A pulsar timing array (PTA) is a set ("array") of pulsars observed by one or more radio telescopes, to gather data on the apparent timing of their pulses (pulsar timing data), for analysis aiming to detect very-long wavelength (light-years) gravitational waves (GWs) through identifying otherwise-unexplainable discrepancies in that timing. PTAs constitute galactic-scale gravitational-wave detectors, significantly scaled up from LIGO-like ground detectors or LISA-like space detectors. Some PTA initiatives:
The observations look for very long period gravitational waves expected from closely orbiting binary SMBHs, which would presumably be on track to merge, but actual detectable mergers might be sufficiently rare as not to be expected in our lifetime. The gravitational waves make the space between a pulsar and the Earth longer and shorter, so the steady pulses take more and less time to reach Earth. To find these, PTA initiatives look for long-term changes in the timing of pulses received from millisecond pulsars (This type of pulsar is the most consistent, producing fewer their own glitches in the timing than other pulsars). Since such pulsars emit pulses with a consistency comparable to our best (i.e., atomic) clocks, how to time their minute variations is a challenge. The timing of pulses and their variations can be gathered by periodic (e.g., monthly) viewing of the pulsars, and the recorded variations over time constitute all the necessary data. The results of many observations is "averaged". It is expected that on the order of ten years of data is needed to progress. No gravitational waves or gravitational wave background has been detected so far, but some claims have been made that this period of non-detection is informative, using assumptions regarding the sensitivity and reliability of the efforts.
The wave periods would be year-long and more (the range of 2-4 nHz, i.e., 4-15 year periods being the "sweet spot" for PTA detection), and the waves move at the speed of light, so for a pulsar some kpc distant, many wave cycles can sit between, Earth and the source, and each such entire wave (to a large extent) "cancels", since part of its phase is making the EMR path longer and another part making it shorter. The waves stem directly from the supermassive black hole orbits (in the simplest case, a circular orbit, there is a wave for each half orbit). The timing differences are due to the waves passing the line of sight between the pulsar and the Earth, the waves being transverse, meaning distances across the wave direction are shortened and lengthened. GW effects at the Earth end (called the signal's Earth term) should affect the timing of (virtually) every pulsar being viewed, the degree depending upon the direction of the specific pulsar, thus observing a number of pulsars helps. The exact delta in the timing of each depends upon the angle between the wave front and the pulsar's direction from Earth. Effects at the pulsar end (called the signal's pulsar term) may be useful, but require more effort to use: each pulsar would be a different distance from the GW source, so different waves would be passing over them and the phases won't match. To detect the longest detectable waves, an ongoing change in timing may be all that is observable (the differential of the timing deltas), adding more challenges to sorting out a signal. If the pulsar term is isolated, data from two different times (and places) is in hand (at Earth and at the pulsar), which can serve as a baseline for further analysis, a temporal equivalent to aperture synthesis (which may reveal the chirp mass and luminosity distance).
Processing includes removing all the other effects on timing, which includes position of the Earth in its orbit (Roemer delay), the motion of the Sun, and the effect of planets (from solar system ephemerides data, e.g., Jupiter is massive enough to affect EMR paths passing close to it), the uncertainties and noise in the measuring equipment (timing noise/TN due to radiometric noise of the radio telescopes and clock errors in the clocks and time standard used to time the pulses), and then distinguishing one or more frequencies in the signal (frequencies the implied GW waves rather than of the EMR waves or pulse periods), each frequency the result of some binary pair of SMBHs. It helps that clock errors will be monopole, ephemeris noise will be dipole and the signal will be quadrupole, but generally, timing PTAs could use more precise ephemeris data than is currently available. PTA initiatives are attempting to improve ephemeris data, aiming for orbit-position data within 100 meters of correct. Efforts use ongoing collection of data regarding Jupiter's and Saturn's orbits, using Bayesian statistics methods to factor in collected information.
To identify waves from a specific binary SMBH, an "un-blending" of periods of all the waves needs to be accomplished. It is felt that an accuracy of about 100 ns in timing deviations is required. A particular detected frequency with a consistent phase showing from all the pulsars would indicate waves passing Earth from a particular source. Getting a direction on the source would require analyzing the effect on different pulsars according to the angle between wavefront and the lines of sight to the pulsars, so the more pulsars being observed, the better. The data from multiple pulsars are also used to refine the precise space/time reference used, somewhat in analogy to the processing done in high-precision astrometric surveys: statistical processing to (in effect) "minimize the sum of least squares" of apparent divergences, i.e., to identify the most likely time reference based upon all the data.
The PTA effort is also trying to detect and characterize the gravitational wave background (GWB) over this frequency range due to all the producers of such waves throughout the universe.
Software for PTA analysis includes: