The Study On Detection Method For The Polarization Of The Stochastic Gravitational-wave Background

The successful detection of gravitational waves is a major breakthrough in the field of astronomy and marks the beginning of the era of multi-messenger astronomy.The analysis of the detected gravitational-wave signal can in turn test the gravity theory,and one of the important aspects is to test the polarization mode of gravitational waves.While general relativity(GR)predicts only two tensor modes for gravitational-wave polarization,general metric theories of gravity allows up to four additional modes.There exists a kind of special gravitational wave source: the stochastic gravitational wave background(SGWB).It is composed of a large number of tiny gravitational-wave signals incoherent superposition,in which individual gravitational-wave signals cannot be recognized by the detector.The SGWB can be identified by special data analysis methods,when the overall intensity is comparable to the detector noise.The polarization mode of gravitational waves can be tested by probing SGWB,and the key problem is how to determine whether alternative polarizations are included in the background signals.In this work,the detection method of SGWB and the resolution of polarization mode are studied,focusing on the data analysis method of space gravitational-wave detectors.First,we analyze and calculate the response functions of various detectors to the SGWB.According to the characteristics of the SGWB,cross-correlation is the most typical detection method.The consistency between the response functions of the two detectors determines the strength of the cross-correlation signal of them,from which the overlap reduction function(ORF)can be defined to describe the response of the two detectors to the SGWB.The ORF is critical in the data analysis of the SGWB.With a new integration method,the ORF of the pulsar timing array for different polarization modes can be calculated analytically.For space laser interferometric gravitational-wave detectors,the high-precision ORF expressions can be obtained by extending the low-frequency approximation.Secondly,we evaluate the detection ability of space gravitational-wave detectors on SGWB with different polarization modes.The data analysis method for different type detectors to detect the SGWBs is similar,and only the ORFs for detectors need to be applied.There are abundant SGWB sources for future space gravitational-wave detectors,and it is of great significance to analyze their detection capabilities.Different space gravitational-wave detectors have different regions of the sky that are sensitive to different polarizations and may vary with detector motion.By calculating the average ORF,combined with detector noise,the detection capability for SGWB with different polarizations can be evaluated.Finally,two methods are proposed to distinguish different polarization modes in the background of random gravitational waves.Different polarizations are mixed in the SGWB signal at the same time,and how to identify and distinguish them is a major problem.For space gravitational-wave detectors,the varying ORF provides a new way to resolve different polarizations.Cross-correlation data from two detectors running to different locations,which respond differently to different polarizations,can be equivalently considered to be from different pairs of detectors,and the intensity of different polarization companents can be inferred from the cross-correlation data sets.Bayesian statistical methods can also be applied to identify different polarization companents in the SGWB signal.However,the varying ORF will create new problems in the construction of statistics of Bayesian analysis,and the average weighted statistics over different time periods is too weak to lose the signal-to-noise ratio.By multiplying the ORF for each time period,the polarization weighted statistic can be constructed to avoid the loss of signal-to-noise ratio.