Main Experiments for Detection of Gravitational Waves at Frequency below 3 kHz: A Quick Review

Abstract

Gravitational Waves were detected at last with a laser-interferometric detector in 2015 with a 4 kilometers long laser-interferometric detector. It took more than 100 years of effort to reach such a goal. This achievement is one more piece to prove the Einstein General Theory of Relativity. Besides new detections with these experiments, a lot of effort has been allocated to the current laser-interferometric detector to improve its performance and detect signals from sources farther away with the intention of searching all the known Universe for Gravitational Wave sources. Nevertheless, this kind of experiment has a frequency range limited by seismic noise around 10 Hz and lower. Efforts are being made for the detection of Gravitational Waves at different frequencies, for instance, laser interferometer in space, measurement of pulsar timing and deviations of polarization of the microwave background. All these experiments are discussed in this chapter as their sources. A very broad frequency range of detectors should be available in the next decade.

1. Introduction

Gravitational waves (GW) are space–time ripples generated by accelerated massive objects, to have a reasonable intensity, these massive objects must be of a cosmic origin like compact stars such as Neutron Stars or Black Holes. Considering the Einstein General Theory of Relativity, these GW move at the speed of light and can accelerate masses or excite quadrupolar normal-modes of elastic bodies as the equivalent principle predicts. The potential sources of GWs include binary compact star systems composed of white dwarfs, neutron stars and black holes.

The existence of GW is also a consequence of the Lorentz Covariance of Einstein General Theory of Relativity. GW does not exist in the Newtonian theory of gravitation, which postulates that physical interactions propagate at infinite speed.

The first detection of GWs came from the inward spiral and merger of the Black Hole (BH) binary. The event is called GW150914 [1], and the name is given by the Letters GW followed by the year, month and day of the detection, then the detection happened on September 14, 2015. In 2017 a simultaneous detection of GW radiation and electromagnetic radiation was made from what is called a hipernova, a binary Neutron Star (NS) system that merged. It is called GW170817, which could have started the era of multi-messenger astronomy [2], which involves GW, optical radiation, radio, gamma-rays and X-rays radiation. Studying the universe with these different types of radiation opens a new era for understanding the universe.

In 2017, the Nobel Prize in Physics was awarded to Barry Barish, Kipe Thorne and Rainer Weiss for their role in detecting gravitational waves.

Before the first GW detection, there was indirect evidence of these GW. Measurements of the Hulse and Taylor binary pulsar system suggested that GW was more than a hypothetical concept, at least for the emission of such waves; the authors of this measurement won the Nobel prize. This system is one of the potential sources of detectable gravitational waves, but because of the frequency with which this system operates, a new kind of detector can detect much smaller frequencies than the one that detected GW150914. The kind of detector responsible for this detection are interferometric ones, whose sensitivity is limited at frequencies close to 10 Hz and lower because of seismic noise on the mirrors.

Another option to detect GW radiation is using resonant-mass detectors (this was the first kind of detector proposed in the 1960s). From those, the only remaining detector is the Mario Schenberg Brazilian GW detector that uses the detection of the vibration modes of five quadrupole modes of a spherical resonant-mass of 1124 kg with a radius of 32.33 cm made of CuAl6% alloy [3], this mass vibrates when a GW passes through it with a resonant frequency. Figure 1 shows a schematic of such a detector that operates at a temperature of 4 K.

Figure 1.

Drawing perspective of Schenberg detector.

Detectors for GW are the topic of this book chapter and will be addressed in the next section. Then, in the following section, a spectrum with the main sources and main experiments will be shown.

2. Gravitational waves experiments

2.1 Laser-interferometric detectors

The Interferometry system essentially works by measuring the variations that occur in laser light beams, which are arranged along two orthogonal arms, as a normal interferometer works, the main difference is the size of these detectors, with arm lengths around 3–4 kilometers long. The detection occurs when the variations in the interferometer arm’s length cause variations in the interference patterns in the photodetectors that are observed because the velocity of the light beams is constant even in the presence of GW. This difference could also cause a difference of arriving time in the mirrors, but the time difference is too small to be measured. Using arm length of kilometer size makes these detectors capable of measurements in length of less than a thousandth of a neutron diameter.

A powerful laser beam (with a power of tens of Watts) passes through a beam splitter allowing the two generated beams to have the same phase and to be separated orthogonally, at the end they are reflected by mirrors that exist in the ends of the arms, some are semi-reflective (the power in each laser beam inside the arms reach 400 kW). The phases of the reflected laser beams are adjusted to generate a destructive interference pattern at the photodetector, so no signal is detected by the photodetector in the detector with no GW passing through. For the occasion of a GW across it, it causes space–time to expand and contract infinitesimally in orthogonal directions, thus changing the interference pattern in the photodetector and a signal is detected. Figure 2 shows the schematics of such a detector.

