Topic outline

  • General

  • 1) Introduction and Background

    In this course you will learn how LIGO detects gravitational waves. The basic idea behind the experiment is simple: that a passing gravitational wave will change the length of the arms in a laser interferometer, and as a result, it will create a changing amplitude in the interfering laser beams. However simple this idea is in concept, to put it into practice has required great care. New technologies have had to be created, and old ones have been refined. This was necessary in order to attain the highest precision measurements ever made in an experiment: a change in the length of each interferometer arm of only one part in 1021. After 40 years of design studies, technology development, prototyping and testing, construction of a suffieciently sensitive experiment was completed in 2015.

    In the final stages of commissioning, even before the fi rst science runs had begun, the experiment met with success. On September 14, 2015, at 09:50:45 UTC, the LIGO experiment made the first-ever direct detection of gravitational waves (Abbott & et al., 2016).

    No better way could have been conceived to mark the centenary of Einstein's General Theory of Relativity (Einstein, 1916), or his prediction of gravitational waves (Einstein, 1918).

    Section 2 recounts LIGO's observations to date and the implications for the sources of the signals. Section 3 describes the LIGO instrumentation. Section 4 describes Sources of Noise that need to be overcome in order to detect the waves. Section 5 explains the Signal Extraction processes used to find signals in LIGO data.

    For those who would like to review General Relativity, or what was known about the Astrophysics of Gravitational Wave sources prior to LIGO's detections, please feel free to access the material from last year's LIGO course. Some of the material is also included below in the  penultimate section of this Moodle site.

    For a conceptual guide to LIGO's original detection, GW150914, please see the LIGO Educator's Guide: Direct Observation of Gravitational Waves. It is available in different formats (including 508-compliant PDF) at https://dcc.ligo.org/LIGO-P1600015/public

    You may also enjoy a cartoon introduction to gravitational waves from PhD comics: 


  • 2) Direct Observations

    This unit explains the observations by LIGO of gravitational waves. The first direct detection of gravitational waves occurred on September 14, 2015 (GW150914), and the second confirmed detection occurred on December 26, 2015 (GW151226). There is also a possible detection that was not strong enough to claim as a confirmed detection: this event occurred on October 12, 2015 and is known as LVT151012. LVT stands for "LIGO-Virgo-Trigger".

    The text is in the PDF file "Direct Observations" linked below. Additional resources and homework problems are also linked below.


    • Direct Observations File

      This section of the text describes the sources of gravitational waves that LIGO has detected in its first several months of operation.

    • HW for Section 2 Assignment

      This is the PDF file that includes the HW problems for Section 2.

      There are three homework problems in the PDF file. Each homework problem is worth 5% of the total points for the course.

      Many of the homework problems for the course are simple numerical exercises designed to give you a feel for some of the physical scales relevant for LIGO. You can use paper, pencil and a calculator to complete the assignments, or you can use a spreadsheet. A spreadsheet is actually easier, since it allows you to conveniently store constants you will use often (like the speed of light, for example) and then use them with many different calculations. If you are not familiar with spreadsheets, there is a nice tutorial from Microsoft  about Excel, their popular spreadsheet program. It is linked below. Even if you will use a different package, like OpenOffice or Numbers, these tutorials might be useful. Spreadsheets are all fairly similar in the basic way they work.

      If you are not very practiced with spreadsheets, use the first few homework assignments to learn about them. The last assignments, in Section 5, will require you to use spreadsheets or some other programming, so now is a good time to hone your skills.


    • Inspiral Signal URL

      This website is part of gwoptics.org, which was developed by LIGO scientists in Birmingham, UK. You will only be able to run this activity using Firefox browser, and you must first ensure that you have the updated Java plugin, See the instructions linked below for how to update the Java on your local machine (either Windows or Mac).

      Once the activity runs, explore the chirps generated by merging black hole systems as you vary the masses of the two black holes.

