The Red Herring, Swimming in a Sea of Gravitational Waves

Gravitational waves, whilst only recently having been directly confirmed, can reveal a lot about the Universe that we are unable to see through the electromagnetic spectrum. They can tell us about merging black holes, the formation history of galaxies, if neutron stars have tiny mountains on their surface, and how Einstein’s theory of gravity, General Relativity, holds up against assessment. 

To observe them directly, we normally utilise giant machines - known as interferometers to ‘listen’ and ‘feel’ them as they pass over the Earth, squeezing and stretching everything and everyone, by a variance no bigger than 1/10,000^th the diameter of a proton. 

But we can also observe them indirectly using a number of different objects and techniques. One such way is to time pulsars that are spread across the Galaxy in extremely sensitive timing experiments that measure their ticks over the long term, looking for any changes. 

Pulsars are highly magnetised, rapidly rotating neutron stars that beam radio waves from their poles and act as some of nature’s most stable and accurate astrophysical clocks. They’ve got about 1.4 times the mass of the Sun, squeezed into a sphere no bigger than a small town. 

In the last few months, scientists from around the world - working on experiments known as a pulsar timing array (PTA) - have noticed an intriguing common signal amongst the millisecond pulsars being observed, one that might be the first signs of a class of gravitational waves (GWs) that have yet-to-be-discovered. These GWs exhibit ultra-low frequencies and have wave periods that last about a decade - meaning that each wave that passes over us takes a decade to go from crest to crest, and collectively (yes, there are many floating around right now, and at different frequencies) they are known as the gravitational wave background or GWB.

Now, a team of astronomers have used millisecond pulsar data collected by the Parkes radio telescope (operated by Australia’s national science agency, CSIRO) to simulate and statistically analyse what this common signal might look like, with results indicating that it could be a potentially important signal, but it could also be a potential red herring. That is, there is a possibility that this signal might fool us into it being a sign of a true detection of the GWB signal. The new research is published in the journal, Monthly Notices of the Royal Astronomical Society.

Reporting on their findings, the team of astronomers, led by Dr Andrew Zic from the CSIRO and Macquarie University, simulated a virtual pulsar timing array (PTA) observing a set of 26 virtual pulsars to record their signal time of arrival and testing if the different parameters put into the simulation affected the outcome of the results - to the point where it could be mistaken as the recently observed common signal. 

The 26 pulsars that were chosen form part of the dataset that is currently observed by the PPTA, and the simulation modelled the virtual observations to run at a regular cadence of 40 days, and over a period of 20 years.  

Like the electromagnetic spectrum, which comes in a variety of wavelengths (from radio through to gamma rays), gravitational waves also come in a spectrum - dependent on the masses that are producing them. 

The different sources producing these ripples in space-time can often take different forms – some are transient events, like the sudden merger of two black holes, whilst others are more of a continuous static noise in the background, like the rumbling hum of an asymmetrical neutron star, spinning with a mountain only a few millimetres tall on its almost perfect spherical surface. Some can be ancient and primordial, like the quantum fluctuations that occurred in the first few seconds after the Big Bang, and others can be more recent bursts like a relatively nearby supernova that collapses in an asymmetrical manner.

The GWs that have been detected so far are the results of merging compact stellar-mass objects, like stellar-mass black holes and neutron stars. To detect these, instruments like the Laser Interferometer Gravitational-wave Observatory (LIGO, and similarly VIRGO and KAGRA) tune into the frequencies that these objects radiate, as they spiral and merge together. 

But for objects of bigger masses, then we need a bigger detector - which is where the proposed space-based Laser Interferometer Space Antenna (LISA) and existing pulsar timing arrays (PTAs) come in. These look for frequencies from massive objects like the black holes in the centre of galaxies, or when stellar-mass black holes are caught in a death dance with their supermassive cousins.

Scientists and engineers are currently looking for ways to improve our existing technologies to make these instruments much more sensitive or invent new types of detectors which can tune into different frequencies of the GW spectrum. 