Figure 2.

Schematics of a laser-interferometric GW detector.

There are two such detectors in operation: the Laser Interferometric Gravitational Observatory (LIGO) detector (an American detector [4]) and VIRGO (a Franco-Italian detector [5]). A third detector is being built in Japan, the Kagra detector, as can be seen in [6]. Efforts are being made to build a fourth detector to complete the sky coverage for GW in the range of 10–3000 Hz; the position of this next detector is probably in India.

Also, the existence of more than one of these detectors is a way of preventing the possibility of false detections due to small earthquakes, vibrations in the mirror suspensions, some phase variations, or some other local source of noise. When detecting a signal, this signal will be compared with signals detected by other detector or detectors, and the signal is only confirmed if signals are measured in more than one detector, with a right coincidence time between the detectors and the signals have the same characteristics: exactly the same profile in frequencies considering the detector characteristics and the arriving time is coherent with the position of the detectors. All of these measurements happen in a vacuum, avoiding the possibility of interactions of the laser in some molecules that could mimic the effect of a GW signal. The characterization of one of these detectors can be seen in [1]. Some of these are: lasers operating in higher frequency, mirror suspension made of fused silica to reduce creep noise and the improvement of mirror suspension to reduce thermal and seismic noise.

2.1.1 The real laser-interferometric detector

The interferometric GW detectors are very complicated and complex machines. As the interferometer must be set in a dark fringe condition, the vibrations acting on the mirrors can change the dark fringe condition as the mirrors are somehow connected to the ground and are finite temperature, so they vibrate, which changes the dark fringe condition. Then a very good suspension that attenuates the vibrations must be used, even adding some active system to lower the vibration. Figure 3 shows a schematics of such suspension; this example is about the LIGO detector.

Figure 3.

Schematics side view of the mirror suspension system of the LIGO detector showing the electrostatic actuator which is used to keep the detector locked in at a dark fringe condition.

The Italian detector Virgo has a more sophisticated suspension, which makes this detector more sensitive at lower frequencies, for each mirror suspension is composed of an inverted pendulum and six masses suspended by their centers. As it is not enough, add to it a collection of 18 LVDTs (Linear Variable Displacement Transducers), five accelerometers, 23 coils, three piezoelectric devices and 21 motor drivers for each mirror. All this system is called the supperatenuator [5].

These details show that it is very difficult to keep the GW interferometric detectors locked in a dark fringe condition, even depending on active systems.

But how sensitive the interferometer must be to make measurements of GW. For a 4 kilometer size GW detector, the first measurement of GW was of a displacement of 10⁻¹⁸. As the arm length is 4 kilometer, the variation in length was 4 × 10⁻¹⁵ m. As the power inside the arms was 100 kW with an input power of 20 W, the detector has a recycling factor of 5000, which makes the real sensitivity of the interferometer close to 10⁻¹² m.

2.2 The resonant-mass gravitational wave detector

Figure 4 shows an example of a second-generation resonant-mass GW detector which operated for about two decades at Louisiana State University. This detector was called Allegro, as can be seen in [7]. This kind of detector operating in their quantum limit can be used to calibrate interferometric GW detectors, as can be seen in [8, 9], as these detectors are narrowband they cannot give the behavior of the GW with the frequency.

Figure 4.

The figure shows the schematics of a bar resonant-mass gravitational wave detector, in this case, the detector called Allegro, which operated for two decades in the Louisiana State University.

When a GW passes through a resonant-mass GW detector, its resonant-mass (called antenna) vibrates in resonance with the GW. Then, the antenna surface motion is measured by motion sensors which are transducers that transform these vibrations into electrical signals. These signals are then analyzed and the intensity of such GW can be obtained by modeling the system detection. The transducer is usually composed of a mechanical oscillators that increase the coupling of the vibration modes of the antenna to the electronic sensor, selecting and filtering the frequency of interest [10, 11, 12, 13] and (for a spherical detector) the direction of the signal can be obtained, as can be seen in [14, 15, 16]. The Brazilian detector uses microwave parametric transducers that match the antenna’s 3.2 kHz quadrupolar mode to the electronic sensor. This transducer has a superconducting cavity into which a resonant, very-low-noise monochromatic microwave signal is injected, and changes in this signal as the cavity vibrates, allowing the measurement of the GW’s effects on the antenna. Other options are capacitive and inductive transducers.

When no GW is present in the system, the transducer is never still, as it vibrates because of the thermal noise, the noise that usually limits the sensitivity of a resonant-mass GW detector.

When GW resonant-mass detectors operated for about two decades and formed a worldwide network, this network set upper limits for amplitudes of GW signals in their operational frequency range that they covered while refining its sensitivity. Figure 5 shows this worldwide network (when its third-generation antennas were operational). Those antennas were cylindrical bars tuned to GW with frequencies around 1 kHz.

