Beam Me Up
Student Handout
Once it was determined that GRBs were located at cosmological (very vast) distances, another problem was dropped into astronomers' laps: what could generate so much energy?
This problem was known before the distances were determined, and was actually used as a key argument against large distances for GRBs. The farther away an object is, the more energy it must emit to be seen. Think of it this way: the Sun is by far the most brilliant object in the sky to our eyes, ten billion times brighter than Sirius, the brightest nighttime star. Yet in reality Sirius is actually more luminous than the Sun; it gives off more total energy. But Sirius is 550,000 times farther away from us than the Sun is, and so the star's light is diminished by distance.
In fact, the brightness of an object decreases by the square of the distance. A 100 kW light bulb 1 meter away will actually appear 4 times brighter than one 2 meters away (the distance doubles, so the amount of light you see drops by a factor of 4). It will be 100 times brighter than one 10 meters away, and 10,000 times brighter than one 100 meters away.
This is called the "inverse square rule" of brightness. It occurs because a star (or a light bulb) emits light isotropically, in all directions. The light expands away from the star in the shape of a sphere. The area of that sphere is equal to 4 π r2 where r is your distance from the light source. If the distance from the star is tripled, the area goes up by a factor of 3 x 3 = 9, and the light you see hitting your eye drops by 1/9.
From 10 meters away, 1 square meter covers only a small portion of the emitted light.
Now think of what this means for GRBs . They are so far away that for us to receive any energy from them at all means that they must be incredibly luminous. In fact when astronomers calculated how much energy they must be emitting in total, the numbers were so big that no known source of energy could possibly power a burst of that size. This was a major puzzle.
But there was a way out. What if the light were not emitted isotropically? What if it were beamed?
Some objects do not emit light in all directions, but instead send out light in narrow beams, like the beams from a lighthouse. Beams are emitted from young stars, still circled by a disk of debris that may form planets. Neutron stars, ultra-dense cinders left over from supernovae explosions, are known to emit their energy is very tightly-constrained beams. Even the giant black holes in the centers of active galaxies can emit narrow beams which can stretch for hundreds of thousands of light years. It is therefore logical to suppose that GRBs also might beam their emission.
If the light is beamed, the detector sees all the light.
In the following activities, you will investigate how beaming energy saved the day for astronomers, and the implications on the total number of GRBs in the universe.
A. Megaphones and Gamma Ray Bursts
Step 1: Setup
In this activity you will compare the loudness of someone speaking with and without a megaphone.
First, split up into teams of two people each. Then make a megaphone out of construction paper. Simply roll up the paper into a cone such that the narrow end has a small opening, but large enough to fit around your mouth. The large opening of the cone should be several times wider than the narrow end. When it has the right shape, tape the flap so it stays together.
Step 2: Shout Out
Pick roles for each student. Student A will be the one who will make the noises with and without the megaphone, while Student B will be the one listening.
The two members of each team should then stand several meters apart; at least four or five, but no more than ten. Try to separate yourselves from the other teams to minimize confusion. When you are properly placed, turn and face each other.
Student A: Without using the megaphone, speak normally to Student B. It doesn't matter what you say, but it would be helpful if you use some sort of sequence that is easy to follow, like the alphabet, or counting upwards. As you speak, talk more and more quietly.
Student B: Listen carefully to Student A. When Student A's voice is no longer or just barely audible, let them know by raising your hand.
Student A: When Student B lets you know you are just barely audible, continue speaking at that level, and raise the megaphone up to your mouth. Make sure you keep your voice tone and volume level. Continue to speak as you did before.
Student B: When Student A uses the megaphone, listen for their voice. Can you hear it better now? If so, let Student A know.
Student A: When Student B lets you know your voice is audible, once again begin to lower the volume.
Student B: Similar to before, listen carefully, and let Student A know when their voice is barely audible through the megaphone.
- Does Student A's voice get quieter, remain the same, or get louder when the megaphone was used?
- When you speak, you generate sound waves. The loudness of the sound is related to the energy put into the sound waves. Given that, compare the amount of energy Student A put into their voice when it was barely audible without the megaphone to the energy at the end, when it was barely audible with the megaphone. Was the sound wave energy of the barely audible voice greater with the megaphone, or without it?
- In your own words, describe what the megaphone did to Student A's voice.
Step 3: Gigaphone
Now apply what you have just experienced to the field of high-energy astronomy. At first, astronomers thought that gamma-ray bursts emitted their light isotropically (in all directions). Then they realized the GRB energy must be beamed. Imagine two GRBs are at the same distance from Earth, but one is beaming its energy while the other one emits its light isotropically. Astronomers on Earth measure their apparent brightness and find them to be equal.
Imagine two GRBs are at the same distance from Earth, but one is beaming its energy while the other emits its energy isotropically. Astronomers on Earth measure their apparent brightness and find them to be equal.
- Which one was the more energetic event? Why?
B. Spin the Flashlight
Step 1: Setup
In a clear a space on the classroom floor, from a circle of sitting students. Don't crowd each other! Keep about 30 centimeters of space between you and the person on your right and left. Sit down on the floor so that all the students in the class form a circle with a radius of about 2 meters. Adjust your position so that each student is an equal distance from the students on your left and right.
- Write down how many students are sitting around the circle.
The teacher is going to spin a flashlight in the center of the circle several times, and will announce the number of that spin. When the flashlight stops, note whether you can see the filament of the bulb or not (not just the bulb, but the part actually making light). You may need to crouch down a bit to see the filament. Every time you see the filament, make a tally mark on the student worksheet (Question 7).
When you are done spinning the flashlight return to your seats.
Step 2: Won't You Beam Mine?
- How many times was the flashlight spun?
- How many times did you see the filament?
- How many times did you not see the filament?
- What is the ratio of how many times you saw the flashlight filament to the number of times the flashlight was spun?
- Using the number of students sitting at the circle, determine approximately how many degrees apart you were from the student next to you.
Step 3: Opening Up
The beam from the flashlight has an opening angle; that is, the beam is not perfectly straight, but expands out from the bulb in a cone. The opening angle is defined as the angle from one side of the cone to the other, as measured from the vertex. Note that if you are anywhere inside that cone, you can see the flashlight filament. You can verify this: put the flashlight on a flat horizontal surface (a desk or table, for example), then put your head down on the table. By placing your eye along the edge of the opening cone, you can see the filament. If you are outside the cone, you cannot see the filament.
- Imagine a flashlight with an opening angle of 90°. If it were spun 100 times, how many times on average would you expect to see the filament?
Now take the flashlight you used and lay it down on a piece of paper (or put it up against the blackboard). There will be a triangle or parabolic shape of bright light coming from the flashlight on the paper. The edges of this light should have fairly straight lines. Using a ruler, trace these lines. Remove the flashlight, and use the rulers to extend the lines so they connect at a point. Using a protractor, measure the angle between the lines. This is the opening angle.
- Knowing the opening angle, what are the odds you will see the filament in any given spin?
- Knowing the number of spins actually made, how many times would you expect to see the filament of the bulb?
- Compare the ratio of the times you saw the filament (from question 5) to the expected ratio (question 9). In your own words describe the similarities or differences.
Step 4: Light Up My Life
The Swift satellite is expected to see about 100 gamma-ray bursts per year. These bursts almost certainly emit their light in a beam.
- If the opening angle of the GRB beam is the same as your flashlight, what is the actual number of GRB events per year?
- How many do astronomers miss?
