Pulsar timing array

A pulsar timing array (PTA) is a set of

The proposal to use

The Hellings and Downs work was limited in sensitivity by the precision and stability of the pulsar clocks in the array. Following the discovery of the more stable millisecond pulsar in 1982, Foster and Backer^[11] improved the sensitivity to GWs by applying in 1990 the Hellings-Downs analysis to an array of highly stable millisecond pulsars and initiated a ‘pulsar timing array program’ to observe three pulsars using the National Radio Astronomy Observatory 43 m telescope.

Millisecond pulsars are used because they are not prone to the

GWs cause the time of arrival of the pulses to vary by a few tens of nanoseconds over their wavelength (so, for a frequency of 3 x 10⁻⁸ Hz, one cycle per year, one would find that pulses arrive 20 ns early in July and 20 ns late in January). This is a delicate experiment, although millisecond pulsars are stable enough clocks that the time of arrival of the pulses can be predicted to the required accuracy; the experiments use collections of 20 to 50 pulsars to account for dispersion effects in the atmosphere and in the space between the observer and the pulsar. It is necessary to monitor each pulsar roughly once a week; a higher cadence of observation would allow the detection of higher-frequency GWs, but it is unclear whether there would be loud enough astrophysical sources at such frequencies.

It is not possible to get accurate sky locations for the sources by this method, as analysing timings for twenty pulsars would produce a region of uncertainty of 100 square degrees – a patch of sky about the size of the constellation Scutum which would contain at least thousands of merging galaxies.

The main goal of PTAs is measuring the amplitude of background GWs, possibly caused by a history of supermassive black hole mergers. The amplitudes can describe the history of how galaxies were formed. The bound on the amplitude of the background waves is called an upper limit. The amplitude of the GW background is less than the upper limit.

Some supermassive black hole binaries may form a stable binary and only merge after many times the current age of the universe. This is called the final parsec problem. It is unclear how supermassive black holes approach each other at this distance.

While supermassive black hole binaries are the most likely source of very low frequency GWs, other sources could generate the waves, such as cosmic strings, which may have formed early in the history of the universe. When cosmic strings interact, they can form loops that decay by radiating GWs.^[15][16]

Globally there are five active pulsar timing array projects. The first three projects (PPTA, EPTA, and NANOGrav) have begun collaborating under the title of the International Pulsar Timing Array project, InPTA became a member in 2021. Recently China has also become active although not a full member of IPTA yet.

1. The Parkes Pulsar Timing Array (PPTA) at the Parkes radio-telescope has been collecting data since 2005.
2. The European Pulsar Timing Array (EPTA) has been collecting data since 2009; it uses the five largest radio telescopes in Europe:
   • Lovell Telescope
   • Westerbork Synthesis Radio Telescope
   • Effelsberg Telescope
   • Nancay Radio Telescope
   • Sardinia Radio Telescope.
3. The
   Green Bank radio telescopes
   .
4. The Indian Pulsar Timing Array (InPTA) uses the upgraded Giant Metrewave Radio Telescope.^[17][18]
5. The Chinese Pulsar Timing Array (CPTA) uses the
   Five-hundred-meter Aperture Spherical radio Telescope (FAST).^[19]
6. The MeerKAT Pulsar Timing Array (MPTA), part of MeerTime, a MeerKAT Large Survey Project. The MPTA aims to precisely measure pulse arrival times from an ensemble of 88 pulsars visible from the Southern hemisphere, with the goal of contributing to the search, detection, and study of nanohertz-frequency gravitational waves as part of the International Pulsar Timing Array.

In 2020, the NANOGrav collaboration presented the 12.5-year data release, which included strong evidence for a power-law stochastic process with common strain amplitude and spectral index across all pulsars, but statistically inconclusive data for the critical Hellings-Downs quadrupolar spatial correlation.^[22][23]

In June 2023, NANOGrav, EPTA, PPTA, and InPTA announced that they found evidence for a gravitational wave background. NANOGrav's 15-year data on 68 pulsars provided a first measurement of the distinctive Hellings-Downs curve, a tell-tale quadrupolar signature of gravitational waves.^[24] Similar results were published by European Pulsar Timing Array, who claimed a ${\displaystyle 3\sigma }$-significance, the standard for evidence. They expect that a ${\displaystyle 5\sigma }$-significance, the standard for detection, would be achieved around 2025 by combining the measurements of several collaborations.^[25][26] Also in June 2023, the Chinese Pulsar Timing Array (CPTA) reported similar findings with a ${\displaystyle 4.6\sigma }$-significance; they monitored 57 millisecond pulsars over just 41 months, taking advantage of the high sensitivity of FAST, the world's largest radio telescope.^[27][28] Four independent collaborations reporting similar results provided cross validation of the evidence for GWB using different telescopes, different arrays of pulsars, and different analysis methods.^[29] The sources of the gravitational-wave background can not be identified without further observations and analyses, although binaries of supermassive black holes are leading candidates.^[3]

• Gravitational-wave observatory