Figure 5.

Network of resonant-mass GW detectors that was operational for about two decades.

The design of resonant-mass GW detectors did not allow their antennas to vibrate frequencies less than 1 kHz [17]. After the report of direct detections and the following direct detections, the frequency range around 128 Hz seems to be a possible range for GW detection. One of the reasons these detectors never made a detection was the operational frequency chosen because there is no signal in this frequency region. A possibility to use these detectors would be to change their design and develop a new resonant-mass GW detector with quadrupole modes near the frequency of 128 kHz that could operate in coincidence with laser-interferometric detectors.

These detectors are easier and cheaper to build. Such massive detectors properly designed and positioned near interferometric GW detectors can be used to make coincidence detections of the stochastic GW background, as it can be used to provide data for veto procedures (which help identify false detections), helping more accuracy in the data analysis. They can also be used to increase calibration, as mentioned before.

Monolithic sapphire parametric transducers can be used to improve the sensitivity of the resonant-mass GW detectors as can be seen in [18].

2.3 Pulsar timing

Pulsar timing is an indirect measurement of GW. Using signals that come from pulsars (a neutron star that rotates and sends, like a lighthouse, electromagnetic radiation at very regular intervals). Observatories around the world are trying to mine these signals to look for some small differences in these regular intervals, as can be seen in Figure 6. If a GW passes through this signal, the part of the signal orthogonal to the GW will arrive at Earth with a certain delay. The pulses are folded on top of each other, looking for some residuals. The problem is that they only work for big periods of time, like some decades. That is because these experiments detect signals in the range of nanoHertz. A review of these experiments can be seen in [19]. Some results are appearing in the literature, but with no concrete results yet.

Figure 6.

Signal arriving at Earth coming from a pulsar.

There are three major experiments: Parkes Pulsar Timing Array (PPTA, Australia), European Pulsar Timing Array (EPTA, Europe) and NanoGrav (American project).

A review of these advanced ground based detectors can be seen in [20].

2.4 Polarization of cosmic microwave background

Another range to explore GW radiation is the ultra-low frequency domain around 10⁻¹⁸ Hz. Trying to find the effects of GW radiation imprinted in the cosmic microwave background (CMB) when the universe was 300,000 years old. So far, no experiment has been able to measure the respective B-modes (magnetic modes) of the CMB, and more information can be obtained in [21]. Some researchers believe that because of the weakness of the signal, no signal could ever be detected. Figure 7 shows the E and B-mode polarizations of the CMB.

Figure 7.

Representation of electric and magnetic polarizations of the microwave background.

2.5 Space interferometric detectors

Space interferometric detectors are interferometers mounted in satellites that are not affected by seismic noise, and, as they are much bigger, they are sensitive to frequencies much lower than their terrestrial relative. Some information about them and other future detectors can be found in [22]. As they are built in space, they are not limited by the seismic noise that limits the sensitivity of ground detectors.

A list of these experiments include: LISA (Laser Interferometer Space Antenna, NASA-ESA), DECIGO (Deci-Hertz Interferometric Gravitational Wave Observatory–Japan), TianQuin (China) and Taiji (China).

3. Experiments at all the frequency spectrum

Figure 8 summarizes all the expected sources and the expected main detectors for the observation of GW radiation in the audio regime (some kHz) and lower. The green area is the background of binary sources. Below it, with a lower amplitude, there is a region where is expected the presence of the GW relic background, fossil radiation from the very beginning of the universe, probably hidden because of the binary background.

Figure 8.

Spectrum for the detection sources and detectors.

4. Conclusions

We are living in a very exciting moment in the history of science and astronomy, a new window for the observation of the universe is opening. With the new experiments coming in operation, all ranges of frequencies could be observed. This is for GW astronomy as the observations in visible, infrared, ultraviolet, x-rays and gamma-rays are for astronomy.

With all that information, some of the most hidden astrophysical phenomena could be finally explored. It will be possible to make gravitational observations together with electromagnetic observations. The first one, the kilonova observation with gravitational and gamma-rays gave a glimpse of the merge of two neutron stars, the gravitational signal gives the masses of the merging objects and the electromagnetic signal gives information about the electromagnetic emission of the process, a much more complete description.

With the new GW detector much more information can be gathered, with the space laser-interferometric detectors, the orbits of compact objects can be found, objects that do not emit light and are part of binary systems, and white dwarf binaries. With the pulsar timing, the merger of galaxies with their central black holes can be better understood and if the measurement of the primordial GW can be achieved, a glimpse of the very first instants of the universe can make what information it can bring.

These are really exciting times.

Acknowledgments

The author acknowledges Conselho de Pesquisa e Desenvolvimento Cientifico (CNPq, Brazil) for Grant number 312454/2021-0 and Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) Grant number 2013/26258-4.

Conflict of interest

The author declares no conflict of interest.