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Mark Chang

February 22, 2016

Math 89S

Professor Hubert Bray

Gravitational Waves: A New Perspective of the Universe

Brief Background on Gravitational Waves

Over a century ago, Albert Einstein used the theory of general relativity to predict the existence of gravitational waves: ripples caused by the curvature of spacetime. This curvature is caused by the movement and acceleration of objects of mass in spacetime, and these waves are released from the source of mass as gravitational radiation. As these waves pass by objects, spacetime is distorted by the effects of strain, and the space in between objects will change according to the frequency of the wave. However, the magnitude of these gravitational waves become extremely miniscule as the distance from the source increases; therefore, the waves formed by inspiralling binary neutron stars and black holes that contain extremely large mass and has large acceleration are thought to be detectable on Earth by very sensitive machines. Albert Einstein theorized the existence of these miniscule waves, but he was still skeptical on the ability for the detection of these waves. Despite the doubts and difficulties, on September 14, 2015 at 09:50:45 UTC, the Laser Interferometer Gravitational-Wave Observatory detected gravitational waves.

Laser Interferometer Gravitational-Wave Observatory (LIGO)

Originating from Joseph Weber’s basic prototypes and concepts of laser interferometry, there were massive improvements and efforts put into the creation of a machine that may one day detect gravitational waves. Laser Interferometer Gravitational-Wave Observatory (LIGO) was a promising initiative that was completed in the early 2000s. This detector was designed to have large potential to increase sensitivity massively, and the efforts to do so are continuing to even this day. The two LIGO detectors, which are financed by the National Science Foundation and operated by MIT and Caltech, are found in Livingston, Louisiana and Hanford, Washington.

  1. Operations

In order to detect the gravitational waves, the LIGO detectors were designed to distinguish between gravitational waves and other environmental disturbances, while determining the wave polarizations. There had to be various upgrades on the sensitivity, such as the improvements made on the Michelson interferometer. Another way the sensitivity was improved was by placing resonant optical cavities (the test mass mirrors) that are placed 4 km from the ends of the LIGO arms (see Figure 1 for the diagram). These mass mirrors play an extremely large role, as they multiply the effect that gravitational waves have on the laser by an astounding factor of 300. Furthermore, the power-recycling mirror also adds to the strengthening of the laser light.

It is important to create a design that will clearly show the effects of strain through the optical signal. In order to do so, the test masses were designed to have low thermal noise and taking the variable of seismic noise out, which helped to decrease the displacement noise by a significant amount. To further improve the sensitivity to strain from other noises, every single part of the detector except the laser source are placed on vibration isolation platforms in ultrahigh vacuum. There are even more enhancements that made LIGO detectors so sensitive.

Figure 1

The laser is first shot into the power recycling Michelson interferometer, and thena laser reaches the beam splitter, which splits the laser into the two perpendicular LIGO detector arms. The beams travel downthe arms and are reflected back by the mirrors placed on the ends of the detectors. Once the laser travels up and down the arms around 75 times, the two separately traveling beams meet and combine at the beam splitter. When there are no gravitational waves observed in the detectors, the returning beams are in coherence and the light waves will subtract each other. However, if the gravitational waves go through the LIGO detector, the waves will distort space and alter the distance between the two arms, so the returning light will not cancel each other out, leading to light passing onto the photo detector. This phenomenon occurs because as one arm stretches on the other contracts due to the effects of gravitational waves, the peaks and valleys of the two light waves will not align and not cancel out when added together in the signal recycling component. The differing intensity of the light detected by the photo detector as the lengths of the arms are altered will measure the intensity of the gravitational waves passing through the detector.

As shown in Figure 1, there are two places in the United States where two identical LIGO detectors were built. In order to make sure that the signals detected from the detectors are not from environmental disturbances, these two detectors will need to measure the same signals to further support the results.

  1. Funding for These Detectors

In order to detect these small gravitational waves, a lot of money and research goes into enhancing these LIGO detectors. For the LIGO project to have reached this level of precision, organizations have and are continuing to fund millions of dollars into the enhancement of these detectors. However, it is important to realize that receiving funding for this project was extremely difficult at times, because the limited technology and knowledge at the time limited the amount of progress.

Considerable funding by the NSF with the LIGO project started in 1980, when the NSF supported MIT in studying large interferometers. At a similar time, Caltech succeeded in producing a prototype that was 40 meters per arm, so the NSF combined MIT’s research on interferometers with Caltech’s successful prototype to create the LIGO project. However, the project did not receive funding for 1984 and 1985. Finally, in 1988, the project was funded for research and development. Without much progress from 1989 to 1994, the funding seemed to be minimal, but the U.S. congress granted the project $23 million. Unfortunately, the terms of funding were not met on the LIGO project, until 1994, when LIGO changed the laboratory director from Vogt to Barry Barish and got one last change with NSF. The LIGO project got $395 million funding from the NSF, making LIGO the highest funded project by NSF. LIGO project got to work right away and began creating building the first LIGO detector in Hanford, Washington in 1994 and began constructing the other detector in Livingston, Louisiana in 1995. Both facilities were nearly completed in 1997, and the LIGO created two sectors: LIGO Laboratory and LIGO Scientific Collaboration. LIGO Laboratory included all the facilities and the parts of the project funded by NSF, while LIGO Scientific Collaboration is a forum of hundreds of scientists that conduct research for LIGO.

