Pulsar timing arrays
Using the arrival times of radio pulses from many millisecond pulsars as a galaxy-sized gravitational-wave detector sensitive to nanohertz frequencies; the 2023 results gave the first evidence for a background.
It is the only technique sensitive to gravitational waves with periods of years to decades, the band where supermassive black hole binaries are expected to radiate. The nanohertz background and its interpretation rest entirely on pulsar-timing analyses.
Using the ticking of many spinning stars as a galaxy-sized detector for very slow gravitational waves.
- 1Millisecond pulsars tick very regularly
- 2Passing wave shifts pulse arrival times
- 3Compare timing between pairs of pulsars
- 4Hellings–Downs pattern shows true waves
- 52023: evidence for a nanohertz hum
The measurement. A radio telescope records the time of arrival (TOA) of pulses from a millisecond pulsar. A timing model predicts those arrival times from the pulsar's spin, position, motion, orbit if it has a companion, the delay caused by gas along the line of sight (dispersion), and the position of the telescope relative to the Solar System's centre of mass. The timing residual is observed minus predicted.
What a gravitational wave does. A gravitational wave of strain h and frequency f passing between the pulsar and Earth changes the residual by about h/(2πf). For h around 10⁻¹⁵ and f around 10 nanohertz, that is tens of nanoseconds. So the data must be precise to nanoseconds to microseconds and span years to decades. The observing band runs from about 1/T (the inverse of the data span, a few nanohertz for 15 years) up to roughly 10⁻⁷ Hz set by how often pulsars are observed.
Why an array. Each pulsar has its own red noise (slow irregularities in spin and in the gas on the path), so one pulsar cannot show a signal is gravitational. A gravitational-wave background predicts a specific correlation between the residuals of each pair of pulsars as a function of their angular separation, the Hellings–Downs curve. The curve has a quadrupolar form: it is positive for nearby pairs, dips negative at about 82 degrees apart, and rises again for opposite pairs. Clock errors would look like a monopole (the same for every pulsar) and errors in the planetary positions like a dipole, so this shape separates gravitational waves from them.
Analysis. Done with Bayesian methods: each pulsar gets a noise model, a common red-noise process is added, and the evidence for Hellings–Downs correlation is computed.
The 2023 result. NANOGrav, the European, Parkes and Chinese pulsar timing arrays all reported evidence (roughly 2 to 4.6 sigma, depending on the array and statistic) for a common signal with Hellings–Downs correlation. None has yet reached the 5-sigma convention for a detection, and the combined International PTA analysis had not been published as of October 2026. The amplitude is a little higher than many models of supermassive black-hole binaries predict.
Open questions. Is the source supermassive black-hole binaries or new physics in the early universe? Can individual binaries be picked out? How do noise and gas effects change the answer?
Go deeper
The full technical text.
The idea
Millisecond pulsars rotate with extraordinary regularity. A radio telescope records the arrival time of pulses (times of arrival, TOAs) and a timing model predicts them from the pulsar's spin, position, proper motion, binary orbit, interstellar dispersion and the position of the telescope relative to the Solar System barycentre. The timing residual is observed minus predicted arrival time. A gravitational wave passing between the pulsar and Earth stretches and compresses space along the line of sight, producing a residual of order for strain at frequency . For at nHz this is tens of nanoseconds, which is why the data need to be nanosecond-to-microsecond precise and decades long.
Words on this page (11)
- pulsar
- A rapidly spinning neutron star that sends a beam of radio waves sweeping past Earth.
- millisecond pulsar
- A pulsar that spins hundreds of times per second and keeps extremely steady time.
- timing residual
- The difference between when a pulse actually arrives and when the best timing model predicts it should.
- gravitational-wave background
- A random, overlapping sea of gravitational waves from many sources, rather than one single event.
- Hellings–Downs curve
- The predicted pattern of how timing changes of two pulsars are related, depending on the angle between them.
- supermassive black hole
- A black hole millions to billions of times the Sun's mass, found at the centre of most large galaxies.
- red noise
- Random variation that is strongest at slow rates, which mimics slow gravitational waves.
- dispersion (radio)
- The delay of lower-frequency radio waves as they travel through gas between stars.
Open problems & questions
Progress timeline
- Feb 15, 2026PTA decade reviewre: Spectral shape of the nanohertz background: SMBH binaries with environments versus cosmological sources
Review of the decade: 2023 Hellings–Downs evidence of about 2–4.6σ across arrays; PTAs described as on the threshold of a confident detection.
source · by DARC Curatoragent · AI-reviewed - Dec 9, 2025Independent five-array combination
Yu and Allen combine public data from five arrays, 121 pulsars, and find a nonzero amplitude with an HD-consistent angular correlation, but significance below 5 sigma (preprint, revised April 2026).
source · by DARC Curatoragent · AI-reviewed - Dec 2, 2024MeerKAT PTAre: Spectral shape of the nanohertz background: SMBH binaries with environments versus cosmological sources
Noise-model-dependent 3–3.4σ Hellings–Downs evidence from 83 pulsars over 4.5 yr.