Black Hole Lesson

Overview

Black Holes are objects which are extremely massive and extremely dense. The gravitational pull of these objects (like any mass) increases as you get closer. With a Black Hole, you can get so close that no force you apply will be strong enough to pull you away. Not even light which passes through this zone (called the event horizon) can escape! But, if we cannot see the light from a black hole, how do we know it is there? This lesson will have the students learn how scientists detect black holes by modeling the rotation of galaxies with large masses in the center.

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.

This lesson also requires making calculations with GalaxSee data, and showing plots. A spreadsheet should also be installed on any student or display machines.

Objectives

Students will

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.
learn that while some events cannot be directly observed, their effects may be observable on other ways.

Standards

This lesson fulfills portions of the following standards and curriculum guidelines:

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

If the students have not learned about black holes, Virtual Trips to Black Holes and Neutron Stars has some excellent animations about how gravity would affect the light you see near one of these massive objects. Imagine the Universe has some introductory information on what Black Holes are, as well as one other method we use to detect them. There is also new data from the Chandra X-Ray observatory which may give us direct evidence that black holes exist!
Make the following points about black holes:
1. Since light cannot escape a black hole, we have to detect black holes by noticing their effect on nearby material. In-falling matter gives off X-rays, which is the main method of observing black holes.
2. The more massive an object is, the faster an object has to move in order to stay in orbit.
3. Scientists always have to find ways to observe the predictions of their theories, otherwise the theories cannot be tested.
In the Model Settings window which can be found under the Galaxy menu, set the time step to 1.0 M yr (you can play with this to find a time step that will allow the students to accurately observe what is happening), the shield radius to 0.1 kly, the dark matter to zero percent, and the integration method set to Improved Euler. Press Set and then close the Model Settings window.
With the monitor displayed so that the students can see it, 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 1. Press OK to generate a new galaxy. 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 galaxy flattens out. Show the students the model using the redshift option, and explain that we can measure the velocity of objects moving towards us and away from us using Doppler shifts. Stop the simulation, and save the model.
Open the saved file in a spreadsheet such as Excel. An example spreadsheet is provided. Use the spreadsheet to calculate the distance along the plane of the galaxy from the center (the radius), the rotational velocity, and the angular velocity for each star. The directions for using the spreadsheet are found on the spreadsheet. You simply cut and paste your data into the example spreadsheet and it is set to do the calculations for you. You may need to adjust the scale of the graph in order to get a better view of your data. The equations used are as follows:
- r = sqrt(x*x+y*y)
- rotational velocity = (x*vy-y*vx)/r
- angular velocity = (x*vy-y*vx)/(r*r)
Make a scatter plot of angular velocity versus radius, and then repeat for rotational velocity. Notice how each changes as one goes from the center to the outside of the galaxy. Should insert explanation for teachers here. In my graph without the dark matter, angular velocity was relatively constant (which would be expected for objects orbiting in constant circular motion) except for a few data point exceptions. In my graph with the dark matter the angular velocity is certainly not a constant, angular velocity is greater toward the center of the Galaxy, which implies that this is not constant circular motion.
Have students use the dark matter setting to create galaxies with a massive object in the center. To do this, increase the dark matter value in the Model Settings window. Be sure to start each trial with a new galaxy.
Have the students run models with different values of the central mass, and for each one save the file and plot the rotational and angular velocity curves of the galaxy.

Note: As you increase the central mass, you may find that error accumulates in the model for the time steps being used. One of your best indicators of error in the model is to check the total energy from the Show Info window. If the final energy is significantly different from the initial energy, you have accumulated error in your model. Try the model again with a smaller time step.
For more information about detecting and controlling error, see the section about the info window in the GalaxSee tutorial.

Discussion of the Simulation

Ask the students how the rotational speed within a galaxy with no central mass changes as you get closer to the center. Does the same thing happen with the angular velocity. If so, does this make sense? If not, how can this be explained?

Ask the students why having a greater mass in the center would increase the rotational speed. Consider having the students (carefully) swing an object connected to a string in a circle. Do they have to provide a greater pull to get the object to rotate faster?

Discussion of Observation

Ask the students how the curves for galaxies with larger and larger central objects were different. Remind the students that we can measure the difference in how one side of a galaxy is rotating from another side using redshift. How would the students propose measuring the mass of a black hole in the center of a galaxy?

Assign them to write a report of what they modeled. Have them include in it a proposal for how they might use such a model to measure the mass of a black hole. 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

After they have polished their reports, have another group of students attempt to repeat the experiment as described in the report, verify the findings of the first group, and provide feedback about their methods and conclusions.

Encourage both groups to ask questions of each other's procedure and observations. If another group of students is not available, you could split one class into two large groups and require them to communicate only through writing.

Extensions

Further Experimentation

Show the students the Black Hole Companion galaxy. Open it with the Earth-Sun scale set. The black hole companion galaxy has two equal mass objects going in opposite directions, in orbit around each other. Before showing it to the students, hide one of the stars. Have the students try to build a galaxy which reproduces the motion that you show them.
Thinking Harder

Ask the students how else we might detect black holes. Remind them that we generally learn about massive black holes by the x-ray radiation given off as matter falls into the black hole. Have students look up different galaxies on the SkyView Non-Astronomer page, in visible and in x-ray. Do the galaxies they look at have an x-ray component?
Be sure to point out to the students that the images are different scales. The web page will show how many degrees in the sky each image covers.