In September 2021, we wrote an earlier article on another PPTA GWB paper, describing how the potential common signal was emerging amongst the data set of pulsars, observed by Parkes. This signal was also being observed by several other teams who are also hunting for these types of gravitational waves, all using different telescopes around the world - so there was a bit of excitement about it. 

Pulsar astronomers started to consider that we could finally be on the verge of detecting nanohertz frequency, long-period gravitational waves and start to unlock the secrets of the history of mergers and collisions as supermassive black holes grew and consumed over the history of the Universe.

The fact that all global teams were able to analyse their own datasets, and see the same common noise process is still very interesting. And the properties of this common noise process is consistent with what a GWB signal will look like when it first starts to be detected. 

But the simulation analysis in these recent findings that have been published by Dr Zic and colleagues, errs on the side of caution and with the paper stating that we should be wary to avoid a potential red herring. 

Whilst these first tantalising signals could potentially be the real deal, they don’t give us the silver bullet of a true detection. However, pulsar astronomers do have another card up their sleeve to make this detection and have thought of a clever way to help them make this absolute determination. 

We know that different mass objects generate different gravitational waves, and each of the frequency bands requires a different type of detector. In the case of the nanohertz, low-frequency band, that generates the gravitational wave background from merging supermassive black holes, we need our pulsar timing array. 

To make a detection in this regime, PTAs use a series of millisecond pulsars located all across the galaxy, including those located within the Galactic plane, as well as above and below it. This experiment is analogous to a giant detector with many LIGO-like arms, where instead of the lasers bouncing between a mirror and a detector which change when a GW washes over the Earth, we have the periodic pulsar signals of pulsars that exhibit a tiny delay in their arrival times, induced by a GW that washes through the Solar System. 

So sensitive are PTAs, that using the right pulsar (i.e., millisecond pulsars, where the right noise conditions are accounted for) can lead to measuring a variance on the scale of approximately 100 nanoseconds. That means we can calculate the distance between us and the pulsar moving by approximately 30 metres in some cases, from light-years away. 

This certainly yields an interesting result when we consider a single pulsar bound by its beam to Earth, but this limits it to one part of the sky, with nothing to compare it against. This provides useful data about this particular pulsar and its environment, but not much more. 

The key to a true detection lies in using many of these millisecond pulsars, and in particular, the angular separation between them.  When calculating if a GWB has been detected, astronomers look for a correlated signal between these pulsars - a signal that is known as the Hellings and Downs curve. 

Gravitational waves that form the GWB come from all directions due to the historical merger of galaxies which have occurred everywhere in the history of the Universe. What pulsar astronomers want to do is detect a signal as it passes through the Solar System - which from our perspective, would affect all the pulsars we observe in a correlated manner.

That’s because the passing gravitational wave distorts space by a small amount, and so the beam between the Earth and each pulsar is squeezed and stretched by this distortion, revealing itself as a delay in the pulsar’s accurate ticks. Looking at all the pulsars across the sky from Earth would therefore show a correlated signal of delayed ticks, thanks to the distortion making its way across the sky from our perspective. 

What astronomers then do is statistically analyse these distortions and their correlation to one another amongst all the different pulsars, and work out how this correlation should be spatially presented - i.e., the Hellings and Downs curve. 

This correlation is considered firm evidence of a GWB detection, as all pulsars will show a correlated effect generated by gravitational waves as they slightly change the distance between the pulsars and our observatories. Pulsars with small angular separations will show slightly similar correlations, whereas pulsars with large angular separations, will exhibit a much more pronounced correlation. 

But unlike the GWs we see from stellar-mass objects, which only last a few mins or seconds, the wave period for the GWB is in decades, which is why scientists have been observing these pulsars for almost 20 years now. Datasets are now starting to get to the point at which a detection might soon be made. 

And so, until then, the search continues by continually listening in on the regular, periodic ticks of the millisecond pulsars around the Galaxy. In a few years, more data will start to reveal if the common red noise observed is indeed the first sign of the detection of the GWB, or if it's just another red herring. 

We acknowledge the Wiradjuri people as the traditional owners of the Parkes radio telescope observatory.

Disclaimer: Rami Mandow is one of the authors of the Zic et al. 2022 paper featured in this article