The proposal to use
pulsars as
gravitational wave (GW) detectors was originally made by
Mikhail Sazhin in the late 1970s. The idea is to treat the
Solar System barycenter and a galactic pulsar as opposite ends of an imaginary arm in space. The pulsar acts as the reference clock at one end of the arm sending out regular signals which are monitored by an observer on Earth. The effect of a passing long-wavelength GW would be to perturb the galactic
spacetime and cause a small change in the observed time of arrival of the pulses. In 1983, Hellings and Downs extended this idea to an array of pulsars and found that a
stochastic background of GWs would produce a distinctive GW signature: a quadrupolar and higher multipolar spatial correlation between arrival times of pulses emitted by different
millisecond pulsar pairings that depends only on the pairing's
angular separation in the sky as viewed from Earth (more precisely the solar system barycenter). The key property of a pulsar timing array is that the signal from a stochastic GW background will be correlated across the sightlines of pulsar pairs, while that from the other noise processes will not. In the literature, this spatial correlation curve is called the
Hellings-Downs curve or the overlap reduction function. 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 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
starquakes and
glitches, accretion events or stochastic timing noise which can affect the period of slower classical pulsars. Millisecond pulsars have a stability comparable to
atomic-clock-based time standards when averaged over decades. One influence on these propagation properties are low-frequency GWs, with a frequency of 10−9 to 10−6
hertz; the most likely astrophysical sources of such GWs are supermassive
black hole binaries in the centres of
merging galaxies, where tens of millions of
solar masses are in orbit with a period between months and a few years. 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 × 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 degreesa 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. ==Active and proposed PTAs==