14 mins read 13 Jun 2023

The Universe’s Roaring Low-Frequency Gravitational Wave Background

Gravitational waves were predicted by Einstein’s General Relativity but remained undiscovered for over 100 years - until a binary pair of stellar-mass black holes merged and collided, with the signal reaching us in 2015. In part two of this series, we take a look at what the gravitational wave spectrum is, what low-frequency gravitational waves are, and what happens when we finally detect these types of gravitational waves.

Credit: R. Hurt/CALTECH-JPL: NASA.

Einstein’s 1915 revolutionary General Theory of Relativity (GR) has, for over 100 years now, been our leading theory of gravity. This elegant solution, which superseded Newton’s theory,  outlines how the observed effects of gravity we see around us in the Universe are a result of mass curving four-dimensional space-time. This framework has, on many occasions, been utilised to confirm astrophysical phenomena to a high degree of accuracy with experimental data. 

One of the most fascinating outcomes of GR is gravitational waves. These ‘waves’ manifest as distortions in the fabric of the cosmos, created by accelerating masses, due to changes in their quadrupole moment in time. Technically, all accelerating masses produce gravitational waves (even something as small as a human doing exercise squats at the gym), but these are not within the detectable ranges of current technology. What we can observe, however, are gravitational waves made by the largest of masses, such as those found in binary systems that feature neutron stars or black holes. For these heavyweights, they can really shake up the Universe. 

Historically, most of what we have known about the Universe has come from the observation of light across the electromagnetic (EM) spectrum, with a little more insight from cosmic rays and neutrinos. Gravitational waves (GWs) were first indirectly measured in the mid-1970s by observing the orbital radius of a pulsar-neutron star binary system slowly shrinking. The measured reduction of distance between the two objects, even though it was small, could be explained by the loss of gravitational radiation from the system (in the form of GWs), which matched the predicted values of GR. Then in 2015, GWs were confirmed when dedicated instruments (giant laser interferometers) made the first direct measurements of them - giving us a new way to ‘hear’ (or some say ‘feel’) the Universe too.

We can now use GWs to analyse populations of black holes (which are invisible to the EM spectrum), observe inspiral binary systems of compact remnants (like neutron stars), and complement our EM observations to reveal more about astrophysical events. Scientists can also use them to provide further precision tests of GR, help us build more accurate models of the equations of state of matter, or describe the last few moments of core-collapse supernovae events. If that wasn’t enough, there’s also a suite of cosmological uses that GWs assist in, such as helping us probe some of the earliest epochs in the Universe’s history.

One of the aspects that makes GWs tantalising to astronomers, is that they can provide the ability to probe signals that have traversed across the Universe which have not been affected by matter and radiation like the EM spectrum is, through interference and scattering. They can reveal a lot of information about the sources that produce them, even when those sources are extremely far away.

A Spectrum of Gravitational Waves

The gravitational wave spectrum as outlined by the wave period (timescales) and frequencies of these waves. Different sources produce different wave period gravitational waves, and so require different detection techniques and instruments. Credit: ESA.

Like their EM counterparts, GWs exhibit properties that astronomers can measure as they interact with masses along their traversed paths - such as amplitude, frequency, wavelength, two polarisation configurations (an ‘x’ and ‘+’ configuration) and the speed at which they travel (the speed of light). Armed with data that reveals details of these properties, scientists have been able to determine the strength of passing GWs - known as the ‘strain’ - with direct evidence from binary stellar-mass object mergers, showing that this is extremely small, measured to 1/10,000th the diameter of a proton. The events that have caused these waves are also very distant, and so these waves are feeble by the time they reach us.

GWs can be classed into four category types. The first are continuous waves (CW) which can be generated by asymmetrical rotating objects such as neutron stars with centimetre-high mountains on their surfaces. The second are compact binary mergers, where binary black holes or neutron stars undergo decaying orbits and finally merge (these are the ones we currently have evidence for). There is also the stochastic background of GWs, which is the randomly distributed background noise of many sources, and finally burst GW events, which are transient events such as the GWs released by core-collapse supernovae. 

Different sources, events and phenomena across the cosmos produce a cacophony of GWs, each at different frequencies and wave periods - which much like its EM counterpart - produces the GW spectrum. What this spectrum outlines is that different mass objects (either singular or in binaries) produce a different GW strain amplitude - that stretches from the very low frequencies of around 10-18 Hertz (Hz) to the highest frequency GWs, around 104 Hz. 

At the lower end of the GW spectrum are cosmological events such as quantum fluctuations in the early epochs of the Universe (which have been amplified by inflation), first-order phase transitions, and isolated loops of cosmic strings which decay through GWs, which range from approx 10-18 to 10-15 Hz. This is the theoretical lower limit of GWs, as wave periods lower than this correspond to the size of the Universe itself. 

