Visiting LIGO: Gravitational Wave Observatories

With the measurement of gravitational waves in 2015, a new kind of astronomy emerged that may allow us to look behind the veil of cosmic background radiation

Some of the largest astronomical observatories in the world today do not capture light or radio signals from space, but gravitational waves. Two of them are the LIGO twins (Laser Interferometer Gravitational Wave Observatory) installed in Washington and Louisiana, respectively. Both instruments work as a team. Each observatory uses two 4 km long orthogonal tubes - but the observatories are 3000 km apart.

Meanwhile in Italy took the observatory Advanced Virgo started operations in August 2017. This allows the measurements to be taken and compared in three different places in the world in order to be able to better separate the noise from the signals. Fig. 1 and Fig. 2 show the Washington State observatory that I recently visited. A gravitational wave was detected there in 2015, which was generated by the collision of two black holes 1.3 billion years ago.

Electromagnetic waves are well known to everyone: they are used to transmit data by radio. Cell phones put us in touch with the whole world today. Electromagnetic waves are generated by the acceleration of charges. Since the gravitational and the electrostatic force both decrease with the square of the distance, it is conceivable that there are also gravitational waves and these could be generated by accelerated masses.

However, gravitational waves behave differently to other waves that are more familiar to us. A sound is simply a linear pressure wave propagated through the air. A "detector" for such a pressure wave can be a membrane which oscillates back and forth in the direction of the wave. Electromagnetic waves, on the other hand, are transverse waves. The electric and magnetic fields oscillate across the direction of propagation. An antenna is therefore placed perpendicular to the direction of the wave, so that the electrons in the antenna are accelerated and the signal-to-noise ratio is improved.

Gravitational waves propagate from the source, but they change the geometry of the space perpendicular to the direction of propagation, as a kind of "tidal force". This means that the space contracts in one direction and at the same time expands in the orthogonal direction. Fig. 3 shows the sequence of expansion-contraction processes for a type of gravitational wave. However, the figure exaggerates (for a better understanding) the conceivable deformation of a ring of test particles in space, since the gravitational force is actually the weakest of the known natural forces. With the LIGO detector, the contraction of a 4 km long arm measured in 2015 was about one thousandth the diameter of a proton! The contraction is even smaller than the thermal noise of the atoms in the mirror of the detector. That is why the LIGO detector is not only a new type of "telescope", but above all a technical engineering achievement that is second to none.

Propagation of the gravitational waves

In Newton's theory of gravity, the effect of gravity on a mass is assumed to be infinitely fast. Newton himself was unsure of how such action at a distance could attract bodies. Although he was able to describe the force of gravity mathematically, he simply wrote "hypotheses non fingo" (I'm not speculating) about the spread of the force or the medium for it.

In 1805, Pierre-Simon Laplace was probably the first to grapple with the finite speed of the spread of gravity. 1 He was able to show that it would have long-term consequences on the planetary orbits around the sun if gravity did not act instantaneously. Only when electrodynamics reached its almost definitive form through the equations of James Clerk Maxwell, physicists were able to derive the finite speed of light from fundamental principles. In analogy to electromagnetism, a limited speed of gravitational propagation was postulated and it was assumed that this would be equal to the speed of light.

It is obvious that a finite speed can generate an impact wave when a force is propagated. If a star moves back and forth in relation to us (by this star orbiting another star), then its attraction changes periodically to a test mass in space. However, the gravitational force is so weak that the attraction of distant stars cannot actually be measured. In addition, all parts of a small device would "fall" towards the star at the same time and with the same acceleration, so that ultimately nothing can be measured. It turns out that in the gravitational theory of Einstein gravitational waves are rather deformations of space and time and they deform the length of objects, as explained above, periodically and alternately in orthogonal directions.

In order to detect a gravitational wave, one would need a ring of test masses, as shown in Fig. 3, whereby the deflections would still be minimal. For the World Observatory LISA (Laser Interferometer Space Antenna) the European Space Agency would like to launch three satellites into space in the near future, which would form the corners of an isosceles triangle. Each edge of the triangle would be several million kilometers in size. The deformation of the lengths can then be detected by laser interferometry if a gravitational wave changes the triangular shape.

The mathematics necessary to explain gravitational waves were only presented by Albert Einstein in 1915. In the context of Newtonian mechanics, gravitational waves can, as noted above, be postulated intuitively (if a finite speed of propagation of gravity is assumed), but not really justified. Even within the theoretical physicist community, it took decades for all doubts to be dispelled. Computer simulations were used to calculate the expected deformation of space, which describes the progress of a gravitational wave. For better visualization, test weights are located at the corners of the cylindrical grid.

