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Gamma Ray Burst Educational Unit

An Educator's Guide with Activities in Science and Mathematics

Contents

• Preamble: Gamma-Ray Bursts and the Swift Education and Public Outreach Program
• Introduction:Gamma Rays and Gamma Ray Bursts
• Stepping Into The Classroom!
• Activity 1: Sorting out the cosmic Zoo
• Activity 2: Angling For Gamma-Ray Bursts
• Activity 3: GRB Distribution on the Sky: The Plots Thicken
• Activity 4: Beam me up!
• Glossary
• National Science Standards
• National Math Standards
• Resources and Web Links

Preamble

Gamma Ray Bursts and the Swift Education and Public Outreach Program

Busy educators sometimes have trouble finding ways to help their students feel the excitement of science in action. As a part of its educational effort, the NASA Education and Public Outreach group at Sonoma State University has put together a compact presentation based on the science of one of NASA's exciting space missions: The Swift Gamma Ray Burst mission.

Since many children remember and understand better when they actively engage in manipulating the concepts about which they are learning, we have included several hands-on activities to help keep their interest and reinforce their comprehension and retention of the scientific concepts covered in the presentation of the mission. We have also included information about Swift, what kind of objects it will observe and why astronomers are interested in them. To help you determine when this project might be of most use to you in your science and/or math curriculum, we have included a matrix of the math and science standards covered. This introduction to the activities includes some frequently asked questions.

What is Swift?

Swift is a NASA satellite that is planned for launch in Summer 2004, and is part of NASA's Structure and Evolution of the Universe theme. The astronomical satellites in this theme are designed to explore the structure of the Universe, examine its cycles of matter and energy, and peer into the ultimate limits of gravity: black holes. Swift's primary mission is to observe gamma ray bursts, extraordinary explosions of matter and energy that astronomers think signal the births of black holes. These explosions, as huge as they are, fade very rapidly, so Swift must react quickly to study them. The satellite moves so quickly that astronomers decided to name it Swift, after a bird that can dive at high speed to catch its target. It is one of a very few NASA missions that has an actual name and not an acronym!

What instruments will Swift use?

There are three scientific instruments on board Swift: the Burst Alert Telescope (BAT), the X-ray Telescope (XRT), and the Ultraviolet/Optical Telescope (UVOT). The BAT is sensitive to X-rays, a very energetic form of light. Gamma ray bursts emit X-rays when they explode, and the BAT will be the first instrument onboard Swift to detect them. Swift will then "swiftly" turn toward the burst and point the XRT and UVOT at the target. They will observe the burst in X-rays and in ultraviolet and optical light, respectively.

What will my students learn from these activities?

This series of activities uses gamma ray bursts - distant explosions of incredible fury - as an engagement to teach basic concepts in physical science and mathematics. The mapping of the activities to the national science and math Standards is shown by the list below. A more detailed listing of the science and mathematics learning objectives can be found at the end of this educators guide.

How are these activities organized?

The next section has a general introduction to gamma ray bursts and their history. Depending on the age and ability of your students, you may need to tell them about this information, have them read it, or have a few advanced students put together a presentation to the rest of the class based on this introduction and other sources they may find. With this introduction, try to convey the excitement of the scientists when they first discovered these enigmatic explosions and the decades-long pursuit to understanding them.

Each activity has the following components to help you make it an exciting learning experience for the students:

1. Science concepts and estimated time (note: time varies significantly for different age groups and levels of science understanding.)
2. Background information specific to this activity (see the suggestions above for possibilities of presenting this background information.)
3. The "essential question" asked by the activity. Take the time to help students understand that scientists ask questions. Each activity states the essential question that this activity is designed to answer, or to help the student explore.
4. The materials needed to complete the activity.
5. (For some activities) a list of abbreviations used and possible additional notes to the teacher.
6. The specific learning objectives of this activity.
7. The procedures to be followed step-by-step for the most efficient and effective use of the activity.
8. The assessment for the activity. It is important that before you start an activity you have a clear understanding of what constitutes a successful activity. This assessment area of the activity gives some suggestions for ways of evaluating your students' work in mastering the activities' objectives.
9. Transfer activities: One of our goals in science is to help students see science and scientific concepts as tools to be used throughout their lives, not just as a small part of their education. Including transfer activities after the activity is completed will not only reinforce the specific objectives, but also help your students learn to apply scientific concepts to their "real lives."
10. (For some activities) suggested extension and reflection activities. These extras help the student follow up the activity with comprehension exercises so that they better assimilate the information, and use the concepts they have learned to better understand phenomena in everyday life.
11. Lesson adaptations that will help you cope with the special needs students in your classroom.
12. An answer key which provides you with the answers to the mathematical questions given to the students, and will help you evaluate the products the students may produce as a part of this activity.
13. Student worksheets that contain the information and directions necessary for the student to complete the activities. NOTE: giving the students the work sheet without the appropriate background information and procedures will not only decrease the learning of the students, it may also cause frustration and feelings of inadequacy to master science principles.
14. Specific standards list that presents more detailed information about the national science and math standards covered in each activity.

Who developed these activities?

The activities that describe Gamma Ray Bursts has been developed as part of the NASA Education and Public Outreach (E/PO) Program at Sonoma State University, under the direction of Professor Lynn Cominsky.

Contributors to this education unit also include Dr. Philip Plait, Tim Graves, Sarah Silva, Dr. Garrett Jernigan and Dr. Mary Garrett. We greatfully acknowledge the advice and assistance of the Swift Education Committee, the NASA SEU Educator Ambassabor (EA) team, with extra thanks to the EAs Dr. Tom Arnold, David Beier, Teena Della, Dee Duncan, Tom Estill, Mandi Frantti, Dr. Mary Garrett, Walter Glogowski, Bruce Hemp, Rae McEntyre, Janet Moore, Marie Pool, Dr. Christine Royce and Rob Sparks.

Where can I get more information?

The last page of this booklet (before the reply card) contains a list of resources for Swift and gamma ray bursts.

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Introduction to Gamma Rays and Gamma Ray Bursts

The electromagnetic spectrum comes in many flavors, from low-energy radio waves, through microwave, infrared, visible light (the only part of the spectrum we can see with our unaided eyes), ultraviolet, X-ray and up to extremely high-energy gamma rays. Astronomical objects of different sorts emit some or all of these kinds of radiation, and we can only get a complete picture of these objects by studying them in all the different regions of the electromagnetic spectrum. Otherwise, we are like the Blind Men and the Elephant: by only seeing an incomplete part of the whole, we cannot imagine what the total picture really is!

The type of radiation emitted by an object tells us quite a bit about it. Low energy or relatively cold objects like planets and dust clouds emit mostly radio waves, which are low-energy waves. Hotter, more energetic objects like stars and nebulae can emit high-energy waves in the ultraviolet range. Even more energetic objects like pulsars (the collapsed remnants of a star that exploded as a supernova), extremely hot gas, and black holes can emit X-rays. But to emit gamma rays you need something incredibly energetic, something that dwarfs the energy emitted by "cooler" objects. Some pulsars which have unusually intense magnetic fields can generate gamma rays. The fierce magnetic energy in a huge solar flare can (very briefly) generate gamma rays. Twisted magnetic fields from spinning super-massive black holes can channel particles and accelerate them to velocities near light speed, generating focused jets of gamma rays.

But even these pale in comparison to gamma ray bursts (GRBs). In the 1960s, the United States was concerned that other countries might test nuclear weapons in space, despite a treaty to ban such events. Nuclear detonations produce bursts of gamma rays, so the U.S. military launched a series of satellites designed to detect these high-energy explosions. To their surprise, scientists soon began detecting dozens of explosions, but discovered they were not coming from below the satellites, near the surface of the Earth. Instead, the bursts were coming from deep space.

The source of these bursts was a mystery (and to a large extent still is today). Some bursts lasted for only milliseconds, while some dragged on for seconds or minutes. At first astronomers assumed these must be "local" phenomena – somewhere in our own Milky Way Galaxy. Because of the energy involved in producing such a large number of gamma rays, a distant object would have to be unimaginably powerful to account for a GRB.

As time went on, and astronomers began to use ever-more sophisticated instruments, it became clear that not only were GRBs not local, they were really not local – the more distant ones are billions of light years from the Earth! In the 1990s, the Burst And Transient Source Experiment (BATSE) instrument onboard NASA's Compton Gamma Ray Observatory provided the initial evidence for this in the form of the distribution of GRBs: BATSE found that GRBs were scattered evenly across the sky (see diagram on previous page). If GRBs were coming from inside our own Galaxy, we should see more of them toward the center (an analogy would be seeing more buildings when looking toward the center of a city when you live in a suburb). Since the GRBs were randomly distributed, this argued for sources well outside our Galaxy. This means GRBs are at vast distances, which in turn means they are incredibly powerful events - in fact, they are the largest explosions seen in the Universe today, second only to the Big Bang itself in the release of energy.