The stochastic background of inspiral and merging supermassive black hole binaries (which reside in the hearts of galaxies and have masses of millions to billions of times that of the Sun) over the history of the Universe are thought to be the loudest source of GWs in the range of 10-9 - 10-7 Hz (nanohertz regime) - though, other cosmological sources like cosmic strings are also thought to generate GWs at these frequencies too. The wave periods for these events last about a decade. 

GW frequencies between 10-4 and 1 Hz are created by binary sources, that can exhibit both continuous and transient signatures. These sources include the inspiral of massive black hole binaries (where masses are below 108 solar units) and unequal mass binaries that are inspiraling (like stellar mass compact remnants merging with a supermassive black hole). For these events, the wave periods can extend from minutes to hours. 

Higher frequency GWs (1 - 102 Hz) are usually associated with transient events, such as stellar mass systems of neutron stars and black holes (or intermediate-mass black holes) which are following inspiral orbits, radiating GWs and eventually merging.  With nearly 100 of these events now confirmed by LIGO / VIRGO / KAGRA (LVK) collaboration, these events have wave periods that usually last for minutes or seconds. Of the confirmed cases so far, the majority are binary black hole systems, with a couple of binary neutron star systems.

Detections made in the first three observing runs from LIGO / VIRGO / KAGRA (LVK). These events are all considered ‘stellar-mass mergers’ and produce gravitational waves that the terrestrial interferometers can detect. Credit: C. Knox/Swinburne University of Technology.

Finally, at the upper end of the spectrum are the highest-frequency GWs, which also produce both transient and continuous signatures. This band covers the range of 102 - 104 Hz, and are produced by rotating neutron stars with asymmetries on their surfaces, spin-down dynamics of pulsars and the core-collapse supernova signatures. 

With such a wide range of frequencies, the GW spectrum is observed by a number of different detection methods and instruments - each tuning into a different portion of the spectrum. Currently, terrestrial-based interferometers (e.g. LVK) - which resemble giant Michaelson-Morley experiments - use lasers as the beams of the interferometer and mirrors as test masses to measure any effect passing GWs have on the Earth as the quadrupole wave would extend the length of one arm, whilst contracting the other (technically, stretching and squeezing the Earth).  

As yet, the highest frequency GWs have not been detected in experiments, though upper limits have started to be placed on continuous sources by instruments like the LVK interferometers, as their sensitivity has improved over the years. Unfortunately, these detectors are faced with lots of noise pollution due to human-based sources, gravity gradients (like Earth’s dynamic atmosphere) and vibrations from the Earth itself in this band. 

The LISA observatory - scheduled for launch in the mid-2030s. This ambitious project will use three orbiting spacecraft, configured in a triangle shape with lasers that are millions of kilometres long between them, acting as the interferometer arms. Credit: NASA/WikiCommons.

In the 10-4 and 1 Hz GW regime, wave periods are much longer (as objects have wider orbits or and are potentially more massive than the stellar-mass events that LVK detects), therefore access to this regime will require interferometer arms that are much longer (even bigger than the Earth). Therefore, a GW detector for this regime is best suited to be located in space, where it could have these longer interferometric baselines, as well as avoid all the terrestrial noise we have on Earth (such as seismic activity). This is the objective of a future-planned mission known as LISA (), which features three spacecraft, orbiting in a triangle configuration using lasers to measure passing GWs. This mission is currently expected to head into orbit around the mid-2030s.

Lower yet is the nanohertz-frequency regime of GWs (10-9 - 10-7 Hz), which require detectors larger than the Earth itself. Realising that this would be a physical impossibility to build, astronomers have devised a very clever method of analysing the low-frequency GW background, using one of nature’s most precise natural clocks - pulsars

The Low-Frequency Gravitational Wave Background

Artist rendition of a pulsar timing array, using pulsars surrounding Earth to detect gravitational waves (pink) from distant binary supermassive black holes. Credit: C. Knox/Swinburne University of Technology.

So far, GWs (directly confirmed events or candidates) have been considered from the perspective of the LVK discoveries - that is individual binary systems that emit these waves. That’s to say that for each of the LVK detections, the GWs have been related to a single system of either binary neutron stars or binary black holes (or a combination of either) as they inspiral, merge and ringdown. 

However, there also exists a background of GWs, made up of many different frequencies and different sources. For example, if there are many individual neutron stars with tiny asymmetrical mountains on them, then their collectively emitted high-frequency GWs would form a background in the frequency of their spin periods. Additionally, when astronomers consider all the inspiral orbits of supermassive black holes inside galaxies, as they orbit each other before merging across the history of the Universe, then they are not looking for singular systems emitting gravitational waves, but rather their collective emissions. These GW backgrounds can be spread across a range of frequencies, based on many factors - such as the varying masses of objects, or if their orbit is near circular or elliptical, to name a few. 

