Towards the detection of the nanohertz gravitational-wave background

The European Pulsar Timing Array (EPTA) is a scientific collaboration bringing together teams of astronomers around the largest European radio telescopes, as well as groups specialized in data analysis and modelling of gravitational-wave (GW) signals. It has published a detailed analysis of a candidate signal for the since-long sought gravitational-wave background (GWB) due to in-spiraling supermassive black-hole binaries.

Although a detection cannot be claimed yet, this represents another significant step in the effort to finally unveil GWs at very low frequencies, of order one billionth of a Hertz. In fact, the candidate signal has emerged from an unprecedented detailed analysis and using two independent methodologies. Moreover, the signal shares strong similarities with those found from the analyses of other teams.

The results were made possible thanks to the data collected over 24 years with five large-aperture radio telescopes in Europe (see Fig. 2). They include MPIfR's 100-m Radio Telescope near Effelsberg in Germany, the 76-m Lovell Telescope in Cheshire/United Kingdom, the 94-m Nancay Decimetric Radio Telescope in France, the 64-m Sardinia Radio Telescope at Pranu Sanguni, Italy and the 16 antennas of the Westerbork Synthesis Radio Telescope in the Netherlands. In the observing mode of the Large European Array for Pulsars (LEAP), the EPTA telescopes are tied together to synthesize a fully steerable 200-m dish to greatly enhance the sensitivity of the EPTA towards gravitational waves.

Radiation beams from the pulsars' magnetic poles circle around their rotational axes, and we observe them as pulses when they pass our line of sight, like the light of a distant lighthouse. Pulsar timing arrays (PTAs) are networks of very stably rotating pulsars, used as galactic-scale GW detectors. In particular, they are sensitive to very low frequency GWs in the billionth-of-a-Hertz regime.

This will extend the GW observing window from the high frequencies (hundreds of Hertz) currently observed by the ground-based detectors LIGO/Virgo/KAGRA. While those detectors probe short lasting collisions of stellar-mass black holes and neutron stars, PTAs can probe GWs such as those emitted by systems of slowly in-spiraling supermassive black-hole binaries hosted at the centres of galaxies. The addition of the GWs released from a cosmic population of these binaries forms a GWB.

Dr. Jonathan Gair, Group Leader in the "Astrophysical and Cosmological Relativity" department at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute/AEI) in Potsdam and co-author of the study says: "In analysing pulsar timing data, we are looking for a common red noise in the pulsars that is caused by a gravitational wave background.

"The fact that we are seeing such a red noise is very exciting, but we cannot yet say that it is caused by gravitational waves. The astrophysical implications of the detection of a gravitational wave background from a population of supermassive black holes would be profound. The amplitude and properties of this background are affected by the process through which galaxies assemble and massive black hole binaries form and merge."

However, the amplitude of the red noise is incredibly tiny (estimated to be tens to a couple hundreds of a billionth of a second) and in principle many other effects could impart that to any given pulsar in the PTA.

To validate the results, multiple independent codes with different statistical frameworks were then used to mitigate alternate sources of noise and search for the GWB. Importantly, two independent end-to-end procedures were used in the analysis for cross-consistency. Additionally, three independent methods were used to account for possible systematics in the Solar-system planetary parameters used in the models predicting the pulse arrival times, a prime candidate for false-positive GW signals.

The EPTA analysis with both procedures found a clear candidate signal for a GWB and its spectral properties (i.e. how the amplitude of the observed noise varies with its frequency) remain within theoretical expectations for the noise attributable to a GWB.

Dr. Nicolas Caballero, researcher at the Kavli Institute for Astronomy and Astrophysics in Beijing and co-lead author explains: "The EPTA first found indications for this signal in their previously published data set in 2015, but as the results had larger statistical uncertainties, they were only strictly discussed as upper limits. Our new data now clearly confirm the presence of this signal, making it a candidate for a GWB".

Einstein's General Relativity predicts a very specific relation among the spacetime deformations experienced by the radio signals coming from pulsars located in different directions in the sky. Scientists call that as the spatial correlation of the signal, or Hellings and Downs curve.

Its detection will uniquely identify the observed noise as due to a GWB. Dr. Siyuan Chen, researcher at the LPC2E, CNRS in Orleans, co-lead author of the study, notes "At the moment, the statistical uncertainties in our measurements do not allow us yet to identify the presence of spatial correlation expected for the gravitational-wave background signal. For further confirmation we need to include more pulsar data into the analysis, however the current results are very encouraging".

The EPTA is a founding member of the International Pulsar Timing Array (IPTA). As analyses of independent data performed by the other IPTA partners (i.e. the NANOGrav and the PPTA experiments) also indicated similar common signals, it has become vital to apply multiple analysis algorithms to increase confidence in a possible future GWB detection. The IPTA members are working together, drawing conclusions from comparing their data and analyses to better prepare for the next steps.

"As the signal we are looking for is stochastic, it is easy to confuse it with other random processes occurring in the pulsars or in the instruments used to observe them", says Lorenzo Speri, PhD student in the "Astrophysical and Cosmological Relativity" department and co-author of the study.

"Separating the common red noise, which is our signal, from individual noises, requires careful statistical analysis." And Jonathan Gair adds: "The statistical techniques have been carefully developed over the last decade and it is gratifying to see them finally yielding promising scientific results."

Jonathan Gair has been a member of the EPTA for the past decade, working on developing the statistical formalism used to analyse EPTA data. Lorenzo Speri has been working on the analysis of EPTA data for the past year, including, among other things, the optimal selection of pulsars to use in the analysis.

Over the coming year, Gair and Speri will be working on the analysis of the full EPTA data set, and the IPTA data set that combines this data with data from other pulsar timing collaborations. The hope is that these data sets, containing many more pulsars, might have sufficient sensitivity that the origin of the background may begin to be identified.

Related Links
International Pulsar Timing Array
The Physics of Time and Space

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