The vast amounts of energy inferred from the distant locations of the GRBs puzzled scientists until they realized that the energy might be beamed, that is, concentrated into tight jets instead of being sprayed in all directions. Beaming the gamma rays dropped the total energy needed to produce GRBs into the range just barely understandable using the most catastrophic of all events: the birth of a black hole.

Currently, there are two (not necessarily competing) theories on how GRBs are produced. One is called a hypernova, or a super-supernova. When a star with about 10-40 times the mass of the Sun reaches the end of its life, it explodes, sending matter and energy sleeting into space. These supernovae are very energetic events, but not powerful enough to make gamma rays in the quantities necessary for GRBs. But if a very massive star - one with 50-100 times the mass of the Sun - explodes, the energies involved may be enough to create a gamma ray burst. Indeed, at least one GRB was seen at the site of a supernova in a relatively nearby galaxy, and there is indirect evidence the two are connected.

The other theory involves a binary system comprised of two neutron stars. These are the extremely dense and massive cores of stars that previously exploded as supernovae. As they orbit each other, the collapsed stars lose energy through gravitational radiation, a complicated process predicted by Einstein's Theory of General Relativity. As the system loses energy the stars slowly spiral inward. When they are close enough, their mutual gravitation rips the stars apart, and they coalesce. As they merge, they form a black hole with an extremely dense ring of material spinning madly around it. When that matter falls into the black hole some time later, a burst of energy is released which could power a GRB. There are indications that at least some GRBs fit into this merging collapsed star category.

Whichever theory turns out to be correct, we know that GRBs appear without warning somewhere on the sky at least once every day, indicating that somewhere, far off (we hope!) in the Universe a black hole is born. NASA’s Swift mission will allow scientists to study GRBs better than ever before. Some GRBs are followed by a fading afterglow of light that cools down through X-rays on into the optical, infrared, and even radio wavelengths. Follow-up observations of this decay allow astronomers to better pinpoint the location of the GRB and even look into its local environment. The Swift satellite will quickly lock onto GRBs, using the gamma ray-sensitive Burst Alert Telescope to get a rough location in seconds, and a more accurate one within minutes as its X-ray and Ultraviolet/Optical Telescopes nail the target. The information on the location and strength of the GRB will be relayed to the ground to allow faster and more detailed follow-up observations of the rapidly fading catastrophe. Astronomers hope they will get enough data to finally solve the riddle of these explosions that are so vast that they equal the energy of a billion billion (10¹⁸) Suns.

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Stepping into the Classroom!

Follow the Footsteps:

Elicit Engage	The instructor assesses the learners' prior knowledge and helps them become engaged in a new concept by reading a vignette, posing questions, doing a demonstration that has a non-intuitive result (a discrepant event), showing a video clip, or conducting some other short activity that promotes curiosity and elicits prior knowledge.
Explore	Learners work in collaborative teams to complete activities that help them use prior knowledge to generate ideas, explore questions and possibilities, and design and conduct a preliminary inquiry.
Explain	Learners should have an opportunity to explain their current understanding of the main concept. They may explain their understanding of the concept by making presentations, sharing ideas with each other, reviewing current scientific explanations and comparing these to their own understandings, and/or listening to an expanation from the teacher that guides them toward a more in-depth understanding.
Elaborate Evaluate Extend	Learners elaborate their understanding of the concept by conducting additional activities. They may revisit an earlier activity, project, or idea and build on it, or conduct an activity that requires an application of the concept. The focus in this stage is on adding breadth and depth to current understanding. The evaluation phase helps both learners and instuctors assess how well the learners understand the concept and whether they have met the learning objectives. There should be opportunities for self assessment as well as formal assessment. Learners should also be given an opportunity to extend their new found knowledge.

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Activity 1: Sorting out the Cosmic Zoo

Science Concepts

Astronomical objects can be categorized by such characteristics as position in the sky, duration of an event (like a flare), periodicity, and distance.

Duration

45 minutes

Essential Question

How do astronomers tell one type of astronomical object from another?

Background Information

Gamma ray bursts (GRBs) were first detected in the late 1960s by U.S. satellites designed to look for space-based nuclear weapons testing. GRBs are characterized by a short burst of gamma rays (from milliseconds to a few minutes), and rarely have an easily detectable glow more than a few minutes after the event. GRBs are flashes-in-the-pan: they explode once, never to return.

GRBs were a big mystery to astronomers when they were first seen (and in fact, they still are). The situation became worse when, on March 5^th, 1979, intense flashes of gamma rays were detected coming from the direction of the Large Magellanic Cloud, a companion galaxy to the Milky Way. Then, over the next few months, more flashes of gamma rays were detected coming from the same region of the sky. For a while, the idea that GRBs only flashed once was in doubt, but then it was realized that the repeating sources were a totally different class of object. Dubbed Soft Gamma Ray Repeaters (SGRs), because they peak at a slightly lower (also called "softer") energy of gamma ray than GRBs, these were found to be neutron stars - incredibly dense remnants of supernova explosions - which have extremely strong magnetic fields, far stronger than typical neutron stars. For reasons still unknown, the super-magnetic field can cause the crust of the neutron star to slip, much like an earthquake. The intense gravity of the neutron star makes such a slip a dramatic event indeed; the energies can be enough to generate huge bursts of gamma rays. Over time, the pressure builds up again, and another flash is seen. This is how gamma rays are seen from the same object more than once.

Also in the mid-1970s, different kinds of high-energy events were starting to be identified. So-called X-Ray Bursters (XRBs) were discovered. Like SGRs, they were neutron stars with repeating bursts, but their magnetic fields, while strong, were not at the level of the strength. And unlike SGRs, which are isolated, individual neutron stars, XRBs are caused by neutron stars in binary systems. The neutron star in such a system can accrete, or draw in, matter from a normal companion star. The matter builds up on the surface of the neutron star, and then suddenly explodes in a thermonuclear blast. It is this explosion which creates the burst of X-rays. After the matter burns up in the blast, the accretion starts again and the pattern repeats. This causes repeated XRBs from the same object.

During the 1970s through the 1990s, much confusion arose because it was not clear at first that there were actually three different types of physical mechanisms that were producing the bursts of energy. Placing something in its correct category is half the battle in understanding it. It took 30 years for astronomers to sort out these different types of phenomena, and in fact they are still working on classifying and understanding them. Your students will do the same, but in just 45 minutes!

The Mystery Source Cards

The cards in this activity contain real data determined from characteristics of actual astronomical objects that emit bursts of high-energy electromagnetic radiation, either as X-rays or gamma rays.

On the front of each card is the name of the object, and a graph showing the burst's energy versus time; what astronomers call the light curve. The back of each card has the name of the object, its coordinates using the Galactic coordinate system, the energy at which the spectrum of the object peaks, whatever object is seen at the source's position using optical light (if any), the distance to the object, whether the bursts repeat, and whether there is any periodicity associated with the object other than the bursts. These characteristics are detailed below.

On the front of the cards:

1. Object Name: The name of the object based on its coordinates on the sky. The sky is mapped by astronomers using a coordinate system similar to longitude and latitude, but the axes are called Right Ascension (or RA) and declination. RA is measured in the direction of East-West on the sky, goes from 0 to 24 hours (and is further divided into 60 units called minutes). Declination is measured in North-South on the sky, and goes from -90 to 90 degrees. An object's name on the card is its RA (a four digit number where the first two digits are the hours, and the second two are the minutes) and its declination in degrees, including the plus or minus sign. An object at an RA of 5 hours 30 minutes and a declination of -20 degrees would thus have the name 0530-20. The name of the object is also on the back of the cards.
2. Light curve: The amount of light emitted by an object plotted against time. Some of these objects have bursts that are very short, so they have narrow profiles and sharp peaks, while others take many seconds or minutes, stretching out the profiles and broadening the peaks. Some also emit multiple bursts. Note that time scales on the light curves are different on each card, and that the units of the flux are arbitrary; in other words, the y-axis units cannot be compared from card to card. Make sure the students understand that they cannot compare the heights of the peaks of different bursts, and instead should look at the widths. Tip: Most students will try to group the bursts using only the light curves, and may spend the majority of their time doing it that way instead of looking at the information on the back sides of the cards. If you see a group spending too much time (say, more than five minutes) on the light curves, gently urge them to look at the other physical characteristics of the bursts on the other side of the cards.

On the back of the cards (clockwise from top of card):

3. Galactic coordinates: The galactic coordinate system is a way of measuring the position of an object on the sky using the Milky Way galaxy as a base. Our Galaxy is a flat disk, and the Sun is in that disk about 30,000 light years from the center. Astronomers have defined the galactic coordinate system based on the center of the Milky Way and the plane of the disk. Galactic longitude (l) is measured along the plane of the Milky Way, where the position of the center of the Galaxy on the sky is defined as 0 degrees. Galactic longitude goes from 0 to 360 degrees. Galactic latitude (b) is measured away from the plane of the Milky Way, in degrees. Galactic latitude goes from -90 degrees at the South Galactic Pole to +90 degrees at the North Galactic Pole, similar to latitude on the surface of the Earth.

