Study of nanohertz continuous gravitational waves based on pulsar timing array

Nanohertz continuous gravitational waves (CWs) offer a unique window into the properties of supermassive black hole binaries (SMBHBs). Pulsar timing arrays (PTAs), which precisely measure the timing of arrival, have emerged as the primary tool for detecting these elusive signals. This review summarizes the progress in PTA searches for CWs, focusing on two key approaches: all-sky searches and targeted searches for specific sources like 3C 66B.Several PTA collaborations, including NANOGrav, PPTA, and EPTA, have conducted extensive all-sky searches using data from numerous millisecond pulsars. These searches have significantly improved the sensitivity of GW detections across the nanohertz frequency band. Early efforts, like the 10-year PPTA search, demonstrated the complementary nature of PTA sensitivity to other GW detectors like LIGO and LISA, covering the nHz to mHz range. Subsequent searches with longer data sets have further refined the sensitivity, leading to improved upper limits on the strain amplitude of GW signals. For instance, NANOGrav's 12.5-year data set achieved a strain amplitude upper limit of h_95< (6.82 ± 0.35) × 10^-15at 7.65 nHz, showcasing the growing sensitivity of PTA observations.Targeted searches focus on specific sources with known characteristics, reducing the parameter space and increasing the chances of detection. The SMBHB candidate 3C 66B, predicted to emit nanohertz GWs, has received particular attention. Studies using NANOGrav data have placed upper limits on the chirp mass of the black holes in 3C 66B, providing valuable insights into its properties and evolution. The most recent NANOGrav analysis with 12.5 years of data suggests a chirp mass upper limit ofmathcalM95geq 0.34 × 10^9 M_ødot indicating the potential for detecting GWs from SMBHB with PTA observations.Simulation studies play a crucial role in understanding the detectability of nanohertz GWs with PTAs. Our 5-year simulation with 20 millisecond pulsars showcases PTA's high sensitivity for nanohertz GW detection, surpassing past results. The study also highlighted the effectiveness of targeted searches in constraining the properties of specific GW sources like 3C 66B, achieving a chirp mass upper limit ofmathcalM95geq 5.7 × 10^9 M_ødotunder ideal conditions. This simulation demonstrates the potential of PTAs for detecting nanohertz GWs and provides valuable insights into the challenges and opportunities associated with these searches.The ongoing efforts of PTA collaborations, combined with advancements in data analysis techniques and the expansion of pulsar catalogs, hold great promise for the detection of nanohertz GWs. Upcoming projects like the square kilometer array (SKA) will further enhance the capabilities of PTAs, opening new avenues for exploring the mysteries of the universe through GW astronomy. These future observations will likely improve the sensitivity of PTA searches, enabling the detection of nanohertz GWs and providing valuable insights into the early universe and the evolution of SMBHB.