Detecting nanohertz gravitational wave bursts with pulsar timing arrays

Pulsar timing arrays (PTAs) provide a unique and crucial window for detecting nanohertz gravitational waves. Unlike ground- or space-based interferometers, pulsar timing arrays utilize an array of high-precision millisecond pulsars and monitor their pulse arrival times over extended timescales to sensitively detect perturbations in spacetime. In addition to the expected signals from supermassive black hole binaries, increasing evidence indicates that other astrophysical processes—such as cosmic string cusps, gravitational wave memory effects, or other unknown cataclysmic phenomena—may also produce transient gravitational wave bursts within this frequency range. This paper provides a systematic review of recent advancements in the search for gravitational wave burst signals using pulsar timing arrays, with a particular emphasis on methods targeting unmodeled bursts. Within a Bayesian inference framework, we assess a search algorithm on simulated pulsar datasets that have been injected with burst signals, demonstrating its ability to reconstruct such events. In future work, we plan to apply this method to real PTA data to identify potential gravitational wave burst events or to impose stricter constraints on burst amplitudes.