   Galactic coordinates are usually plotted on an Aitoff projection, which is similar to familiar Cartesian coordinates except that the plot is oval in shape (see "Additional Information: Aitoff Maps" below). Over 2700 GRBs are plotted on an Aitoff map in the "Introduction to Gamma Rays and Gamma Ray Bursts" section).

4. Peak energy: These objects are luminous at a variety of different energies. The peak energy is the photon energy at which the object emits the largest number of photons. X-rays have an energy of about 1000 electron Volts (abbreviated eV; an optical light photon has an energy of about 1 eV) to about 50,000 eV (50 keV). "Hard" X-rays (which are sometimes also called soft gamma rays) range from about 50 keV to 1000 keV. Gamma rays go from about 1000 keV through a million keV and on into the billion keV range and beyond.
5. Optical: The identification of the object seen at the position of the burst using optical light. Some objects appear to be associated with galaxies, some with stars, others with supernova remnants (the debris left over when a star reaches the end of its life and explodes in a supernova.)
6. Distance: The distance from the Earth to the object in light years. Note that there is a large range of distances.
7. Burst Repetition: This indicates whether the high-energy bursts are seen to repeat or not. "None" means there is no repetition, and "N/A" means no information is available.
8. Spin or Orbital Period: Any pattern of cycles seen in the object's light. This is different than repetition, which just notes if a given burst repeats. If the object that is bursting is spinning, or orbiting another object, then there might be a periodic pattern during the bursts, or a periodicity seen in different wavelengths. "None" means there is no period, and "N/A" means no information is available.

The students' task is to look at the data on the cards, try to find out how many categories of objects there are, and sort the objects into their respective groups. For example, they may sort them by distance, and find that they fall into, say, two groups, one near and one far. Or, they may sort them by peak energy into, say, two groups, and find out each energy group can be further divided into the object type, or by position on the sky.

In the end, you can take a survey or have the students vote on how many categories of objects there should be, and how they divided the objects into these groups. Remind them that the data they used were painstakingly determined over decades of time, and that astronomers from 1975 would have given anything to have a copy of those cards!

Additional Information: Aitoff Maps

In this exercise the students will be plotting the distribution of the mystery objects on the sky. Typically, when making all-sky plots, astronomers use an Aitoff projection, which is a method of mapping a sphere so that distortions are kept to a minimum. Most people are familiar with a map of the Earth projected onto a rectangle. While this is an intuitive way of mapping the Earth, it generates big distortions near the poles, making Greenland, for example, look much larger than it really is. An Aitoff projection (see figure below) maintains the correct relative areas for all the continents.

In an Aitoff map of the sky, the center vertical line represents 0 degrees longitude, and longitude increases to the left to 180. Then it skips over to the right side (which is also 180) and continues increasing to the left, from 180, through 270, and finally to 360, which is the same as 0.

The center horizontal line is 0 degrees latitude, and latitude increases upwards to +90 degrees at the north pole, and decreases to -90 degrees at the south pole.

The sky map is the same! In that case, we call the coordinates "Galactic longitude" and "Galactic latitude" (see the description above for "Galactic coordinates").

Materials for each group of 2 or 3 students

• Student worksheets for each student
• 1 set of Mystery Object cards
• A set of six or seven different colored pencils or crayons for plotting (or small stickers)
• Blank Aitoff projection sky map for plotting for each student (included with student handout)

Objective

By analyzing the data on the cards, students will see that astronomical objects have many observable properties, and that these properties allow scientists to categorize these objects into different groupings. The students will also see that discrete categorization is not always easy, which is why it takes time for scientists to understand the objects they study.

Procedure

1. Pre-class: read through the entire activity, including the answer sheet. Make copies of the Student Worksheets, one per student.
2. In class: Introduce the activity to the students by reviewing information in the section "Introduction to Gamma Rays and Gamma Ray Bursts" and in the activity overview. However, do NOT tell the students that there are three different groups of objects (gamma ray bursts, soft gamma repeaters, and X-ray bursters).
3. Explain to the students that they will be given a series of cards with information about astronomical objects on them. These objects fall into different categories. They are to determine any trends in the objects, determine how many categories there are from those trends, and which objects belong to which categories.
4. They will also be plotting the positions of the objects on the sky maps (using the enclosed blank Aitoff projection map) to see if there are trends there as well. They can use colored pencils to represent the different types of objects, or you can use small stickers as a substitute.
5. The activity can be done individually or in teams of two or three people each.
6. Post-class: After the activity is completed, discuss the results with the students. Ask them how much time they spent looking at each characteristic of the bursts, and which physical properties were useful and which weren't. Was there one best way to categorize the objects? How many burst groups did they find, and what was the key characteristic of each group? Engage them in thinking about what they did, and discussing their methods. Were they frustrated in any way, or did they find categorization to be easy? You can compare and contrast the methods of the different groups of students, and even make a table of the number of groups into which they sorted the objects (i.e., how many students sorted the objects into two different groups, how many into three, etc.).
7. When you are done, show them how astronomers categorize the objects using the information in the introduction to the activity, and compare these results to what the students found. Tell the students that the amount of information they had on the cards was very limited, and the current information about these objects has been gathered after decades of observations and analysis by hundreds of astronomers. Finally, remind them that the data on the cards represent everything astronomers knew about these objects for many years, and that astronomers are even today still frustrated by our limited understanding of gamma ray bursts!

Transfer Activities

Different luminous objects can look very similar when they are at a large distance. For example, when driving at night, the headlights from a distant truck and small car may look similar, and the difference may only be obvious as they get nearer. Students can try to identify different vehicles from a distance, and devise ways to tell them apart. This also applies to birds, which can look very similar when high in the sky. How can you differentiate them? Color, shape, style of flight? Once you categorize them, can you determine anything else about them from these categories?

Extension Activities

Categorization of different objects is essential in all fields of science. One obvious example is zoology. As a warm-up activity, choose four or five animals with widely different characteristics (for example, elephant, alligator, insect, bird). Divide the students into groups of three or four, and present them with pictures of the animals and ask them to describe them in as many ways as they can. After they are done, have them then categorize them into groups based on similarities (for example, the elephant and alligator both have four legs). Compare the results of each group and have them discuss them as a class. If you want to challenge them, add in a bacterium or virus.

Sorting objects into various categories is also a major challenge in astronomy. There are several activities in which students can classify objects. An excellent one is the Galaxy Classification Activity located at https://imagine.gsfc.nasa.gov/educators/galaxies/imagine/act_classifying_galaxies.html.

Lesson Adaptations

Students who are visually impaired may have difficulty in reading the light curves on the fronts of the cards. To aid them, glue yarn or string over the light curve, trying to follow the bumps and wiggles in the plot. When dry, the students can run their fingers over the string to literally feel the shape of the light curves. Be careful to tell them the time scale along the x-axis! A light curve may feel more sharply peaked than another, but if the timescale is much different than the other the shape may be misleading.

Assessment

• 4 points: The students correctly identify the categories, all objects are in the correct categories, plotting is accurate, and reasoning for grouping is supported.
• 3 points: Plotting is adequate, most objects are in the correct categories, one or two objects are not in the correct categories, although reasoning for grouping is supported.
• 2 points: Plotting is somewhat inaccurate, category number is off by one or two, many objects placed in wrong categories, reasoning for grouping minimally or not well supported.
• 1 point: Plotting is inaccurate, category number is more than 5, objects all in wrong categories
• 0 points: No work turned in

Answer Key for Sorting out Nature's Second Biggest Bangs:

1. Astronomers have categorized the objects into three groups. The table below gives the name of the object in the correct grouping.

   X-ray Bursters	Soft Gamma-Ray Repeaters	Gamma-Ray Bursts
   0748-67	0526-66	0501+11
   1636-53	1627-41	0656+79
   1659-29	1806-20	1156+65
   1728-34	1900+14	1338-80
   1735-44		1525+44
   1820-30		1935-52
   1837+05		2232-73
   1850-08		2359+08

   Several of the properties are useful for categorizing the objects. Peak energy is perhaps the best. The first group has a low peak energy, around 2-3 keV. The second group peaks somewhat higher, at 30 keV, and the last group peaks much higher at 175-1500 keV, with a few at somewhat lower energies (this is also the answer to Question 3).

   Another good property is the optical counterpart. The GRBs all have host galaxies. The counterparts to the XRBs are all stars, while the SGRs are all found in supernova remnants.

   The GRBs are spread out over the whole sky in Galactic coordinates, while the two other groups tend to be more in the plane (at 0° Galactic latitude). An exception is that one of the SGRs is in our neighboring galaxy, the Large Magellanic Cloud.

   The SGR bursts and the XRBs repeat every few hours, while the GRBs are never seen to repeat.