“Advanced LIGO” was completed in 2015, and the total cost was $200 million. Therefore, the total cost of the LIGO project is currently standing at $620 million.

  1. Initial LIGO (2002-2010) Failed [Improvements]

LIGO detectors failed to observe any gravitational waves between 2002 and 2010, so the LIGO project enhanced these detectors with “Advanced LIGO,” which changed almost every part of the interferometer from the initial LIGO design. “Advanced LIGO” has four times more sensitivity than the initial LIGO, which took a lot of modifications and enhancements in order to reach this level. The design is continuing to become more sensitive, as the LIGO project plans to reach new levels of sensitivity by 2021.

The sensitivity of the data obtained by the strains was essential to the success of the project, so the laser power was enhanced from 10 Watts to around 200 Watts. In order to reduce thermal noise and keep the radiation pressure noise at a certain level, the mass optics used increased the diameter to 34cm and increased to 40kg. Furthermore, a seismic isolation system with suspension systems was added to the new LIGO detectors, which decreased the “seismic cutoff frequency from 40 Hz to 10Hz.” Enhancements are continuing to be made as new research into this topic of study in increasing.

  1. Recent Findings (Why is this Discovery Significant?)

LIGO detected the same signals from the two facilities on September 14, 2015 at 09:50:45 UTC. After many years of machinery enhancement and research, the LIGO project was the first to detect gravitational waves. According to the nearly identical gravitational wave strains discovered in both detectors, scientists extrapolated that these gravitational waves were remnants of the merging of two black holes: one 29 times the mass of the sun and the other 36 times the mass of the sun. The gravitational waves detected were from the source of the merging of two black holes that happened approximately 1.3 billion years ago. The merging of the black holes is likely to have taken place in the Southern Hemisphere, as the detector in Hanford received the signals 7 milliseconds before the Livingston detector.

As shown through Figure 1, both detectors in Hanford and Livingston received very similar strain signals, that represent the same gravitational wave passing through the detectors. The graphs on the first row compares the two strains received by the detectors, and it shows how the seismic waves share the same intensity and pattern. For the second row of graphs, the shaded dark regions encompassing the strain lines are the “binary black hole template waveforms” that allow the comparison of the recorded gravitational waves with those results of a calculated black hole. Lastly, the two graphs on the bottom row represents the increasing signal frequencies over time.

Figure 2

From Einstein’s theory of general relativity, the large masses and the acceleration of two black holes orbiting each other loses energy through gravitational waves, which then slowly brings the two black hold together. As the two black holes approach each other, the orbits become faster as closer together approach each other, and they create gravitational waves of greater strain in the final moments of merging. These two black holes collide at the speed of up to half the speed of light and form one large black hole. The strain of the gravitational waves over time is shown in Figure 3. The diagram shows the relative strain of the spiraling black holes and also the strain when the black holes coalesce.

Figure 3

  1. Previous Doubts on the Detection of Gravitational Waves

In order to test the accuracy and to keep scientists focused on the data, the LIGO team has a group of individuals who produce blind injections that mimic the signals of gravitational waves. When initial LIGO was going o its last run in 2010, they inputted a fake signal into the system, and the scientists were notified of this right before they put in the results for publication. There were some conjectures that thought the signals found on September 14, 2015 may be a fake-input, but they committee admitted that this was not the case. However, there is always a possibility that somebody could have altered the signal to fabricate the results. This question will be answered once more successful tests of LIGO are conducted in the future.

Events of large scale collision between neutron stars or black holes are believed to create gravitational waves that are detectable from the Earth. Also, these astrophysical events are known to produce short gamma-ray bursts that are visible. These gamma-ray bursts are theoretically supposed to be accompanied by gravitational waves, so there were many efforts to detect gravitational waves while observing the gamma-ray bursts. However, they failed to detect any gravitational waves through satellites, which is probably due to the lack of sensitivity of the machines. With the further development of LIGO and other initiatives like eLISA, the detection of gravitational waves in the presence of gamma-ray bursts will hopefully become a possibility.

Evolved Laser Interferometer Space Antenna (eLISA), is a European Space Agency project that attempts to detect gravitational waves space-based with laser interferometry. The basic structure of this machine is aligning three spacecraft into an equilateral triangle and making it go into orbit around the earth. These three spacecraft will be interconnected with laser interferometry, and the length of the arms will be 1 million kilometers. They hope to use eLISA’s new technology to detect gravitational waves from outer-space.

Conclusion

The enhancements done to the LIGO project since the early 1980s finally paid off, as there was a first detection of gravitational waves in September 14, 2015. With a tremendous amount of funding and research, the LIGO project may have opened up a new perspective on the universe and how we can interpret events in the past. This is just the beginning of the great discoveries may surprise us and change our perspectives on many aspects of the universe. Einstein was proven right once again.

Works Cited