mass Ejection
The outer solar atmosphere, known as the corona, is structured by strong magnetic
fields. Where these fields are closed, often above sunspot groups, the confined
solar atmosphere can suddenly and violently release bubbles of gas and magnetic
fields called coronal mass ejections (CME). A large CME can contain a billion tons
of matter that can be accelerated to several million miles per hour in a spectacular
explosion. Solar material streams out through the interplanetary medium, impacting
any planet or spacecraft in its path. CMEs are sometimes associated with flares but
can occur independently.
Preparation
Before beginning this activity you must complete the Sunspot Cycle activity.
Instructions
1. Use the online catalogue of CME data from the SOHO LASCO instruments to
create a table of monthly numbers of CMEs for the time period 1996–present. You
can find this data at http://cdaw.gsfc.nasa.gov/CME_list/index.html
2. Each entry in the table contains information about a single CME event. Count up
events for each month and create your own data table of monthly CME totals. To
make this task quicker, you can divide the number of months between the class,
assigning each student a group of months to count.
3. Add the CME numbers to the solar sunspot cycle plot, using a separate y-axis
scale.
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Evaluation
Compare the two curves on your graph. Does the number of CMEs rise and fall in a
manner similar to the solar sunspot cycle? If so, this demonstrates a correlation
between the two phenomena. Remember, though, that correlation does not imply
causation. We may have good cause to believe that sunspots and CMEs are
somehow related, but the correlation does not prove that one causes the other.
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