   The SGRs often have spin periods of seconds to minutes (reflecting the spin of the actual neutron star), the XRBs show orbital periods around their companion stars of minutes to hours, while the GRBs show no periodicities at all.

   The distances to the XRBs and SGRs (with the one exception in the second group; 0526-66 which is located in the Large Magellanic Cloud galaxy) are the smallest, as the objects are located inside our Milky Way. The GRBs are all very distant (billions of light years).

2. Below is the Aitoff sky map with the objects plotted correctly. The GRBs are the Xs, the soft gamma-ray repeaters are the diamonds, and the X-ray bursters are the stars.
   

   The GRBs are randomly distributed. The other two groups tend to be near the Galactic plane (except 0526-66).

3. The first group has a low peak energy around 2-3 keV. The second group peaks somewhat higher, at 25-30 keV, and the last group peaks much higher at 175-1500 keV, with a few at somewhat lower energies.

4. The distance to the first and second groups (with one exception in the second group; 0526-66) is the smallest, inside the Milky Way. The first group averages about 30,000 light years, and the second group about 70,000 light years. The GRBs are all very distant, ranging from 100 million to 10 billion light years, with an average of 6.5 billion light years.
5. See the answer to question 1.
6. The peak energies would be a big help, as this fairly cleanly separates the groups (see Question 3). The position on the sky helps (Question 2). Also, GRBs do not repeat, which separates them from the other two groups.

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Activity 2: Angling for Gamma-Ray Bursts

Science Concepts

1. Satellites can be used to determine the time when a gamma-ray burst occurs, and this information can be used to get the direction to the GRB.
2. It takes several satellites to accurately get the direction to the GRB using time delays.
3. Light travels in a straight line and at a constant speed in a vacuum. From a distant object, the light rays are parallel.

Duration

1 hour

Essential Question

How can the directions to GRBs be determined using the properties of light?

Background Information

Note for the Teacher: This information is split up into a section for you, and one for the students to read. You will of course need to read the student portion as well. It is included in the Student Handout section. The information provided to the student is sufficient to do the exercise, but the additional information given to you below will complement the student's understanding of how the direction to a GRB is triangulated. Going over this information with the students the day before they perform the exercise will increase their understanding of the activity and its concepts.

Remember to emphasize the point that the people in the following analogy are hearing sound waves, not light waves. Sounds wave are transmitted through a medium (such as air) while light waves (or photons) are not, and can travel through the vacuum of space. Also, in this analogy, it is important to stress the difference in speed between sound and light waves, and that the lightning and thunder occur simultaneously.

Imagine you are outside and a storm is approaching. There is a flash of lightning, and a few moments later - say, ten seconds - you hear the thunder. The flash of light traveled from the lightning bolt to you in less than a millisecond, since the speed of light is 300 million meters per second. But the sound waves are much slower, around 300 meters per second, so they take an appreciable amount of time to reach you.

If a friend stands a few hundred yards to your left but the same distance to the lightning bolt as you, she will hear the thunder at the same time you do. Since you are both the same distance from the lightning, it takes the same amount of time for the thunder to reach you. If you mark the time when you hear the thunder, then compare watches, you will see you heard it at the same time. That means the wave front of the thunder was traveling perpendicularly to the line between you and your friend (right hand figure).

If your friend now stands a few hundred meters away from you, farther from the lightning, she will hear the thunder after you do, because it takes time for the sound wave to pass you and reach her. When you compare watches, you can see that she heard it after you.

So the minimum time delay (0 seconds) happens when a line between you and your friend is perpendicular to the direction that the sound travels. The maximum delay (the distance between the two of you divided by the speed of sound) happens when the line between you is parallel to the direction of the travel of the sound (left bottom figure). If the line between you is at an angle to the sound direction, the time delay will be somewhere between the minimum and maximum. In fact, the time delay depends on that angle.

So, if you know the distance between the two of you, the direction to your friend, the speed of sound, and the delay between the times you heard the thunder, you can calculate the direction to the lightning.

In this activity, the locations in space of different satellites are analogous to the positions of you and your friend(s). Because the satellites are so widely separated, we can use the delay in the arrival times of the light rays to triangulate the direction to a cosmic gamma-ray burst, just as the direction to the lightning was triangulated in the analogy above using sound waves (thunder).

Materials for each group of 2 or 3 students

• Protractor
• Ruler
• Student handout
• Light Rulers (assembled in activity)
• Scissors
• Graph paper (preferably 0.5 cm/square)
• Pencil
• Calculator

Materials for each individual student

• Student Worksheet

Procedure

1. Pre-class: make copies of the Student Worksheets, one per student. The Student Handout can be given out one per group of 2-3 students. Make copies of the light rulers (located on the page just before the Student Handout) on stiff paper (using regular paper makes it difficult to manipulate the light rulers). Make sure each group gets one or two extra light rulers in case they make a measuring or cutting mistake.
2. At least one day before the activity is performed in class, give the students the Student Handout. As homework, have them read it carefully and write out a paragraph describing the procedures of the activity. You can also assign the Extension Activity (see below) as homework before the activity is done.
3. Explain to the students that they will be using the time delays between satellite detections of a gamma-ray burst to find the direction to the burst. instead of just lecturing, try asking your students questions about time delays such as "What is a time delay?" and "How would scientists use this method to locate GRBs?"
4. Go over the material in the introduction above. Use the thunder analogy with diagrams to make sure they understand the concept. The illustration on the front of the wallsheet will also be helpful.
5. In-class: Perform the activity. Note that at the end of the Student handout is a Math Extension exercise. This is for students who are learning trigonometry, and can be considered an “extra credit” portion. When your students get to step two and they are trying to find the solutions, walk around the classroom and assist them with lining the light rulers up.
6. Wrap up/reflection: After the activity is completed, have the students break up into different groups of three and discuss their results. How are their individual results alike, and how are they different? What are possible sources of error, and what might be the biggest ones? After a few minutes, break up the groups so the students can have individual reflection time. Have them think of where else this activity might be useful. Some examples could be finding the direction to a thunderstorm, surveying, and earthquake measurements. How would your students set up an experiment to use this method in those cases?

Transfer Activities

• Using the example of two people listening to a thunderstorm, have the class make a plot showing the time delays measured between the two people as the angle between them and the direction to the lightning changes from perpendicular to parallel. They can measure this directly by using scale drawings. Have them describe the plot. Does it look familiar to them? The delays should fall along (half of) a sine curve.
• Lead a discussion about how this activity could be modified to include the third dimension. Topics could include how many satellites would be needed, how the light rulers would need to be modified (or changed completely) to accommodate the new dimension, and how you would calculate the angle to the GRB from the Earth.

Extension Activities

• Have the students research GRBs and write a short (1 page) report on some aspect of them. This can include how they are discovered, what they are, a biography of a scientist involved in studying them, a paper about the interplanetary network of satellites and/or the satellites it uses, or some other aspect of GRB research.
• Have the students go online and research a recent GRB. Where was it located, what satellite(s) observed it, what else is known about it? They could also write a report on the Gamma-Ray Burst Coordinates Network (or GCN; see http://gcn.gsfc.nasa.gov/), which reports new GRBs to the astronomical community.

Assessment

• 4 points: Graph and calculations are accurate.
• 3 points: Graph is accurate, most calculations are accurate.
• 2 points:Graph is partially accurate, some calculations are accurate but many are not.
• 1 point: Graph is not accurate, most calculations are inaccurate.
• 0 points: No work turned in

Answer Key for "Angling for Gamma-Ray Bursts"

1. This depends on the scale of the graph paper used. You will need to measure this yourself. The answers given below assume a grid scale of 0.5 centimeters per square.
2. 5 minutes; 13 minutes
3. 9 x 10¹⁰ meters; 2.3x10¹¹ meters
4. 5 light minutes; 13 light minutes
5. 2.5 cm; 6.5 cm (for 0.5 cm/square)
6. 19 minutes 24 seconds
7. 19.4 minutes
8. 3.5 x 10¹¹ meters
9. 19.4 light minutes
10. 9.7 cm (for 0.5 cm/square)
11. The angle should be close to 17°, and anything within about 5 degrees of this is acceptable.
12. Answers will vary by student.

Math Extension answers

13. θ = arcsin(opposite/hypoteneuse) = arccos(adjacent/hypoteneuse) = arctan(opposite/adjacent)
14. The three values should be close to 17°
15. The average should be close to 17°
16. Answers will vary by student.
17. From the point-point slope formula: angle = arctan [(y_s - y_E) / (x_s - x_E)]
18. θ_E-s1 = 63°, θ_E-s3 = 135°

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Activity 3: GRB Distribution on the Sky: The Plots Thicken

Science Concepts

• GRBs are distributed randomly across the sky.
• This means they are either very close or very far away.
• The pattern of objects we see in the sky can tell us about their location in the Universe.