    • Installing and Running Java in the Browser URL

      This file provides instructions as to how to install Java on a Mac or Windows Machine

    • GW 150914 Detection Portal URL

      This page contains the resources that were created to support the LIGO press conference on February 11, 2016 announcing the discovery of the first gravitational wave signals. Please review the materials on this page to learn more about GW150914. There are many interesting images, simulations and animations.

      You can watch the press conference here:

    • GW151226 Detection Portal URL

      This page features the resources generated for the press event on GW151226 which was held on June 15, 2016.

      Please review the materials on this page to learn more about the GW151226 event. There are many interesting images, simulations and animations.

      You can also watch the press conference itself here: https://aas.org/media-press/archived-aas-press-conference-webcasts It is the video link entitled "Latest News from the LIGO Scientific Collaboration"

    • Sounds of Spacetime URL

      This website was developed by LIGO scientists at Montclair State University. It has excellent tutorials about the conversion of signals from LIGO into audible frequencies. Please read through the tutorials on this website listed under the heading Sources & Sounds. Some of the animations (especially those by SXS group) do not have sound associated with them. For the others, it helps to wear headphones.

      You may also enjoy exploring the pages that describe GW150914 and GW151226.


  • 3) LIGO: The Basic Idea

    In this unit, you will learn the essentials of the instrumentation that comprises a LIGO interferometer. Starting from a review of a simple Michelson interferometer, the basics of detecting a gravitational wave using LIGO are presented. Next, the additional optics systems are described. 

    The text is in the PDF file "The Basic Idea"  linked below. There are also additional resources and homework problems for this section linked below.

    • The Basic Idea File

      The section of the text discusses how interferometers work and how they are used to detect gravitational waves.

    • HW for Section 3 File

      This is the PDF file that includes the HW problems for Section 3.

      There are three homework problems in the PDF file. Each homework problem is worth 5% of the total points for the course. 


    • Simple Model of LIGO Interferometer URL

      This video shows the basic idea used by LIGO to detect gravitational waves.

    • Michelson Interferometer URL

      This website is part of gwoptics.org, which was developed by LIGO scientists in Birmingham, UK. You will only be able to run this activity using Firefox browser, and you must first ensure that you have the updated Java plugin, See the instructions linked above in Section 2)  for how to update the Java on your local machine (either Windows or Mac).

      Try to explore the way the output signal from the device depends on the relative lengths of its arms. Try to make the output signals (there are two of them in the applet) go to zero. Are the conditions needed to make each signal vanish the same? Try to explain what is happening as each signal goes to zero.


    • Cavity Calculator URL

      This website is part of gwoptics.org, which was developed by LIGO scientists in Birmingham, UK. You will only be able to run this activity using Firefox browser, and you must first ensure that you have the updated Java plugin, See the instructions linked above in Section 2)  for how to update the Java on your local machine (either Windows or Mac).

      In this applet you can tune a simulated Fabry-Perot cavity within a Michelson interferometer and see how your tuning changes the power output of the device. One of the cavity mirrors is curved, while the other is flat. The applet allows adjustments to the position and curvature of the end mirror, and the reflectivity of both mirrors. Try to determine the conditions that maximize the power output.


  • 4) Sources of Noise

    This unit discusses various sources of noise for the LIGO interferometers, including thermal, seismic and quantum.

    The text is in the PDF file "Sources of Noise"  linked below. There are also additional resources and homework problems for this section linked below.


    • Sources of Noise File

      The section describes the sources of noise that LIGO has to overcome in order to detect gravitational waves.

    • HW for Section 4 File

      This is the PDF file that includes the HW problems for Section 4.

      There are four homework problems in the PDF file. Each homework problem is worth 5% of the total points for the course. There are no problems numbered 11 or 12.


    • Gravity Spy URL

      This citizen science website developed by the Zooniverse team with the help of LIGO scientists, invites participants to examine LIGO data and classify noise signals in order to develop inputs for machine learning software that can help clean gliches out of the data. It is currently in beta-test, and welcomes your input!

      Try starting by reading the ABOUT tab to learn about the goals of the project. Then do the beginning tutorial to see some types of glitches, and progress to see the wider zoo of glitches in the apprentice level.


