Figure 1: A computer simulation of a binary system consisted of two supermassive black holes spiraling into each other. Such a system produces gravitational waves that propagate outwards through spacetime. Source Credit: NASA Goddard Space Flight Center (LINK)
Gravitational waves have gained a lot of attention since its first physical observation by the Laser Interferometer Gravitational-wave Observatory (LIGO) detector on Sept. 14, 2015. The ensuing popularization of this observation by the media only spilled gas on the already tempestuous fire. Numerous people were fascinated by this rare astronomical occurrence, which corroborated the belief in both the existence of gravitational waves and binary systems consisting of two merging black holes. Despite the public fascination at this recent observation, gravitational waves are no rare occurrence. In fact, astrophysicists say there are gravitational waves washing over the Earth all the time. The sources of these “stochastic gravitational waves” are yet to be identified, but progress is continually being made.
This leads us to the natural question of “what are stochastic gravitational waves?” In order to answer this question, we must first understand the basics, then work up from there. Any high school student with an interest in physics will have approached the study in the Newtonian formulation. In Newton’s widely applicable (yet fundamentally incorrect) description of gravitation, he describes the phenomenon as the peculiar attraction between any two objects. However, this formulation cannot fully describe what gravitational waves are. A formulation of physics that can accurately describe the phenomenon is that of Albert Einstein. In his theory of general relativity, the existence of gravity hinges on three phenomena:
1. Mass bends the fabric of spacetime: that is, the presence of mass distorts the geometry of the 4-dimensional manifold, consisting of three spatial and one temporal dimensions. This distortion increases with mass, but decreases with the distance between an observer and the said mass.
2. This distorted spacetime geometry allows the existence of geodesics that aren’t necessarily straight, but are rather curved.
3. The journey of masses along such geodesics that aren’t necessarily geometrically straight causes masses to naturally gravitate towards each other.
Gravitational waves, first predicted by Henri Poincaré, naturally follow this formulation of gravity—they are merely waves (a disturbance in a medium, that propagates outward from its source) that propagate through the very fabric of spacetime, thereby creating disturbances in its geometry. The sources of such gravitational waves are accelerating masses that create ripples in spacetime as they move through it (relative to an inertial frame of reference). This phenomenon is analogous to that of electromagnetic waves (light), in which accelerated charges create disturbances in the electromagnetic field.
Figure 2: The gravitational wave spectrum (from larger to smaller periods), their potential sources, and the different mechanisms with which we can detect such gravitational waves.
Source Credit: NASA Laser Interferometer Space Antenna (LISA) mission (LINK)
Stochastic gravitational waves are relics from the birth of the universe. While it’s source has not been identified, most astrophysicists theorize that these weak, random, and thus barely detectable gravitational waves that wash over the entire universe—thereby mapping out a cosmic gravitational background—are actually remnants of the gravitational waves created from the random processes generated by the big bang. By detecting such stochastic gravitational waves, we might even be able to map out the story of the early stages of our universe.
Some sources from which we can detect such gravitational waves, according to professor Bruce Allen’s “The stochastic gravity-wave background: sources and detection,” are coalescing binary systems, pulsars, and supernovae. A coalescing binary system consists of two celestial bodies (most likely neutron stars or black holes) merging into one. When these objects orbit each other closely, they gravitate to, and spiral into each other due to their immense gravity. As they do so, they create very significant gravitational waves that propagate outwards from the system, like mallets striking the surface of a drum. As they propagate gravitational waves outwards, the binary system begins to lose angular momentum, thereby spiraling into smaller and smaller orbits, until they merge into one, whereafter the gravitational waves stop propagating. The aforementioned LIGO detection of gravitational waves had its source in such a phenomenon. Pulsars are compact objects (most likely a neutron star) that are highly magnetized and rotate at very fast rates. These pulsars emit stable and periodic radio waves/pulses whose timing we can very precisely predict from Earth. Thus, if gravitational waves were to interrupt the path of a radio beam headed towards Earth, its path would bend, and its timing will be erratic, thereby giving us clues about such gravitational waves. Lastly, a supernova is an explosion that occurs during the death of a star - as the nuclear fuel of the star runs to depletion, the star, unable to withstand its own gravity, collapses unto itself, crushing even its constituent atoms, and thereafter creating a powerful explosion, during which great gravitational waves are generated.
