Progress in the study of the location of the space gravitational wave source where theoretical physics is located

[ Instrument Network Instrument R & D ] Quickly and accurately locating the source of gravitational waves is one of the important tasks of ground and space gravitational wave observation. Accurate positioning of the wave source is essential for subsequent electromagnetic spectrum observations and determination of the host galaxy of the wave source. After accurately knowing the redshift of the host galaxy, the source of gravitational waves can be used as a standard whistle to independently study the expansion history of the universe.

Recently, PhD students Ruan Wenhong, Liu Chang, and researchers Guo Zongkuan, Cai Ronggen, and Wu Yueliang from the Institute of Theoretical Physics of the Chinese Academy of Sciences have proposed the LISA-Taiji space gravitational wave detection network, which can realize the rapid and accurate positioning of gravitational wave sources.

Since laser interference detectors are sensitive to gravitational waves from almost all directions, it is difficult to determine the spatial position of a gravitational wave source with a single ground gravitational wave detector. Using two detectors built at different positions, in principle, triangulation can be performed by the time difference between the gravitational wave signals reaching the two detectors, limiting the position of the wave source to a ring in space. Using a network of more than two detectors for joint detection, the spatial position of the wave source can be determined by the time difference of arrival of the gravitational wave signals on different detectors, as well as the phase difference and amplitude ratio. For example, using only two LIGO detectors, the confidence interval of 90% confidence in the azimuth angle of the wave source space of GW170814 is 1160 square degrees, which is reduced to 60 square degrees after networking with Virgo. In the future, joining KAGRA and LIGO-India will further improve the detector's ability to locate the source of gravitational wave signals in sensitive frequency bands.

Unlike ground-based gravitational wave detectors, the main target of LISA and Tai Chi is the gravitational waves generated by the merger of massive black holes with masses between 104 solar masses and 107 solar masses at the center of the galaxy. Although the constrained large-mass double black hole systems are difficult to identify by electromagnetic observations, when the double black holes are close enough, the orbital period of the system is less than a few hours, and these systems become strong gravitational wave sources. After orbiting is the merger of two large-mass double black holes. The gravitational waves generated by this process can be observed by a space gravitational wave detector and have a high signal-to-noise ratio. The combined observation of electromagnetic and gravitational waves on these systems can be helpful for studying accretion disks in the process of merging large-mass double black holes into a single black hole.

The gravitational wave signal generated by the revolving and merging of this large-mass double black hole system can last for several days to several years in the sensitive frequency bands of LISA and Tai Chi. Due to the motion of the detector in space, the time-dependent response function will play an important role in the positioning of the source of gravitational waves. Therefore, a single space gravitational wave detector can be regarded as a joint detection network composed of multiple detectors located at different positions in its orbit, and these detectors observe a specific gravitational wave event at different times. LISA is expected to make the angular coordinate accuracy of gravitational wave sources reach 1 to 100 square degrees, which is related to the quality of the binary star and the distance to the detector. However, considering the expected redshift distribution of the wave source detected by LISA, such angular coordinate accuracy is insufficient to determine the galaxy where the wave source is located. If LISA and Taiji conduct joint detection, then the network formed by them can adopt a strategy similar to the ground detector to triangulate the signal to significantly improve the spatial positioning accuracy of the gravitational wave source.

The angular coordinate accuracy of gravitational wave sources achieved by LISA and Taiji joint detection is related to their included angle on the heliocentric orbit. When this angle reaches 180 degrees, the angular coordinate range of the wave source is the smallest. For an equal-mass dual black hole system with a total mass of 105 solar masses, consider the two cases of red shift of 1 and 3. When the included angle is increased from 3 degrees to 40 degrees, the accuracy of the wave source angular coordinate is improved by 2 orders of magnitude, but when the included angle is The accuracy increased by only about 0.6 orders of magnitude when increasing from 40 degrees to 180 degrees. Therefore, the combined angle of LISA and Taiji detection reaching 40 degrees can effectively help people locate the source of gravitational waves quickly and accurately.

The research results were recently published in Nature Astronomy 4 (2020) 108. This research was supported by major projects of the National Natural Science Foundation of China, the Strategic Leading Science and Technology Project of the Chinese Academy of Sciences, and key research projects on cutting-edge science.