Hands-on Gravitational Wave Astronomy: Extraction of Astrophysical Information from Simulated Signals
A Classroom Activity
The search for gravitational waves represents the beginning of a new era in astronomy. Ground based gravitational wave detectors such as the Laser Interferometer Gravitational-wave Observatory (LIGO) and the forthcoming space-based detector the Laser Interferometer Space Antenna (LISA) will probe a broad range of gravitational wave frequencies that will arise from a variety of astrophysical sources. Unlike their cousins, traditional electromagnetic telescopes, gravitational wave detectors don't form images. Instead, these detectors will continuously monitor the space-time in which they rest, sensing ripples in this local space-time fabric (we call these ripples gravitational waves). What is the connection between ripples at the detector and the astrophysical event, perhaps millions of light years away, that caused the ripples? How does a gravitational wave astronomer extract information from the detector's data to build a model of the emitting source?
In this activity students will extract information related to the mass and distance of an astrophysical source by using plots of simulated gravitational wave signals. The process that the students will undertake mimics the way that real gravitational wave analysis occurs. The companion activity, Searching for Gravitational Waves in Noisy Data, asks students to identify pure gravitational waveforms in data that contains instrument noise. Hands-on Gravitational Wave Astronomy presents students with noiseless signals, the type that scientists would characterize and draw out of a noisy data stream.
Learning objectives, connections to standards, and classroom worksheets for this activity were prepared by Dale R. Ingram of the LIGO Laboratory.
Navigate this Web page for the activity by using the following links:
- Learning objectives for the activity
- Connections to science standards
- Connections to science themes and concepts
- Connections to the video "Einstein's Messengers"
- A materials list and teachers guide
- A student activity handout (PDF)
- Teachers Guide/Activity Key (PDF)
- Additional gravitational wave information
Learning Objectives for the Activity
Students who complete this activity in conjunction with viewing "Einstein's Messengers" will demonstrate the following outcomes.
- Describe the changes that occur in gravitational waves emitted from a compact binary system as the system moves towards coalescence.
- Use gravitational wave measurements and relevant equations to calculate the chirp masses and astronomical distances of binary systems.
- Give an overall or general summary of the process that scientists would use to extract information about astrophysical sources from gravitational wave data.
"Einstein's Messengers" can be viewed in streaming video form at http://www.ligo.caltech.edu/einstein.ram
Connections to Science Standards
The key connections between this activity and national science education standards are found in the nature of waves, the nature of gravity, the nature of the universe and the role of mathematics in the development of science knowledge. From Benchmarks for Science Literacy, p 65: "Increasingly sophisticated technology is used to learn about the universe. Visual, radio and X-ray telescopes collect information from across the entire spectrum of electromagnetic waves . . ." Teachers should add gravitational waves and gravitational wave detectors to this list. Also from page 65, "Mathematical models and computer simulations are used in studying evidence from many sources in order to form a scientific account of the universe." From The National Science Education Standards, p 180: "Gravitation is a universal force . . ." What follows on page 180 is a description of gravity in a Newtonian context. Gravitational wave astronomy uses Einstein's framework of gravity rather than Newton's. Einsteins' general theory of relativity states that gravity is a mass-induced curvature in the geometry of space-time. Teachers are encouraged to emphasize the Newton-to-Einstein transition, a change that is descibed in Einstein's Messengers. Also from page 180, "Waves, including sound and seismic waves, waves on water and light waves (and gravitational waves! - ed) have energy and can transfer energy when they interact with matter."
Connections to Science Themes and Concepts
The activity connects to these aspects of physical science:
- Aspects of the scientific method that deal with data analysis and forming conlcusions from data
- Properties and behavior of waves
- The use of mathemataics in scientific investigations
Connections to "Einstein's Messengers"
- 2:12: "From the fiery collision of neutron stars . . ." Viewers see a simulation of the merger of a pair of neutron stars. This is the type of event discussed in the activity that would give rise to the gravitational wave data plots that the students will use.
- 4:15: Another merger simulation. "When a massive object collides with another, it causes waves in the fabric of space-time." As the simulation illustrates, the gravitational waves arise well before the collision, or coalescence, occurs. The changes that occur in the wave pattern as coalescence approaches are evident in the activity's data plots.
- 4:30: ". . . These waves travel outwards from the source, carrying information about the events that caused them." In the activity students will learn how to extract some of the information that the waves carry, such as the mass of the source and its distance from earth.
- 5:00 "You get exactly what happened at the source." This comment is another instance of the notion that gravitational waves tell a story about the bodies and processes that released them. In the activity students will learn how to decode part of the story.
- 9:45: "These small effects are coming from these big masses far away -- black holes, neutron stars -- we will see things happening in the universe by measuring these small effects."
- 14:25 "Take neutron stars in the act of merging. They make a wonderful chirp. It's a cosmic chirp." The chirp signal produced by an inspiral event forms the basis of this classroom activity.
A Materials List and Teachers Guide
Each student or group of students should receive a copy of each of the four data plots:
- Far From Coalescence
- Last Second Before Coalescence
- 1.0 Second Before Coalescence
- 0.1 Second Before Coalescence
Each student should receive a copy of the Student Worksheet for the activity
Teaching the Activity
Each student will need a copy of the student worksheet. Students will need to view the four graphs listed above to complete the worksheet. The student worksheet provides space for the students to record their answers but not for the calculations that the questions will require. Teachers should encourage students to use additional paper to methodically record their manipulations of the equations. Such documentation will facilitate the discovery of computational mistakes. "Showing your work" is a life skill in professional science.
The student worksheet is self-contained and the teachers guide provides solutions and some additional insights for teachers. After watching Einstein's Messengers the students will be ready to undertake the activity. The teacher will need to decide how the students should do the work. If the students work individually or in small groups, the activity will probably require the majority of a 90-minute class period or most of two 50-minute periods. The amount of class time could be reduced by assigning a portion of the activity as homework.
Another key decision for the teacher is the amount of review and practice to provide on the algebra techniques required by the questions in the student worksheet. Several of the worksheet items involve manipulations of fractional exponents. Students might attack the worksheet with greater confidence and accuracy if they have reviewed exponent operations first.
Additional Gravitational Wave Information
- The Penn State Center for Gravitational Wave Physics
- LIGO Hanford Observatory
- LIGO Livingston Observatory
"Einstein's Messenger's" and supporting materials are produced by the National Science Foundation. Any opinions, findings, conclusions or recommendations expressed here are those of the author(s) and do not necessarily reflect the views of the National Science Foundation