Identifying the physical origin of the nanohertz stochastic gravitational-wave background in pulsar timing arrays

Pulsar timing arrays (PTAs) have found evidence for a nanohertz stochastic gravitational-wave background (SGWB), but its physical origin remains unidentified: Bayesian model comparisons give comparable support to a cosmic population of inspiraling supermassive black hole binaries (SMBHBs), cosmic strings, and strong first-order phase transitions, while the domain-wall interpretation is disfavored. The open problem, as framed by Wu, Chen & Huang (2023), who combined the NANOGrav, PPTA and EPTA data sets, is to turn this statistical consistency into a definitive physical identification of the background's origin.

Background

A pulsar timing array (PTA) is a set of Galactic millisecond pulsars whose radio pulse arrival times are monitored for years to decades; a passing gravitational wave shifts the times of arrival at the microsecond level and below, and the characteristic quadrupolar Hellings–Downs angular correlation between pairs of pulsars identifies a gravitational-wave origin. In June 2023 the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the European Pulsar Timing Array (EPTA), the Parkes Pulsar Timing Array (PPTA) and the Chinese Pulsar Timing Array (CPTA) collaborations announced evidence for a stochastic gravitational-wave background (SGWB — a random, statistically isotropic superposition of waves) in the nanohertz frequency band, roughly $2$–$30$ nanohertz as currently measured. The leading astrophysical explanation is a cosmic population of inspiraling supermassive black hole binaries (SMBHBs — binaries with total masses of order $10^{8}$–$10^{10}$ solar masses formed in galaxy mergers), whose superposition produces a power-law strain spectrum with spectral index $\gamma=13/3$. However, several early-Universe sources radiate in the same band and can mimic this spectrum over the narrow measured frequency range: cosmic strings (one-dimensional topological defects from high-energy symmetry breaking, characterized by a tension $G\mu$, the gravitational constant times mass per unit length, and by bursts of gravitational waves from cusps — points on oscillating string loops that momentarily move at nearly the speed of light); first-order phase transitions (FOPTs), which generate gravitational waves through bubble collisions, sound waves in the plasma, and turbulence, described by semi-analytic microphysical templates with shape parameters $(a,b,c)$; and domain walls (two-dimensional topological defects whose annihilation produces an $f^{3}$ low-frequency tail). Model comparison is done with Bayes factors — the ratio of the marginal likelihoods of two models, conventionally read on the Jeffreys scale, on which a factor above 100 is traditionally regarded as decisive.

Wu, Chen & Huang (2023) combined the public NANOGrav 15-year, PPTA DR3 and EPTA DR2 data releases (DR = data release) and computed Bayes factors relative to the SMBHB hypothesis: $0.799$ for FOPTs and $1.699$ for cosmic strings — comparable support — while domain walls were strongly disfavored ($0.009$). Their parameter inference exposed the interpretability bottleneck that motivates this problem: the PTA-inferred domain-wall spectral width $c>1.22$ conflicts with lattice-simulation estimates $c\approx 1$ (from grid-based numerical simulations of domain-wall networks); FOPT conclusions depend on the bubble-collision template parameters and on the treatment of the finite lifetime of acoustic sources, with turbulence neglected; cosmic-string amplitudes depend on the assumed loop-size distribution, harmonic emission spectrum, and the reconnection-probability prior (the probability that two crossing string segments rejoin rather than pass through each other); and some parameter regions conflict with independent cosmological constraints, such as primordial black hole (PBH — black holes formed in the early Universe) overproduction in domain-wall scenarios. The same degeneracy appears in the contemporaneous collaboration analyses: the NANOGrav 15-year new-physics search found Bayes factors of $10$–$100$ favoring several cosmological models over SMBHBs but stressed that these depend on SMBHB population modeling and should not be regarded as evidence for new physics, while the EPTA DR2 + InPTA (Indian Pulsar Timing Array) implications paper stated that at the current stage of emerging evidence it is impossible to discriminate among the different origins. The open problem is to achieve a definitive physical identification of the background's origin.

Problem Statement

Determine the physical origin of the nanohertz stochastic gravitational-wave background detected by pulsar timing arrays — the question left open by Wu, Chen & Huang (2023) and the 2023 PTA new-physics analyses: establish, with decisive and robust statistical evidence, whether the background originates from a cosmic population of inspiraling supermassive black hole binaries, from early-Universe sources such as cosmic strings or first-order phase transitions, or from a mixture. The competing spectral shapes are nearly degenerate power-law-like forms over the currently measured nanohertz band; inferred source parameters presently hinge on theoretical template and prior choices (e.g. cosmic-string loop-size distributions, emission spectra and radiative efficiency; first-order-phase-transition spectra including turbulence and the finite lifetime of acoustic sources) and must be confronted with independent astrophysical and cosmological constraints (e.g. primordial black hole abundance, dark radiation — additional relativistic energy density beyond Standard-Model photons and neutrinos — and SMBHB population and merger models). The problem is completed when a physical identification of the background's origin — or a quantified mixture decomposition, or the exclusion of all but one source class — is supported by decisive statistical evidence, on the Bayes-factor standard defined above, that survives the template and prior variations enumerated in this paragraph; a result that leaves the surviving source classes statistically indistinguishable does not complete it.

References

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