    • I2U2 E-lab on LIGO Seismic Noise URL

      This is one of  a series of interactive e-labs developed by the Department of Energy and the National Science Foundation. In this course,  you will be looking at the seismic data from LIGO in the role of a "student."

      NOTE: Either log in as guest (where you will not be able to save any info) or use the teacher login: lcominsky and password: cosmic

      First, check out the online resources page and watch the the second tutorial video that shows how to access and plot the seismic data.

      Then try the Data portion of the eLab - you may find it interesting to look at the seismic data near the events GW150914 (near 10 AM GMT), LVT151012 (near 10 AM GMT) and GW151226 (near 330 AM GMT). What seismic frequency range(s) should you choose to examine to see seismic events  that might interfere with the gravitational wave detections? Can you draw any conclusions from the data quality near these three events?


    • Cavity Optomechanics URL

      This video features MIT Prof. Nergis Mavalvala discussing thermal noise and quantum noise in LIGO's optics cavities.

    • Quantum Noise Limit in Gravitational Wave Detector URL

      This video features MIT Prof. Nergis Mavalvala discussing quantum noise and squeezed states of light.

    • Pendulum Video File

      This video shows the motion of a simple pendulum and a compound pendulum under different forcing conditions at its suspension point. It illustrates how the pendulums in LIGO help isolate the test masses from ground motion.

  • 5) Signal Extraction

    This unit describes the basic analysis techniques used for analyzing LIGO science data, with an emphasis on the matched filtering techniques used for the detection of merging black hole binaries.

    The text is in the PDF file "Signal Extraction"  linked below. There are also additional resources and homework problems for this section linked below.


    • Signal Extraction File

      How does LIGO extract gravitational wave signals from the very noisy signal output from the interferometer? This section explores several ways signals are found in the data.

    • This is the PDF file that includes three of the four HW problems for Section 5. The fourth HW problem for this section uses the LOSC. Additional materials for this last problem are found below.

      Note: there are no problems numbered 11 or 12. Sorry!

      Each homework problem is worth 5% of the total points for the course.

      These three problems use the three datasets linked below that are in the format of .csv files. They can be read by a computer program or into a spreadsheet application.


    • LIGO Open Science Center URL

      The LIGO Open Science Center includes data for GW150914, LVT151012, and GW151226, as well as tutorials and exercises. It uses the Python language. See the starter guide below "LOSC Starter Guide" for information about using Jupyter notebooks through your browser.

    • LOSC Starter Guide File

      This guide shows how to get started using Jupyter notebook tutorials in a Microsoft Cloud Azure library. The Azure library includes two tutorials about the Python language which you may also enjoy. The LIGO tutorials were created as part of the LIGO Open Science Center (LOSC). The direct link to the library is:https://notebooks.azure.com/library/y5LSf4Z1s7k

    • Last Homework Problem for Section 5 Assignment

      For this problem, read through the LOSC tutorials for GW150914, GW151226 and LVT151012. Write a short (1 page) reflection as to the differences that you have observed when carefully studying the analyzed data for these three events and upload your essay here. This problem is worth 5% of the total course grade.

  • 6) Final Reflection

          For the final assignment (worth 20% of the course grade), we would like you to write a short (no more than 5 page) essay describing how you think you could fit gravitational waves into your lower-division calculus-based  or AP high school physics coursework. Which material(s) do you think are most easily used, and how do you think you will use them to engage your students?

    • 7) Conclusion

            In this course we have tried to provide some understanding of the LIGO instruments that are being used to open up a brand new field in astronomy and physics, one in which the universe is viewed (or “heard,” if you prefer) using gravitational waves. As we have seen, building these instruments called upon many different areas from physics. Some of them were familiar, even if under a slightly different context or physical regime than we are used to. Others were truly bizarre, pushing the limits of our understanding of the quantum nature of light and matter. Building LIGO required the development of new technologies and manufacturing techniques, and enormous facilities to measure the most minute quantities ever attempted. It required the expertise of literally thousands of scientists and engineers.