Duration

1 hour

Essential Question

How does the perceived distribution of objects in the obsevable sky depend on their actual location in space?

Background Information

Note for the Teacher: This information is split up into a section for you, and one for the students to read. You will of course need to read the student portion as well. It is included in the Student Handout section. Read that part first. The information provided to the student is sufficient to do the exercise, but the additional information given to you below will compliment the student's understanding of how the GRBs are distributed in the sky, and what this tells us about them. Going over this information with the students the day before they perform the exercise will increase their understanding of the activity an its concepts. Be careful not to give away any answers, though!

The distribution of positions of GRBs in the sky is one key to understanding their distance. As more and more were detected over the years, it became clear that they were distributed evenly across the sky. Even after careful examination by astronomers who divided the sky into several different sections, there were no apparent clumps of GRBs or voids in any direction, meaning they were evenly spread out in every direction of the sky. This immediately tells us that they are either very close or very far. Why?

Let's assume for a moment that the GRBs are inside our own Milky Way galaxy. We know the Galaxy is shaped like a disk about 100,000 light years across, with a central "hub", a ball of stars roughly 10,000 light years across. The Sun is located about halfway to the edge of the disk, off to the side from the central region. If GRBs are some sort of phenomenon that occur in the disk, then we should see more toward the center, since in that case we are looking across the bulk of the Galaxy (as in the case above when you were near the edge of the field). Since GRBs are not seen to be concentrated in any one direction, we can deduce immediately that they are not distributed across the Galaxy, even without knowing their exact distance.

Since they are not at intermediate distances, which leaves only very close or very far. As it happens, astronomers have postulated that the Sun is surrounded by a large sphere of comets called the Oort cloud (named after the 20^th century Dutch astronomer who first proposed it). It is perhaps a trillion kilometers across, and since it is so big and spherical, the Earth sits very near the center of it. If GRBs come from there, then the distribution on the sky would be very close to what is actually seen. The problem with this idea is that the comets are very cold, low energy objects, and there is no known way to make them generate bursts of high-energy gamma rays.

Perhaps we need to think bigger. A lot bigger. If we look at the Universe as a whole, we see that galaxies like the Milky Way are distributed throughout it. In every direction we look, we see galaxies, and there are hundreds of billions of them. If a GRB occurs in a particular galaxy only rarely (explaining why we have never seen one in our own Galaxy), then we should still see plenty when looking across the whole Universe. In that case, we would see them everywhere we look. That's just how they do appear! But that leaves a new problem: this means that GRBs would have to be phenomenally energetic, since galaxies are so far away.

This left astronomers with the riddle: are GRBs nearby, coming from objects with no known mechanism to generate gamma rays, or very far, coming from objects generating fantastic energies that couldn't be explained?

That discovery had to wait until actual distances could be determined, and, in the end, it was found that GRBs were very far away, implying huge energies were involved (see Activity 4). But even without knowing the distances, astronomers were able to determine quite a bit about the location of GRBs. In the following activity, your students will follow the same logic used by the astronomers of that day, and figure out for themselves how the pattern of distribution of objects can tell us about where they are.

Aitoff Maps

GRB distributions in the sky are plotted using Aitoff maps (see Activity 1, "Additional Information: Aitoff Maps" for more about these). In the student worksheet, the first Aitoff maps are simulated apparent distributions of GRBs (the way they appear in the sky), assuming different spatial distributions of GRBs (the way they are distributed throughout space). The next is the actual distribution as seen by a NASA satellite.

Other notes, possible pitfalls for teacher to be aware of:

1. In this activity, we will be distinguishing between the apparent distribution of objects in the sky versus their actual location in space. As an example, two stars in the sky may appear very close together, but one may be close, while the other is much farther away. Because we cannot directly perceive the difference in distances to astronomical objects, they all effectively appear to be infinitely far away. This makes the sky look like a bowl over our heads with the objects painted on it. So in this activity, when we refer to the distribution of objects "in the sky" we mean their two-dimensional distribution, without regard to their distance. When we refer to their location "in space" we aso include the third dimension. To apply this to the example above, the two stars appear near each other in the sky, but are actually located very far apart in space. You will need to be very clear about this when explaining the activity to your students.
2. The students will be comparing a one-dimensional distribution of foil balls along the circumference of a circle to a two-dimensional distribution of GRBs in the sky. Make sure they understand the analogy.
3. Some students may be confused about Aitoff maps, thinking that their location is somewhere on the map. Make sure you review the information about Aitoff maps from Activity 1, "Sorting Out the Cosmic Zoo."

Materials for each group of 2 or 3 students

• Student worksheets for each student
• Student Handout
• Aluminum foil (enough to make 100 balls total~75 foot roll)
• Graph paper for plotting aluminum ball distributions
• Glue
• Yarn (~24 meters)
• Scissors
• 4 popsicle sticks or pipe cleaners

Objective

Students will count and plot the number of aluminum foil balls distributed around a circle on the floor using different bins. The plots will be compared to simulated gamma-ray burst distributions on the sky so that the students will see how simply mapping the locations of GRBs will give insight on their real spatial distribution.

Procedure

1. Pre-class: The day before you plan to do the activity, introduce the activity by using the Background Information section. Give the students the example of the fireflies in the field, making sure you discuss the binning of directions to aid analysis.
2. Explain to the students that they will be investigating how the apparent distribution of objects yields clues to their distances and real spatial distribution. They will be counting the number of aluminum foil balls in placed in a circle on the floor, then moving their point of reference and counting them again. The results will be plotted, and compared to various simulated distributions of GRBs. In essence, they will be performing the same technique used by astronomers to understand GRBs before their distances were known. You will also need to explain Aitoff projection maps to them.
3. To eliminate any misconceptions: Give each student a copy of the student worksheet to take home and read. As homework, have them read it carefully and write out a paragraph describing the procedures of the activity. You can also assign the Extension Activity (see below) as homework before the activity is done.
4. The day before the activity, create the "wedge assembly".
   1. Take 2 popsicle sticks and glue them together at their centers to form a plus-shape. Repeat this with two more popsicle sticks. Glue the two pluses together to form an asterisk-shape with 8 arms, each 45 degrees apart. Pipe cleaners can be used as well; they do not need to be glued, but can instead be wrapped together at their centers.
   2. Cut 8 pieces of yarn, about 3 meters in length each.
   3. Glue one end of each piece of yarn to the tip of each popsicle stick, so that when fully extended you have an asterisk-shape several meters across. If you are using pipe cleaners, tie the yarn to the ends of the pipe cleaners.
5. Crumple approximately 100 aluminum foil balls so they are about 3-4 cm in diameter (we recommend handing out sheets of foil to the students to help).
6. In-class: Prepare the exercise.
   1. In an open area about 5 meters across (you may have to go outside), place the foil balls more-or-less evenly distributed along the circumference of a circle 4 meters in diameter. It is not critical that the balls be perfectly evenly distributed, but try to make the circle as close to 4 meters across as possible, since the diameter is used in the exercise. You can have a student measure the diameter and report it to the class. As long as everyone uses the same number it will work out.
   2. Place the popsicle stick/pipe cleaner wedge assembly in the center of the circle, and extend the yarn out so that the circle is divided into 8 even pie-wedge-shaped bins. Try to make the wedges as equal in size as possible.
7. Begin the exercise. After the students fill out the first table in the exercise, get some volunteers to move the wedge assembly as outlined in the student handout.
8. Post-activity: Discuss the actual distribution of GRBs in the sky, and how they really are at vast distances. Astronomers' first step in figuring this out was to do what the students just did: plot GRB positions on the sky. Does the actual distribution really tell you anything about the distance to the GRBs (imagine they are in a sphere surrounding the Sun just past Pluto, for example, and compare that to GRBs being at cosmological distances)?

Transfer Activities

Encourage the students to go outside on a clear night and look at the stars in the sky. Do they appear to be evenly distributed, or do they have a pattern? What does this imply about their spatial distribution?

Extension Activities

In the late 1700s, astronomer William Herschel tried to determine the size and shape of the Milky Way by counting up stars in different directions. Jacobus Kapteyn repeated this effort in the 1920s. Have the students research how astronomers used this method, how well it worked, and what the failings of it are. They can compare this to the method used in the activity of finding the distribution of GRBs.

Lesson Adaptations

Sight-impaired students can be encouraged to actually feel the balls with their hands as they move around the circle. They can feel where the yarn is, and can count the balls that way. It might be helpful to put some distinguishing object such as a rock or a blackboard eraser where the yarn intersects the circle.

Assessment

• 4 points: Comparisons are all complete and accurate, calculations are all accurate.
• 3 points: Comparisons are mostly complete and accurate.
• 2 points: Comparisons are somewhat complete and accurate, some calculations are accurate.
• 1 point: Comparisons are not complete and accurate, calculations are inaccurate.
• 0 points: Nothing turned in.