In comparison to detecting the gravitational waves generated by the merging of two celestial bodies, detecting stochastic gravitational waves are analogous to trying to distinguish the sound of a conversation in a boisterous party, due to its comparatively minute magnitude. For the past several years, interferometer technology, such as the LIGO and VIRGO detectors (alongside the less-known geo-600 and tama-300) and numerous radio telescopes have been put into use in order to detect such waves. A newer technology called Laser Interferometer Space Antenna, consisting of interferometer technology in outer space (with three spacecraft situated in a triangular manner following a heliocentric orbit) is currently under development. Furthermore, recent reports show that the North American Nanohertz Observatory for Gravitational Waves (otherwise known as the NANOGrav Institute), a leading force in using radio telescopes to observe pulsars and detect gravitational waves, has successfully received some strong signals that hint at gravitational waves from an unknown source. There is still much work to be done, and the detection of stochastic gravitational waves is a ripe frontier of exploration.
Q&A:
Xavier: What would the confirmation of these stochastic gravitational waves mean? Why are they important?
By mapping out the stochastic gravitational wave background, we will be able to map out how the universe evolved after its creation.
Jiwon: In your article, you mentioned that astrophysicists say that gravitational waves are a continuous occurrence. Then, why is it taking so much time to detect and analyze these waves?
This is mainly because gravitational force is the weakest of the four fundamental forces of nature. Thus, perturbations in the gravitational field are barely felt by any detector. Moreover, gravitational waves come in various wavelengths. The technology we have at the moment can detect gravitational waves of small ranges of wavelength (and this is partly why we want LISA and pulsar timing array technologies - to detect waves of different wavelengths).
Sally: What are some other potential sources of stochastic gravitational force since you mentioned in the beginning that the sources are yet to be identified?
Here is a comprehensive list of the possible sources of stochastic gravitational waves:
The Big Bang, Binary systems (of black holes, white dwarves, and neutron stars), Neutron star spin, Compact stellar masses spiraling into black holes, Supernovae.
Wooseok: Do these gravitational waves have significant impacts on human life? (e.g. health conditions)
The answer is no. While the gravitational waves stretch spacetime, they do it at such small scales that it is barely felt or heard by humans.
Josh: How could the analysis of stochastic gravitational waves help in future space exploration?
“By mapping out the stochastic gravitational wave background, we will be able to map out how the universe evolved after its creation.” This means that we will be able to gather more information about the location and properties of celestial bodies.
Eric: What threshold of mass do neutron stars/black holes need to be to generate gravitational waves? As long as any size combines, are gravitational waves produced?
Yes - as long as anything has mass, it has an effect on gravity. Analogously to large binary systems, if you and I were to dance around each other (or really accelerate in any fashion), we would create gravitational waves (though very minute in amplitude).
Hugh: What is the significance of the 3 points about the theory of general relativity?
The 3 points about the theory of general relativity are the propositions from which we can hypothesize (and confirm) the existence of gravitational waves.
Works Cited:
“'Galaxy-Sized' Observatory Sees Potential Hints of Gravitational Waves.” ScienceDaily, ScienceDaily, 11 Jan. 2021, www.sciencedaily.com/releases/2021/01/210111125614.htm.
Allen, B. “Sources and Detection.” CERN Document Server, 17 Apr. 1996, cds.cern.ch/record/301296?ln=en.
Cofield, Calla. “What Are Pulsars?” Space.com, Space, 22 Apr. 2016, www.space.com/32661-pulsars.html.
Garner, Rob. “NASA's Goddard Space Flight Center.” NASA, NASA, 10 Feb. 2015, www.nasa.gov/goddard.
Hensley, Kerry. “Can We Detect Gravitational Waves from Core-Collapse Supernovae?” AAS Nova, 5 July 2019, aasnova.org/2019/07/05/can-we-detect-gravitational-waves-from-core-collapse-supernovae/.
“Introduction to LIGO & Gravitational Waves.” LIGO Scientific Collaboration - The Science of LSC Research, www.ligo.org/science/GW-Stochastic.php.
“LISA - Laser Interferometer Space Antenna -NASA Home Page.” NASA, NASA, lisa.nasa.gov/.
North American Nanohertz Observatory for Gravitational Waves, nanograv.org/.
“What Is LIGO?” Caltech, www.ligo.caltech.edu/page/what-is-ligo.
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