            And LIGO is not all hardware. Every bit as vital as the vacuum system and the sensitive optics, shielded from vibration, are the computational systems that allow the data collected at the observatories to be searched and its secrets to be extracted. Without the contributions of the computational physicists who calculate simulated output for various astrophysical sources, the conclusions we could draw from the interferometers would be far less rich. The same is true for the simulations of the interferometers themselves. Their designs are tested first on a computer in order to squeeze as much sensitivity as possible from the final product.

            LIGO is certainly a remarkable machine. It is the culmination of 40 years of vision and the effort required to make that vision a reality. It has already found success with the first-ever direct detection of gravitational waves, and that within days of being put into observational mode. It directly observed two black holes merging into one, an event that would have - and doubtless has often in the past - gone completely unnoticed. It now stands to open brand new vistas on the universe, providing an entirely new field of observational astronomy. Immune to the limitations inherent in viewing the world with electromagnetic waves, gravitational wave astronomy will let us probe through interstellar dust, and even stellar masses themselves. It will extend our vision past the haze of the early universe, probing back beyond the luminous wall of the microwave background radiation. In the coming years additional observatories will come online, both on the ground and, eventually, in space. Each will be improved by the lessons learned form previous models, and it is di cult to imagine what discoveries await. If history is a guide, LIGO and its descendants will bring us to places that our imaginations would never have done. But LIGO will always remain the first.


      • 8) References

        For your convenience, the papers referenced in this course are provided below.

      • 9) Materials from 2015 LIGO Course

        These two files represent two of the units in the 2015 course LIGO: Waves and Gravity. To see the other publicly available materials, resources and links, go to:

        • Geometry and Gravity of Weak Fields File

          This unit begins by extending Special Relativity concepts into accelerating frames, and connecting it to Maxwell's Equations. Then a slightly more mathematical treatment of curvature is presented, leading up to the Einstein Field Equations. Applications of the Field Equations to weak fields and predictions for gravitational waves conclude the unit.

          The text and 10 homework problems are included within the PDF file. Below is a background supplement with additional mathematical background.


        • Mathematical Supplement for Weak Fields File

          This background handout includes many of the derivations underlying the text for Geometry and Gravity for Weak Fields. It also includes additional information about hyperbolic functions, and matrix operations.

        • Astrophysical Sources of Gravitational Waves File

          Written in 2015, before the discovery of gravitational waves by LIGO, this unit summarizes the physics and expected signals from the three most likely sources of gravitational waves: coalescing binary systems, impulsive events (such as supernovae or gamma-ray bursts) and continuous wave sources (such as spherically asymmetric pulsars). We also touch on stochastic sources of gravitational radiation, and briefly discuss other observatories that are planned for future observations of different bands in the gravitational wave spectrum.

      • 10) Other Fun Resources

        Below are linked some interesting new resources that were not linked in the 2015 course, as they have been developed to highlight the new gravitational wave signal discoveries. As multi-messenger astronomy evolves, these resources will continue to be updated

        • Gravitational Waves Explained in a Minute URL

          Minute Physics has created this short video explaining gravitational waves and inviting prospective wave hunters to join the Einstein@Home project.

        • Einstein@Home URL

          Einstein@Home is a citizen-scientist project that  uses your computer's idle time to search for weak astrophysical signals from spinning neutron stars (often called pulsars) using data from the LIGO gravitational-wave detectors, the Arecibo radio telescope, and the Fermi gamma-ray satellite. Einstein@Home volunteers have already discovered about fifty new neutron stars, and we hope to find many more.

          The long-term goal is to make the first direct detections of gravitational-wave emission from spinning neutron stars. Gravitational waves were predicted by Albert Einstein a century ago, and were directly seen for the first time on September 14, 2015. This observation of gravitational waves from a pair of merging black holes opens up a new window on the universe, and ushers in a new era in astronomy.

        • Other Resources, Explanations, Figures, and Math for Gravitational Waves URL
          gwoptics.org has an entire course on Laser Interferometry which can be accessed for free at this link.