Laser interferometer

A laser interferometer is used in the LIGO detector, an experimental arrangement that Michelson and Morley used in the early 20th century to demonstrate the constancy of the speed of light. The basic idea is to let coherent light waves fly in two different directions, to reflect them with mirrors, to then bring them into destructive interference and to measure any deviation from them. Fig. 4 shows a diagram of such an interferometer.

A laser generates a light wave with very precise wavelengths. This wave is reflected in two orthogonal directions by a "beam splitter". The light rays go through a small opening in a test mass that is suspended from ropes. The light rays are reflected at the end of the long, orthogonal vacuum tubes by specular test masses. The reflection is repeated several times. The distance between the reflecting mirrors in both arms is adjusted so that both beams arrive in destructive interference when the captured light beams are deflected through the opening in the test compound back to the splitter and from there to a photodetector, i.e. the two waves add up to zero and hardly any photons are observed in the photodetector.

But if a gravitational wave arrives, the distance between the reflecting mirrors would be larger in one arm and smaller in the orthogonal arm. The light beams get "out of step" and the interference on the photodetector can turn from destructive to constructive interference. A sequence of dark and light areas is detected on the photodetector, the shape of which reflects the frequency of the gravitational wave.

Such an interferometer could be built in the laboratory. Michelson and Morley's device fitted on a table. However, gravitational waves are so weak that the deformations in LIGO's 4-kilometer arm remain well below the diameter of a proton. A vehicle on the road can generate shock waves of greater amplitude in the apparatus than the gravitational waves. How can you separate the wheat from the chaff in the apparatus?

The first step for a successful signal measurement is to mount all instruments on the floor with the help of "shock absorbers". This already filters the largest seismic effects. In the second step, all mirrors and splinters are mounted on special ropes made of fiberglass, with which all "active" parts of the device behave like pendulums and oscillate at the same time and at the same frequency. The oscillations are reduced to a minimum by a system of multiple suspensions, as shown in Fig. 5.

The final safeguarding of the measurement is achieved by measuring at two distant points on the earth. A gravitational wave from space covers the whole earth. If the same signal is detected in two independent observatories, it can be ruled out that it is a seismic event. That's why LIGO is available twice in the USA, and with Advanced Virgo you now have a third possibility of checking.

Einstein's indecision

It sounds adventurous at first to hear that physicists build an instrument to measure a length contraction that is less than a thousandth of the diameter of a proton. When Einstein discovered the possibility of gravitational waves in 1918, he thought that such small effects could never be detected. In the following years he fluctuated again and again between theoretical acceptance and rejection of gravitational waves.

As early as the 19th century, some physicists had been thinking about the mathematics of gravitational waves in analogy to electromagnetic waves. If one assumes that gravitation creates a potential field and that finite signal propagation takes place, then the delay creates a wave in the potential field. That was the conjecture of James Clerk Maxwell, founder of the theory of the electromagnetic field. The Englishman Oliver Heaviside used equations similar to Maxwell's for the gravitational field and published the very first work on gravitational waves in 1893. Other physicists followed, such as Jonathan Zenneck and Paul Gerber. What they had in common was that the finite expansion of gravity should lead to waves.

In 1913 Einstein summarized the current state of research in a lecture in Vienna. At that time there were already competing approaches to the description of gravitational waves, among them some that postulated a variable speed of light in a vacuum. Shortly after his theory of gravitation was finished in 1915, Einstein wrote to Karl Schwarzschild: "There is no gravitational wave analogous to light waves." Nonetheless, Einstein published two papers on gravitational waves in the months that followed. The second work from 1918 corrected the first and introduced a simplification of the gravitational equations (a "linearization"), which made it possible to predict gravitational waves.

In 1936 Einstein corrected himself again. With the help of Nathan Rosen (the one from the Einstein-Podolsky-Rosen paradox) he tried to solve the equations more precisely, up to the second-order effects, and this time declared that gravitational waves could not exist after all. However, Einstein and Rosen came up with the result through the use of the wrong coordinate system, a fact which the reviewer of the work for a physical journal did not go unnoticed. Despite the correction, Einstein remained skeptical about the possibility of gravitational waves until his death in 1955.

However, this was the wrong time to die. Only a few years later, the combined work of several physicists succeeded in obtaining an exact solution of the Einstein equations, which this time proved the existence of the gravitational waves perfectly. Just a few years later, experimenters began designing the first apparatus for detecting electromagnetic waves. In 1980, the first reasonably large interferometers were designed by Caltech and MIT (only a few meters long), but work was already underway on the design of mile-long interferometers. The rest is history: it was another 35 years Advanced LIGO was completed and the first gravitational waves were captured.