Answer Key:

Step 1: Having a Ball

1. This will depend on how many foil balls are made. For the answer key, numbers will be given assuming 100 foil balls are used.
2. Assuming a diameter of 4 meters, the circumference of the circle is 12.6 meters, so the balls should be about 12.6/100 = .126 meters (12.6 cm) apart.
3. 8 wedges
4. 45°
5. 100 balls / 8 wedges = 12.5 balls per wedge (rounding up or down is acceptable)

Step 2: The Cutting Wedge

6. No. Some wedges are now wider than others where they intersect the circle, so there will be more balls in the wider wedges, and fewer in the smaller ones.
7. The curve for Position 1 should be roughly flat, with some peaks and valleys due to the somewhat random distribution of the balls. The curve for Position 2 is more like a sine wave, also with random peaks and valleys.
8. Some sources of deviation include the balls may not be exactly evenly spaced, the wedges may not being perfectly straight, some balls will fall on a wedge boundary and be moved into one wedge or another.
9. Both tables should add up to the same number of balls.
10. This should not be surprising; the distribution changed but the total number of foil balls did not. This may catch a few students!
11. The average number of balls per wedge is 100 balls / 8 wedges = 12.5, as before.
12. Again, this should not be surprising: the total number of balls and the number of wedges did not change. The average value does not change, only the actual number in each wedge changed.

Step 3: A Twist in the Plot

13. Figure 4 has points distributed evenly throughout it. In Figure 5 the points cluster along the equator, with some vertical thickness. There is also a bulge in the center, which thins out at longitude 180°.
14. Figure 6 should most resemble the plot for Position 1, and Figure 7 should resemble Position 2.
15. In Figure 4, the GRBs are spread evenly across space in a spherical distribution, with us viewing them from the center. In Figure 5, they are distributed in a flat disk, with us viewing them from off-center.

Step 4: BATSE in the Belfry

16. Figure 4 looks most like the real distribution, as does the collapsed plot.
17. GRBs must be distributed evenly throughout space, with us in the center of that distribution.
18. In general, although the actual distances cannot be found using this method, it can distinguish between whether the GRBs are located in the Milky Way or not. If they were, we would see an off-center distribution. So GRBs must be either very close or very far away.

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Activity 4: Beam Me Up

Science Concepts

Many astronomical objects emit energy in narrow beams. This means the total energy we calculate that is emitted by the object is much less than if we assume they emit energy isotropically (in a sphere, in all directions). Also, the number of objects we see depends on the amount of beaming.

Duration

45 minutes

Essential Question

If an object emits light in a beam and not isotropically, how does this affect what we know about it?

Background Information

Note for the Teacher: This information is split up into a section for you, and one for the students to read. You will of course need to read the student portion as well . It is included in the Student Handout section. The information provided to the student is sufficient to do the exercise, but the additiona information given to you below will compliment the students' understanding of how beaming affects the total energy of a GRB and how many of them we see. Going over this information with the students the day before they perform the exercise will increase their understanding of the activity and its concepts.

If GRBs beam their energy instead of emitting it isotropically, there can be a huge concentration of energy. To see how, lets look first at an object that emits isotropically. To find the total light emitted by an object that emits this way, you take the amount of light you see falling on a given area (say, 1 square meter), and then find the ratio of that area to the area of the sphere defined by your distance to the object. For example, say you are 10 meters from a light bulb, and you have a detector that is one square meter in area (a circle about 0.6 meters across). The total area of the sphere around the light bulb at your distance is:

Area = 4πr² = 4π(10 m)² = 1257 m²

So the total light emitted by the light bulb is 1257 times what you see in your 1 square meter detector.

Now think about what this means for GRBs, which are much further away than 10 meters. A GRB that was spotted on January 23, 1999 was nearly bright enough to be seen by the naked eye, but was 10 billion light years away. Assuming it emitted light isotropically, and using the formula above, astronomers found that the GRB must have had the energy of about 2 million billion times that of the Sun! Even for astronomers familiar with big numbers, this energy was so vast that no one could imagine what could power such an explosion.

But if the GRB beamed its energy, we cannot use the equation above, because it will grossly overestimate the total amount of light emitted. To see this, imagine the beam from the GRB mentioned above was so incredibly narrowly focused that by the time the beam reached the Earth, it was only 0.6 meters across so that the area of the beam were one square meter (in reality, no beam could ever possibly be this narrow). If that were the case, our 1 square meter detector will in fact see all the energy emitted by the object instead of some tiny fraction. But if the GRB emitted isotropically, given the distance of 10 billion light years, the light would be spread out over a sphere with an area of:

4 π r² = 4 π (1x10¹⁰ light years x 9.5x10¹⁵ m/light year)² = 1.1 x 10⁵³ m²

In that case, the 1 m² detector saw only 9 x 10^-54 of the total light emitted by the GRB (1 square m out of 1.1 x 10⁵³)

So we see that beaming can, in principle, solve the energy problem. Even a moderately narrow beam can drop the total energy need by a factor of hundreds or thousands (in fact, a beam 1 degree across means a drop in energy of just about 50,000). If this is taken into account, then it becomes possible to have known energy sources for GRBs. In fact, this is one of the reasons why astronomers think that GRBs signal the births of black holes: the energy released in the formation of a black hole is similar to that of a GRB if beaming is taken into account.

There is another implication of beaming besides energy needs. Since the beam is narrow it means that we have to be in the path of that beam to see the GRB. If the beam misses us, we don't see it! Before the idea of beaming, astronomers assumed we were seeing every GRB that went off, but if the energy is beamed, we miss many -- if not most-- GRBs! This means that if we see, say, 100 per year, then there must be many more GRBs going off, perhaps thousands per year, that we do not see. The number we miss depends on how tightly the beam is focused; a broad beam means we don't miss many, while a narrow beam means we miss a lot. If the beam from a GRB is 1 degree across, the energy we calculate for it drops by 50,000, but it also means there are 49,999 of this kind for every 1 we see.

In this activity, your students will use flashlights and megaphones to represent the beam from a GRB. They will see that beaming means the GRB has lower energy, and also that there must be many more GRBs going off then we actually detect.

Additional Information

Part A

Students will be constructing crude megaphones out of paper and using them to project their voice. This may lead to some confusion if the students are placed too close together, so you'll need ample elbow room for this. Spread the students out across the classroom, in the hallway or even outside as necessary.

Part B

For this activity, you will need to spin a flashlight around so that it rotates many times (more than three times) but stays in one place on the floor. This can usually be done with a standard flashlight, but takes practice. Try it several times until you feel comfortable with it. If you cannot get the flashlight to stay in one spot on the floor, you can attach it to a ruler using tape and spin that. If the ruler has a hole in it (for example, the kind that go in three-ring binders have holes) then you can use a pencil or other narrow object as a spindle. Put it through the hole and spin it that way (note: this method makes it harder to spin the flashlight around more than once or twice). A lazy susan (a rotating plate used in restaurants for condiments) could also be used, as long as it doesn’t take too long to slow to a stop!

The students will be sitting in a circle about 4 meters across. You may need to adjust the diameter if you have too few or too many students to fit that size circle. Since the students will be observing the flashlight, it may help to cover any windows and dim the lights. You will be spinning the flashlight a number of times, the more the better, but it should be at least twice for every student in the classroom (if there are 20 students, spin it 40 times). You may want to have a student keep track of how many times you have spun it, or mark a piece of paper every time you spin it.

Materials for each student

• Student Handout
• Student Worksheet
• Calculator
• Flashlight (one for the whole class in Part A)
• A protractor (Part A)
• Construction paper and tape (Part B)

Objectives

• Part A: After using a megaphone, students will see that beaming energy is much more efficient than radiating isotropically, and that the total energy calculated for a GRB will be much less if we assume they beam their energy.
• Part B: By observing the behavior of a spinning flashlight which represents the beam of a GRB, the students will see that the total number of GRBs is much higher than the number detected.

Procedure

1. Pre-class: make copies of the Student Worksheets, one per student. The Student Handout can be given out one per group of 2-3 students.
2. In class: Introduce the activity by reviewing information in the introduction to gamma ray bursts and in the activity overview.
3. Part A : Explain to the students that they will be constructing megaphones from paper, and comparing the loudness of their voices with and without the megaphone. They will then extrapolate this knowledge to GRBs. The activity is done in teams of two students.
4. The activity is done individually, though the classroom will compare results at the end.
5. Part B : Explain to the students that they will be observing a flashlight and noting when they can see the filament and when they can't. This part of the activity is done individually, though in the end, students will compare results with each other and overall.
6. You will need enough space for the students to sit in a circle about 4 meters in diameter, depending on the number of students in your class.
7. In Part B, students may have the misconception that the megaphone is actually amplifying their voice. The megaphone does not amplify their voice; the total energy in the sound waves remains the same. What the megaphone does is focus their voice so the sound waves all move in a narrower beam, rather than spreading out in all directions. By forcing the sound waves into a beam, the megaphone keeps the sound from getting fainter as quickly. Less total energy is needed to be heard with a megaphone.
8. Engage the students in discussing an extrapolation of the activity to much greater distances. Imagine Student A was located a kilometer away from Student B. If Student B were able to hear Student A's voice, they might be puzzled. It would be very difficult or impossible to shout loudly enough to be heard from such a distance. The total energy Student A could put into the sound waves of their voice would get diminished by the great distance, and Student B wouldn't hear them. But if the energy in the sound waves from Student A's voice were able to be focused into a beam, it could be heard across that distance. A megaphone beams the voice, so that sound waves with lower total energy can still be heard.

