Topic outline

  • Introduction and Background

    In this course you will learn how LIGO detects gravitational wavesThe 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: 


  • 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.


  • 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.

  • 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.


  • 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.


  • 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?

    • 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.


      • References

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

      • 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:

      • 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