Pulsar timing arrays: Searching for the nano-Hertz continuous gravitational waves from supermassive black hole binaries

The pulsar timing array (PTA) utilizes the ultra-high precision timing characteristics of millisecond pulsars to construct a galaxy-scale detector, aiming to usher in a new era of nano-Hertz gravitational wave (GW) astronomy. This unique observation window allows us to study the stochastic gravitational wave background (SGWB) generated by the merger processes of numerous supermassive binary black hole (SMBBH) systems in the universe, the continuous gravitational waves (CGW) emitted by individual, stronger SMBBH systems, as well as the gravitational wave signals produced by phase transitions in the early universe and cosmic strings. Detecting and studying these signals holds significant scientific importance. They not only directly reveal the history of galaxy mergers and evolution, tracing the growth paths of supermassive black holes in the universe, but also provide crucial clues for understanding the dynamical behavior of SMBBHs, including addressing the “final parsec problem", and testing fundamental physical theories such as general relativity under strong gravitational field conditions. Global collaboration has brought together various regional arrays, including North America's NANOGrav, Europe's EPTA, Australia's PPTA, India's InPTA, and South Africa's MPTA. These arrays, along with China's CPTA, are collectively committed to continuously improving the detection sensitivity of the International Pulsar Timing Array (IPTA). This review will systematically summarize the latest progress, challenges, and future prospects of these major international PTA collaborations in searching for nano-Hertz SGWB signals, particularly the recent significant evidence, as well as in detecting CGW from individual SMBBHs.