   The gamma ray burst energy problem is like Student A's voice. GRBs are located at distances of billions of light years. If they emitted their light isotropically, like Student A's voice without the megaphone, the energy needed would be beyond any known process to generate.

   But if that energy is beamed, like Student A's voice when using a megaphone, the total energy needed is far less, well within the realm of known physics. This solves the energy problem! But as seen in Part A, it also means that GRBs are more common than previously thought. This is a tradeoff: the more the energy is beamed, the easier they are to detect if we see the beam, but the narrower the beam the more likely it is to miss us.

9. When the students are done with the Part A, collect the values each student got for question 3 and put them on the blackboard. Have the students compare the numbers and discuss any similarities or differences. Ask them what they think the results would have been like had the beam been much narrower, or much larger. Remind them that GRB beams are probably very narrow, only a few degrees across. Some astronomers estimate that we only see one out of every 100 GRBs.

Extension Activities

As a way of explaining how beaming takes less energy than isotropic emission, have the students sit in a circle on the floor. Get 20 or so small objects such as pennies, erasers, or pens, but dont tell the students how many you have. Sit in the middle of the circle and announce that you are a gamma-ray burst (or a penny burst, or whatever objects you have), and that you are emitting isotropically. Give one object to each student. Tell them to think about how many objects you must have started with to be able to give each one of them an object. (they should guess that you have as many objects as there are students in the class). Collect the objects again, and then announce that you are a burst. Then give all the objects to a single student. Ask the class that if they were that student, and they thought that the objects were distributed isotropically as before, how many would you have had to start with. They should guess that it would be the total number of students times the number of objects you gave that one student. But in reality, you had the same number both times. This shows that the total calculated energy of a GRB is much smaller if it is beamed than if it emitted isotropically.

As an advanced math extension, the students can calculate the ratios of the areas of beams of varying opening angles compared to the whole sky. The area in square degrees of a beam of opening angle (θ) in degrees is:

Area = 2(π)[1-cos(θ)]

The area of the sky is 41.253 square degrees. They can then extrapolate how many GRBs are not seen depending on their beam opening angles as an extension to Step 4 of Part A ("Light Up My Life")

Lesson Adaptations

For Part A, if a student is visually impaired, they can be the one doing the speaking (Student A). If they have trouble speaking, they can blow a whistle or use some other sound gererator such as a radio. For Part B, choose them to spin the flashlight for Part A, or keep track of the number of spins.

Assessment

• 4 points: Part A: Answers are complete and correct, calculations are all accurate. Part B: explanation is thorough and accurate, calculations are all accurate
• 3 points: Part A: Answers are mostly correct and complete, most calculations are accurate. Part B: explanation is accurate but not thorough, most calculations are accurate.
• 2 points: Part A: Answers are somewhat correct and complete, some calculations are accurate. Part B: explanation is somewhat accurate, some calculations are accurate.
• 1 point:Part A: Answers are incomplete and inaccurate, calculations are inaccurate. Part B: Explanation is inaccurate, calculations are inaccurate.
• 0 points: No work turned.

Answer Key for "Beam Me Up!"

Part A, Step 2: Shout Out

1. Student A's voice should be louder with the megaphone.
2. Student A had to speak louder without the megaphone, so the energy was higher without the megaphone.
3. The energy in Student A's voice was not amplified by the megaphone. The megaphone prevents the energy from Student A's voice from expanding outward in all directions. Instead, the energy is focused into a beam, focusing more energy in one direction.

Part A, Step 3: Gigaphone

4. The unbeamed GRB has more energy. The beamed GRB put all its energy into one direction, but the unbeamed GRB had to spread that energy out in all directions.

Part B, Step 1: Setup

5. This depends on class size.

Part B, Step 2: Won't you beam mine?

6. For the answer key, we will use 100 as the total number of spins. Scale your answers below to match the number of spins you actually used.
7. This answer will vary from student to student.
8. This will be the total number of spins divided by the number of times they saw the filament.
9. This varies from student to student.
10. This will be 360° divided by the number of students.

Part B, Step 3: Opening Up

11. 11. An opening of 90º is 1/4 of a circle, so they should see the filament 1/4 of the time, for a total of 25 times.
12. This depends on the opening angle measured. The answer is : opening angle/ 360°.
13. This depends on the opening angle measured and the number of spins. The answer is: (opening angle/360°) x number of spins
14. This will vary from student to student. In general, variations will depend mostly on the fact that you don't have many spins, so you have "small number statistics," and you should expect big variations. If you spun the flashlight 1000 times, for example, the variations would be much lower.

Part B, Step 4: Light Up My Life

15. This is the same a question 9: (opening angle/360° x number of GRBs = (opening angle/360°) x 100
16. This is 100 - the answer to question 11: 100 - (opening angle/360°) x 100)

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Glossary

Accretion Disk

The flattened disk of matter swirling just outside the black hole.

Afterglow

the fading light from a gamma ray burst that can last for days or months

Aitoff Map

a way of mapping a sphere two-dimensionally such that regions near the poles are not artificially stretched-out.

BlackHole

An object so small and dense that the escape velocity is faster than the speed of light.

Cartesian coordinates

a way of mapping an objects position using perpendicular x- and y-axes.

Declination

a coordinate on the sky corresponding to latitude on the Earth

Degree

1/360^th of the circumference of a circle

Electron Volt (eV)

a unit of energy commonly used in gamma ray astronomy. A typical gamma ray has an energy of about 100 million (10⁸) electron Volts. A photon of visible light has about 1 eV of energy.

Flux

the amount of energy passing through an area of one square centimeter every second

Galaxy

a collection of gas, dust, and billions of stars bound together by their own gravity

Gamma Ray

a photon with extremely high energy, at the highest energy end of the electromagnetic spectrum

Gamma Ray Burst

a sudden blast of gamma rays coming from random points on the sky

Hard X-ray

an X-ray with in the upper end of the X-ray range. This overlaps with the soft gamma ray energy range.

Jet

A thin, highly focused beam of matter and energy emitted from some black holes. Jets can range from a few light years in length to hundreds of thousands of light years long.

Joule (J)

a unit of energy, equal to 6.3 x 10¹⁸ eV

keV

one thousand (10³) electron Volts

Large Magellanic Cloud

a companion galaxy to our Milky Way

Light Curve

a plot showing the change in brightness of an object versus time

Light Week

the distance light travels in a week; approximately 181 billion kilometers (1.8 x 10¹¹ kilometers)

Light Year

the distance light travels in one year; approximately 10 trillion kilometers (10¹³ kilometers)

Luminosity

the total energy emitted by an object per second

Milky Way

the name of our galaxy

Millisecond

one one-thousandth (10^-3) of a second

Period

the amount of time it takes for a pattern to repeat

Photon

an individual particle of light

Right Ascension

a coordinate on the sky corresponding to longitude on the Earth

Soft X-ray

an X-ray with in the lower end of the X-ray range.

Soft Gamma Ray

a gamma ray at the lower end of the gamma ray energy range. This overlaps with the hard X-ray energy range.

Soft Gamma-ray Repeater

an object that emits a blast of gamma rays in a semi-periodic manner. Astronomers think these are neutron stars undergoing "star quakes".

Solar System

a collection of planets, moons, comets, etc. which orbits a star. Our solar system is roughly 10¹⁰ kilometers (10¹³ meters) across.

Supernova

a star which explodes at the end of its life

Supernova Remnant (SNR)

the expanding cloud of gas left over from an exploding star

X-ray

a high energy photon, but one with less energy than a gamma ray

X-ray Burster

a neutron star that periodically emits a blast of X-rays. Astronomers think these are neutron stars accreting matter from a nearby companion star.

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National Science Standards

Activity #1

• Content Standard A: Science as Inquiry
  • Abilities necessary to do scientific inquiry
    • Students conduct scientific investigations when they sort the cards.
    • Students formulate explanations for how they sorted the cards.
    • Students are encouraged to discuss reasoning and results with their peers.
    • Students are asked to plot the data on cards and analyze their results.
    • Students are asked to communicate and defend the results of their scientific inquiry.
  • Understanding about scientific inquiry
    • Scientists used the same data to arrive at similar conclusions.
    • Scientists rely on tools such as Swift to enhance the gathering and manipulation of data.
• Content Standard B: Physical Science
  • Interactions of energy and matter
    • Students are asked to compare high energy objects and sort the energy of the objects by magnitude.
    • Students learn what type of E M waves are emitted by these objects.
    • Students learn to appreciate the amount of energy emitted by a GRB.
    • Energy is transferred by light waves from GRBs.
• Content Standard D: Earth and Space Science
  • Origin and evolution of the universe
    • One of the proposed progenitors of GRBs is the birth of a black hole.
• Content Standard G: History and Nature of Science
  • Science as a human endeavor
    • By sorting and defining categories with the data on the cards, students see how the individuals and teams have contributed and will continue to contribute to the scientific enterprise.
  • Nature of scientific knowledge
    • Students see how science distinguishes itself from other methods of acquiring knowledge through the use of real, observed data.
    • Students will understand that as technology improves, scientific knowledge may change.
  • Historical perspectives
    • Students can see how useful these scientific data were for scientists, and how they have changed the understanding of burst sources.

Activity #2

• Content Standard A: Science as Inquiry
  • Abilities necessary to do scientific inquiry
    • Students use the light rulers and calculators as a tool in their scientific investigation.
    • Students must determine the direction to the GRB, eliminating false leads. ¥ Students are asked to communicate and defend their results.
  • Understanding about scientific inquiry
    • Students, like scientists, use alternate methods to arrive at same conclusion.
• Content Standard B: Physical Science
  • Motion and forces
    • Gamma rays travel at the speed of light.
  • Interactions of energy and matter
    • Gamma rays are a high energy form of light.
    • The amount of energy in a gamma ray is very high, and gamma rays are the most energetic form of light.
• Content Standard D: Earth and Space Science
  • Origin and evolution of the universe
    • One of the proposed progenitors of GRBs is the birth of a black hole.
• Content Standard E: Science and Technology
  • Abilities of technological design
    • Swift will do the same things as the I P N, i.e. locate bursts.
• Content Standard G: History and Nature of Science
  • Science as a human endeavor
    • Real teams of scientists use this method to locate GRBs.
  • Historical perspectives
    • Students emulate older methods of determining the direction to a GRB, and learn that Swift will update this method.

Activity #3

• Content Standard A: Science as Inquiry
  • Abilities necessary to do scientific inquiry
    • Students discover how objects like GRBs are distributed relative to the student's position.
    • The students model the GRB distribution using an Aitoff projection.
    • Students use real GRB plots (scientific criteria) to find the preferable explanations about the GRB distributions, and in doing so are prompted to recognize and analyze alternative explanations and models.
    • Students are asked to communicate their results and formulate explanations when plotting the distribution.
    • Students are asked to describe, using their own words, how they arrive at the GRB distribution conclusion. Understanding about scientific inquiry.
    • Students learn that Swift will gather additional needed data about GRBs. ¥ Students get more familiar with the use of mathematics, technology, and evidence from their inquiry.
• Content Standard D: Earth and Space Science
  • Origin and evolution of the universe
    • Students discover that the mysterious GRBs can provide important clues about how the Universe has evolved over time.
    • Students are able to get a grasp of how objects and events are distributed in the Universe.
    • One of the proposed progenitors of GRBs is the birth of a black hole.
• Content Standard E: Science and Technology
  • Understanding about science and technology
    • Scientists studying GRBs ask different questions (for example, about different distributions of GRBs) than scientists studying different disciplines.
• Content Standard G: History and Nature of Science
  • Science as a human endeavor
    • The Swift team's goal is to determine the origins of and physical mechanisms behind the mysterious GRBs, which will contribute to the future of GRB science.
    • Students will grasp the general idea of the methods scientists use to solve scientific mysteries.

Activity #4

• Content Standard A: Science as Inquiry
  • Abilities necessary to do scientific inquiry
    • While experimenting with the megaphone, students see that scientists conduct scientific investigations for a variety of reasons.
    • Students learn that the results of scientific inquiry have led to the belief that GRBs beam their energy.
    • Students will also see that even scientists do not understand everything about beaming, and Swift will help to answer these questions.
  • Understanding scientific inquiry
    • The energy emitted by a GRB is sometimes so great that even scientists have difficulty grasping it.
• Content Standard B: Physical Science
  • Motion and forces
    • Gamma rays travel at the speed of light.
  • Interactions of energy and matter
    • Gamma rays are a high energy form of light.
    • The amount of energy in a gamma ray is very high, and gamma rays are the highest energy form of light.
    • Sound waves from the student's voice transmit energy through the air. GRB light waves also transmit energy, through the vacuum of space.
    • Light waves in general transmit energy.
• Content Standard D: Earth and Space Science
  • Origin and evolution of the universe
    • Students are able to get a grasp on how objects and events are distributed in the Universe.
    • One of the proposed progenitors of GRBs is the birth of a black hole.
• Content Standard E: Science and Technology
  • Science as a human endeavor
    • Scientists studying GRBs ask different questions (for example, about beaming) than scientists studying different disciplines.
    • Scientists had to creatively answer the question about the total energy emitted in a GRB.

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National Math Standards

Number and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

• Students develop a deeper understanding of very large and very small numbers and of various representations of them (#1 & 2).

Compute fluently and make reasonable estimates

• Students develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases (#2).
• Students judge the reasonableness of numerical computations and their results (all four).

Algebra

Understand patterns, relations, and functions

• Students generalize patterns using explicitly defined and recursively defined functions (#2 & 3).
• Students understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions (#2).

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• Students analyze properties and determine attributes of two- and three- dimensional objects (all four).
• Students use trigonometric relationships to determine lengths and angle measures (#2 & 4).

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

• Students use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations (#2 & 3).
• Students investigate conjectures and solve problems involving two- and three- dimensional objects represented with Cartesian coordinates (#2 & 3).

Apply transformations and use symmetry to analyze mathematical situations

• Students understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices (#2).

Use visualization, spatial reasoning, and geometric modeling to solve problems

• Students draw and construct representations of two- and three-dimensional geometric objects using a variety of tools (#1,2, & 4).
• Students use geometric models to gain insights into, and answer questions in, other areas of mathematics (all four).
• Students use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture (all four).

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

• Students make decisions about units and scales that are appropriate for problem situations involving measurement (#1 & 2).

Apply appropriate techniques, tools, and formulas to determine measurements

• Students understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders (#3 & 4).
• Students apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations (#3 & 4).
• Students use unit analysis to check measurement computations (#2, 3, & 4).

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• Students understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each (#1).
• Students know the characteristics of well-designed studies, including the role of randomization in surveys and experiments (#1, 2, & 3).
• Students understand histograms, parallel box plots, and scatterplots and use them to display data (#1 & 3).

Develop and evaluate inferences and predictions that are based on data

• Students evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions (#1 & 3).

Understand and apply basic concepts of probability

• Students understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases (#3).
• Students use simulations to construct empirical probability distributions (#3).

Reasoning and Proof

• Make and investigate mathematical conjectures (#3 & 4).

Problem Solving

• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.

Communication

• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.

Connections

• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.

Representation

• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.

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Resources

For more information on Swift and GRBs, see the Swift Education and Public Outreach web site: https://imagine.gsfc.nasa.gov/educators/programs/swift/

This educational unit as well as materials dealing with the electromagnetic spectrum can be found on the Swift E/PO web site at: https://imagine.gsfc.nasa.gov/educators/programs/swift/classroom/

Imagine the Universe! has a nice introductory tutorial on gamma ray bursts: https://imagine.gsfc.nasa.gov/science/objects/bursts1.html

as well as supernovae (with a small amount of math): https://imagine.gsfc.nasa.gov/science/objects/supernovae1.html

More information (with links) about gamma ray astronomy is at the NASA Goddard Space Flight Center's website at https://imagine.gsfc.nasa.gov/science/toolbox/gamma_ray_astronomy1.html

A vast collection of (somewhat more technical) information on GRBs is http://www.mpe.mpg.de/~jcg/grb.html

An introduction to Galactic coordinates (as part of the Multi-wavelength Milky Way poster): https://asd.gsfc.nasa.gov/archive/mwmw/mmw_usemap.html

A NASA introduction to pulsars: https://imagine.gsfc.nasa.gov/science/objects/neutron_stars1.html

The GRB Coordinates Network provides rapid-response information on the locations and follow-up observations for GRBs detected by spacecraft, and can also provide automatic alerts to observers when GRBs are reported: http://gcn.gsfc.nasa.gov

The Third Interplanetary Network maintains a list of GRBs that are detected by many spacecraft throughout the solar system. Information provided by spacecraft in this network are used to refine the GRB positions: http://www.ssl.berkeley.edu/ipn3/

The Swift E/PO team has also used GRBs as the centerpiece of a series of activities developed in a partnership with the Great Explorations in Math and Science Group at UC Berkeley's Lawrence Hall of Science. The Invisible Universe: from Radio waves to Gamma-rays may be ordered through their website at: http://lhsgems.org/gemsInvUniv.html