# Searching for Gravitational Waves in Noisy Data - A Classroom Activity

## Introducation

LIGO's interferometer's collect over 16,000 data points each second, day after day and month after month. Plotting these points against time produces graphs that often show no particular pattern. Imagine slowly sliding the point of a pen across a notepad in a car that is traveling on a gravel road. You'll see a random jiggle in the pen's trace on the paper. This resembles the appearance of LIGO data. The forces that put these random fluctuations in data are called 'noise.' The noisier a data set, the more chaotic its time plot will appear. LIGO scientists must analyze noisy data in order to discover the 'signal' -- the faint patterns of gravitational waves. In this activity students will search for the evidence of simulated gravitational waves in noisy data sets. Although the activity's discussion centers on the science of gravitational waves, the method of data analysis that the students will encounter is used across the sciences.

Download a preprint article about this activity "Science Icebreaker Activities: An Example from Gravitational Wave Astronomy" by Michelle B. Larson, Louis J. Rubbo, Kristina D. Zaleski and Shane L. Larson at (phys/0503198)

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

Students who complete this activity in conjunction with viewing "Einstein's Messengers" will demonstrate the following outcomes.

• Define and describe the terms "signal "and "noise."
• Use filters (templates) to determine the likelihood that a data set contains a signal as well as noise.
• Describe how scientists would use the methods in this activity to search for signals in real data.

"Einstein's Messengers" can be viewed in streaming video form at http://www.ligo.caltech.edu/einstein.ram

### Connections to Science Standards

The activity requires students to use models (templates) to compare the agreement between the models' predictions of wave patterns and (simulated) data. From Benchmarks, p 270: "The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation." And "The usefulness of a model can be tested by comparing its predictions to actual observations in the real world." From Standards, p 176: "Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations and communicating results."

### 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 models in scientific investigations

### Connections to "Einstein's Messengers"

• 50 seconds: Several real-time plots of LIGO data appear on the screen that show the jitter of noise in their baselines.
• 5:10 : "As scientist tried to simulate these waves, they found . . . " The simulations mentioned here are part of the efforts that many scientists have made for years to make models of gravitational waves. In the activity, the signal templates play the role of these models.
• 6:27 : Joseph Weber, the first scientist to attempt to measure gravitational waves directly, is shown with several students and colleagues. They are holding a long piece of paper from a strip-chart recorder that shows data from one of Weber's gravitational wave detectors (large metal bars). The noisy baseline in Weber's data is clearly visible. Students might recognize that this data looks a bit similar to the simulated data that they use in the activity.
• 11:16 : For about 1:40 the narrator discusses noise and noise sources in LIGO. Noise consists of vibrations on the mirrors, or jitter in the sensing electronics, that competes with gravitational waves in the interferometers. (Students should understand that in scientific meausurement, "noise" is broadly defined as what shows up in the data that interferes with detection of the signal. It is possible to watch the film and gather the idea that LIGO is only concerned about audible sounds as noise -- vehicles, trees falling, etc. Any vibration in the data that obscures gravitational waves, whether audible or not, would be called noise.)
• 13:15 : The narrator mentions that LIGO's vibration isolation systems reduce the effects of ground vibrations on the mirrors (i.e. noise) by a factor of ten billion.
• 13:50 : "... even with noise reduced to the lowest possible level, LIGO must still be able to tell when an incoming signal really is a gravity wave."
• 17:35 : "LIGO is now attempting to filter out the noise and pick up the symphony of spacetime." The activity seeks to give students a first-hand look at how this filtering process occurs, by comparing a set of filters to various sets of data. The filters are also called templates or models. They provide an expectation of how the signal might look in the absence of noise.

### A materials list and teachers guide

Materials

3. Student worksheet for the activity

Here are the PDF files that you will need to download for the activity:

### Teaching the Activity

The materials above allow for four activity sets; each set contains one data stream and six templates. There is also an activity key. Each data stream contains a single source with simulated detector noise added in. The four template files represent monochromatic and coalescing sources, and both the cross and plus polarizations of an extreme mass ratio source. The six individual templates within each file have varying signal characteristics, such as period and initial phase.

The icebreaker activity can be conducted with only one, (or as many as four), of the different activity sets. Depending on the age of your audience, and the time available, decide in advance how many sets you would like to include in each icebreaker packet. Print the noisy data signals on transparency film. Print the gravitational wave template files on plain paper. All files contain two images per page. Cut each printed page in half creating signal and template sets of half-sheet size for each icebreaker packet.

At the beginning of the meeting or class have everyone break into groups of two to four people. Pass out an icebreaker packet (containing one to four activity sets) to each group. Start out by explaining that gravitational wave astronomy is a future field of astronomy that will make observations of the Universe in a different way from traditional astronomy. Explain that these are simulated gravitational wave signals from sample astrophysical systems, a detailed description of the systems can be saved for after the activity. An explanation of each system is provided in the activity key.

After the introduction, ask the groups to identify the best template/data stream matches. Give them ten to fifteen minutes to complete the task. Do not provide much instruction about what features to use in identifying a match. The participants, some with encouragement, will discover the need to use the axes as reference lines, and to look carefully at details such as amplitude, period and initial phase differences, or other significant features in the signals.

Encourage interaction, and allow the groups to move around the room if they choose. Once each group has a matched set, lead a discussion about which template matches which data stream and why. Facilitate discussion about amplitude, period, and other features used when determining their answer. Write each group's matching solution on a chalk board for everyone to see. If you have differences among the groups discuss the differences and see if they can come to agreement. If some groups matched the images based on criteria different from what has been discussed, have them explain what they did.

Once the discussion period is over emphasize that gravitational wave astronomers use methods very similar to these to identify sources in real data. As part of the icebreaker activity, the discussion need not go further than describing the different types of binary systems and how they appear differently in the gravitational wave data. More detailed information can be gathered about the source system (e.g. masses and distance to the source) by measuring the gravitational wave signal wavelength and how the wavelength changes in time. A classroom extension related to these measurements is in preparation. Finally, consider giving everyone their own set of images (and a copy of the key) to use at home with their family and friends!