Can we hear the “beats” of gravitational waves to the rhythm of pulsars?

Pulsars suggest that ultra-low frequency gravitational waves are propagating through the cosmos. The signal observed by international pulsar timing array collaborations in 2023 could come from a background of stochastic gravitational waves – the sum of many distant sources – or from a single binary near supermassive black holes.

To differentiate them, Hideki Asada, theoretical physicist and professor at Hirosaki University, and Shun Yamamoto, researcher at the Graduate School of Science and Technology at Hirosaki University, propose a method that exploits the beat phenomena between gravitational waves at almost the same frequency, looking for their imprint in the tiny shifts in the arrival times of the radio pulses from pulsars.

Their work was published in the Journal of Cosmology and Astroparticle Physics.

The sky is filled with exquisitely precise “cosmic clocks”: pulsars, neutron stars that emit radio pulses at regular intervals, like a regular ticking clock. Radio telescopes on Earth monitor their periodicity, not only to study the pulsars themselves, but also to use them as tools for probing the universe.

If something invisible – almost a “cosmic ghost” – distorts space-time along the path from a pulsar to Earth, the regularity of the pulses changes. The anomaly is not random: similar deviations appear between pulsars in certain regions of the sky, as if an undulating ripple is passing through them.

“In 2023, several collaborations with pulsar timing networks – NANOGrav in the US and European teams – announced strong evidence for the existence of nanohertz gravitational waves,” notes Asada.

Nanohertz means wave periods ranging from several months to several years, with wavelengths of several light years. To probe such scales, we rely on distant and stable pulsars located hundreds or even thousands of light years away.

“The signal was statistically reliable but below the 5 sigma threshold usually required by particle physicists,” he continues. “This is ‘strong evidence’ but not yet a confirmed detection, but the cosmology and astrophysics community believes we are approaching the first detection of nanohertz gravitational waves.”

For the moment, certainty is below the reference threshold; If future data bears this out, Asada says, the next challenge will be identifying the source.

“There are two main potential sources of nanohertz gravitational waves,” he explains.

“One is cosmic inflation, which would have created space-time fluctuations at the very beginning of the universe, then extended to cosmic scales. The other concerns binary supermassive black holes, which form when galaxies merge. Both scenarios could generate nanohertz gravitational waves.”

The difficulty is that the correlation patterns in pulsar data – the way the timing residuals of different pulsars correlate – have long been thought to be the same in both cases.

“In our paper, we explored the situation in which a pair of nearby supermassive black holes produces a particularly strong signal,” says Asada. “If two of these systems have very similar frequencies, their waves can interfere and create a beating rhythm, as in acoustics. This characteristic could, in principle, allow us to distinguish them from the stochastic background of inflation.”

Asada and Yamamoto therefore exploit a familiar acoustic effect: beats. When two waves have almost – but not exactly – the same frequency, their superposition produces periodic strengthening and weakening.

Applied to gravitational waves, two binary supermassive black holes with similar frequencies would imprint a characteristic modulation in the pulsar’s timing signal. The method consists of looking for this modulation – the “beat” – in the correlation models of the pulsars. If present, this strongly suggests that the signal is not a diffuse background but comes from specific binaries relatively close together.

“I think that once confirmed detection at 5 sigma is achieved, perhaps within a few years, the next step will be to ask: what is the origin of the waves? At this point, our method could be useful in distinguishing whether they come from inflation or from nearby supermassive black holes,” concludes Asada.