The gravitational wave background can therefore be thought of as the dull roar of many GW sources all blended into one. It’s analogous to being at a busy cocktail party and hearing the sound of conversations coming from all directions across the room. No particular conversation can be clearly made out, but the room is audibly loud and your ears are the detectors. Continuing with this ‘cocktail room’ analogy for the GWB, astronomers are trying to measure the loudness of this cocktail party, what frequencies are louder or more popular than others, and whose voices can be the loudest - which helps them learn more about the source populations that are generating them. 

Given that the GWB is from many sources, it is expected to be isotropic (homogenous in all directions), much like the initial discovery of the cosmic microwave background (CMB) - the EM echo of the Big Bang. Interestingly, when scientists took a deeper look at the CMB after discovering it, it revealed anisotropies (direction-based features) which have since provided a wealth of information about cosmology, galaxy evolution and more. It is expected that once the stochastic GWB has been detected, future studies could potentially start to probe into more of the intricate features of different sources that produce it. 

What Happens When We Detect the GWB?

Artist impression of a pair of supermassive black holes at the centre of galaxy 0402+379 in an inspiral orbit with each other. Credit: J. Valenzuela/Uni. of New Mexico.

To detect the stochastic nanohertz-frequency GWB, astronomers use a network of millisecond pulsars (as these are much more stable over the long term) which are spatially separated across the sky, and measure their pulse times of arrival over long-term periods (these types of GWs that last for decades). A network of pulsars that are continually timed is known as a Pulsar Timing Array (PTA) experiment. 

Currently, there are several global teams that are conducting this experiment, which include the Parkes Pulsar Timing Array project (PPTA - Australia), the North American Nanohertz Observatory for gravitational waves (NANOGrav - USA), the European Pulsar Timing Array project (EPTA - European nations) and the Indian Pulsar Timing Array project (InPTA - India). These organisations operate under a global collaboration known as the International Pulsar Timing Array (IPTA) project. There are also several emerging PTA teams located in South Africa and China as well. 

The PPTA, NANOGrav, and EPTA have now accumulated almost two decades of data for a number of their millisecond pulsars, giving them enough data to commence analysis in search of the GWB signal. These results have been presented through each PTA’s own data releases historically, as well as the first and second data releases at the IPTA level - where combined data sets from all PTAs have improved sensitivities. 

Interestingly, in 2021, the PPTA, EPTA and NANOGrav, as well as the combined data in the IPTA, reported on the emergence of a ‘common noise’ signal across their data sets at the two-sigma level - a rumble from the sky that all teams were able to verify independently. Pulsar astronomers believe that when the GWB signal starts to present itself, it will first appear as a common noise process across all millisecond pulsars being observed. Though, this is not the smoking gun - and could in fact be a false positive

The main factors required to confirm the detection of the GWB signal are data that shows that yes, there is a common signal amongst all pulsars - but additionally this signal has to have a certain spectral index and amplitude which is representative of a background of GWs generated by many inspiral and merging supermassive black hole binaries. 

The last factor, also the most important, is the smoking gun. According to GR, the GWB should induce tiny variations in the distance between the Earth and each MSP, and as it passes through the Solar System, it will create an observable and quadrupolar correlated signature on MSPs that are separated across the sky. This correlated signal distinguishes itself from other noise sources that might look like the GWB, such as clock and ephemeris errors. It is known as the Hellings-Downs correlation, and if the PTAs (and combined IPTA) data sets can showcase supporting evidence for these criteria, then the GWB detection will be confirmed - marking its historic discovery. 

The Hellings-Downs correlation (simulated) on pulsar timing residuals, of pulsars that have angular separation across the sky (shown in radians). This is the expected signal correlation between pulsars generated by a stochastic background of gravitational waves. Credit: Verbiest et al. 2021.

Realising that PTA datasets are now approaching the period in which a detection should be made in the next few years, a group of pulsar astronomers from the IPTA have recently released a checklist for the detection of the nanohertz-frequency GWB signal. 

The checklist contains a number of verification checks to help ensure that any claim to detection has been thoroughly analysed and agreed upon through cross-checking within the collaboration. This includes finding evidence for the Hellings-Downs correlation in the data with five-sigma significance, using both Bayesian and Frequentist formation methods. If only four-sigma is reached, then the detection is considered “evidence for” and if only three-sigma is reached, it is considered as a “possible signature of the GWB” only. 

Another checklist item is that the signal must present the expected angular correlations outlined by the Hellings-Downs curve, thus being clearly quadrupolar. Lastly, the signal must be present in more than at least 20 MSPs, and not be in contradiction with historically published results (like previous data releases). 


In the next part of this multi-part series, we explore what Pulsar Timing Arrays are in detail and how they are utilised in searching for the nanohertz-regime GWB. If you missed part one of this special series, read: ‘The Milky Way’s Cosmic Clocks - Pulsars’.


The Detection checklist is now available on the preprint server, arXiv.org