Overview

Preparation and Materials

The teacher should be familiar with the GalaxSee application (for those unfamiliar with this software, there is an online tutorial), have it loaded on a computer, and have some means of displaying the monitor to the class.

If the teacher is going to use the helper spreadsheet that comes with this lesson, he/she should have Excel installed on the display computer and all student computers.

Objectives

• use a computational model to discover possible answers to a question about a natural phenomenon
• practice accurately observing and recording data from a scientific experiment
• communicate and defend a scientific argument while collaborating with other students.
• describe how equilibrium can occur as the balance of two effects.

Standards

• NSES content standard (9-12 A) on science as inquiry, including:
• Use technology and mathematics to improve investigations and communications.
• Communicate and defend a scientific argument.

• NSES content standard (9-12 D) on origin and evolution of the universe.
• NSES content standard (9-12 E) on understandings about science and technology.
• DoDDs Science 9 objectives, including:
• Use of computational models.
• Use careful systematic observation and data collection to obtain valid information.
• Relate force, motion, energy and power.

Activities

1. If the students have not performed the rotation and flattening activity, consider performing that activity before this one.

2. If the students have not observed images of different types of galaxies, show them images of elliptical galaxies form the SEDS database.

3. Make the following points about elliptical galaxies:
1. Gravity causes objects in space to collapse, but the fact that we observe very old elliptical galaxies implies that these objects are stable over long periods of time (billions of years)
2. Because of the long periods of time over which these objects change, we cannot watch the change happen directly.
3. In order to try to understand galaxy structure, scientists model galaxies on computers and, by watching the model evolve, they hope to learn why real galaxies have the features that we observe.
4. In science, we can express energy due to motion, and also energy due to position.
5. If we are to accomplish anything in science, it is extremely important that we are careful observers.
4. With the monitor displayed so that the students can see it, open the Model Settings and set the Time Step to 1.0 M yr (you can play with this to find a timestep that will allow the students to accurately observe what is happening), and the Integration Method to Improved Euler. The Shield Radius can be left at 0.1 kly and the Dark Matter should be zero percent.

5. Make sure that the Galaxy Setup is for a Spherical galaxy of 256 stars that are 500 solar masses each, with the rotation factor set to zero. Generate a New Galaxy (or, if you also have the Dark Matter parameter set to zero, you can use the pre-generated galaxy "no_rotation.gal" at this web site. Run the simulation, and have the students watch what happens. Rotate the galaxy for them so they can see it from different angles. Let the simulation run until the stars clump together in the center. Let the simulation continue, until many of the stars move past the center, but the majority form an image in the center similar to an elliptical galaxy. The core that forms is smaller than the original configuration, and many stars have been ejected due to interactions during the collapse.

   Note: Be careful of computer error here. As the stars clump to the center, their speeds will increase rapidly, and error may to accumulate in the model. If the time step is too large, or the shield radius too small, the model will become unrealistic, and could, for example, throw all of the stars out beyond the original boundaries. This is an inaccurate result. Keep an eye on the total energy, and if the energy is not conserved in the model, consider running it with either a smaller time step or a larger shield radius.

   For more information about detecting and controlling error, see the section about the info window in the GalaxSee tutorial.

6. Now run a model where all of the stars have some random velocity, instead of starting at rest. Using the helper spreadsheet, virial.xls, create a galaxy with a typical radius of 2 kly, and a typical velocity of 4 ly/Myr, or open the file virial.gal. Run the file and notice that the galaxy expands (you will need to make your timestep significantly smaller to really see it). Make the point to the students that a galaxy with too much random motion will expand, and not enough will contract.

7. Have the students guess what ratio of kinetic to potential energy they think would keep the galaxy stable. (With no rotation, the ratio of KE/PE would be zero, and with the random velocities in the example spreadsheet the ratio of KE/PE is roughly -2.2. It would probably be fair to say that a ratio of -1 might be a good guess.)

8. On the helper spreadsheet, students can vary the v_typ parameter to change the magnitude of the randomly generated velocities. To test, copy only the star data to a new spreadsheet and save as a tab-separated .gal file. Have the students try to find what random velocity configuration will keep the galaxy stable. Does this depend on the size of the galaxy? What is the ratio of the kinetic to potential energy for a stable galaxy?

   NOTE: The students can use the values of kinetic and potential energy from the spreadsheet.

Discussion of the Simulation

Ask the students to discuss why the galaxies just didn't collapse due to gravity. Have them write out a description of the models they ran.

Have the students look at a model with the same amount of potential and kinetic energy. Notice that the galaxy expands. As the galaxy expands, the potential energy decreases in magnitude, but the kinetic energy stays roughly the same. Would you expect the galaxy to become more stable or less stable over time (i.e. does it just keep going, or does it eventually stabilize)?

Discussion of Observation

Ask the students to compare their models to images of elliptical galaxies. Do the results of a "stable" galaxy look more like the images of an elliptical galaxy? less? the same?

Assign them to write a clear and accurate report of what they observed. Emphasize that it is important that they know what software was used, and what parameters were set. Be sure to go through the setup procedure again so that they can record this information.

Collaboration

Extensions

Further Experimentation

Have the students create a rotating disk with 256 stars, 200 solar masses each, and with a rotation factor of 1 in GalaxSee. Save the file and open it in Excel. Cut and paste the data into a copy of the helper spreadsheet, to calculate the kinetic and potential energy of the rotating galaxy. Does the same relation between energy of motion and energy of position hold for the spinning disk? Why might this be different?

Thinking Harder

Ask the students how they would further test the hypothesis that elliptical galaxies do not collapse because of random motion of stars. What observations could be made of elliptical galaxies to test this theory? (what is the range of redshift measurements of stars in the galaxy?) Can this information be determined from the model? (yes, compare to typical velocity.)