The signal processing

Even if you have an expensive instrument like Advanced LIGO, that is not the end of the story. One still has to find the patterns in the interferometric data that indicate a gravitational wave. But in many cases the signal does not stand out clearly enough from the surrounding noise.

Correlation analysis is therefore used. There are a number of software filters that remove the familiar noise. There is, for example, the noise from power sources (115 Hz), from the streets and other known disturbances. If you do your best in the subsequent signal processing, you can calculate the correlation of the signal with expected templates of the possible events (such as a template for the collision of black holes). Fourier analysis is also used to speed up the calculations, or methods from the field of data analytics are used.

You also have the two detectors in Hanford and Louisiana. When a signal passes through the correlation filter in one detector, the same should happen in the other. By comparing the two detectors you can avoid false reports. To make sure that the signal processing is always active and working properly, incorrect signals are regularly injected into the measurements in order to test that the processing chain is in order (and that the surgeons are not sleeping). If the scientists report the wrong signal to the management, the all-clear is given.

Future observatories

If the double LIGO observatory already seems too big to someone, let me know that the observatories will be much bigger (much, much bigger!). Work is already underway on the design of "third generation" observatories, such as the European Einstein Observatory. The problem with detectors like LIGO and Virgo is that the detection method sets narrow limits for the minimum detectable frequency of the gravitational waves. Only high frequency waves can be observed. The collision of medium-sized black holes can be detected, but no other interesting phenomena that take several seconds or days for a single wavelength to pass through.

The Einstein Observatory will suppress the seismic noise of the earth's surface as it will be built underground. It is built in the shape of a triangle, which means that interferometry can be used on several alternative routes. In addition, the sides of the triangle should be up to 10 km long. The draft is still being worked on and the application for construction will be submitted to the European Union in 2020.

But there is also a size bigger, and that is the aforementioned LISA project, which is based on space probes in space. The Laser Interferometer Space Antenna is also configured as a triangle with space probes, each of which is 2.5 million kilometers apart (this corresponds to 6.5 times the distance between the moon and the earth). The greatest difficulty here is to keep the distance between the probes constant with high precision. There is always disturbance due to the attraction of planets and passing celestial bodies, which must be balanced by actuators within the spacecraft. The first measurements with a test probe have already taken place, so that the three necessary components could perhaps be brought into space around 2030.

But how about an observatory the size of a galaxy? Sounds presumptuous, but that is exactly what you want to achieve with the "European Pulsar Timing Array" (EPTA). Pulsars are celestial objects (maybe neutron stars) that send regular radio signals to us. They are ultra-fast rotating stars that complete a rotation in just milliseconds. Their radio signals arrive regularly and form the most precise clocks that are known to this day.

If one can calibrate many of these pulsars in a galaxy and follow their "timing", it is as if one had many light sources in space whose next pulse can be determined very precisely. If a gravitational wave now passes through the galaxy, the distance between the pulsars and the earth changes and these small deviations can be detected because the pulsar signals get out of sync. The gravitational waves could be detected by a kind of clock adjustment. A similar concept has been proposed for dark matter detection based on comparing the atomic clocks of GPS satellites orbiting the earth. Dark matter that crosses the solar system would act on the atomic clocks. For the detection of gravitational waves, however, the GPS clocks are not precise enough or not far enough apart.

The concept for EPTA has been worked on for years and the first long-term measurements were recently submitted for analysis. The accuracy of the data recording still needs to be worked on, several radio observatories in Europe are working on it.

Fig. 9 shows the frequencies and strains that can be detected by various detectors, i.e. the expected shortening of the measurement path as a negative power of ten. Advanced LIGO can detect line compression in the range of the diameter of a proton. EPTA doesn't have to be just as fast, but it does need to be over several days and weeks, something Advanced LIGO can not achieve.

When I visited LIGO-Hanford, the system was switched off because a strong wind caused the buildings to vibrate. A week earlier, a car driver collided with the concrete shield on one arm of the detector at night (this is one of the reasons why the Einstein observatory is better built underground). A detector like EPTA, on the other hand, would be able to track the effects of a gravitational wave over 115 days (hundreds of millions of seconds). LISA could observe gravitational waves that take 100 seconds to pass through one period. In the low-frequency range, one suspects the presence of the waves from the Big Bang.

The last important gap in astronomical instruments has been closed with the new observatories for gravitational waves. The next challenge is to be able to measure the gravitational waves from the Big Bang in order to finally be able to observe the moment of the creation of the universe with the signals from the distant past. (Raúl Rojas)

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