Study Of Sensitivity Function For The Space-based Gravitational Wave Detector

Gravitational waves are ripples in time and space.The detection of gravitational waves can test Einstein’s general relativity and helps to open up a new window for human understanding of the universe.Compared with the ground-based gravitational wave detectors,space-based gravitational wave detection has a lower target frequency band and abundant source information of gravitational waves.Therefore,space-based gravitational wave detection is of great significance to the study of the formation and evolution of the universe.The space-based gravitational wave detection plan is usually achieved by laser interferometry,and its detection ability is reflected by its sensitivity function.The sensitivity function depends not only on the magnitude of various noises,but also on the transfer function.In general,the analytical results of the sensitivity should be presented,which can reflect the performance of the detector more clearly.At present,the noise of space gravitational wave detector mainly includes: laser phase noise,test mass acceleration noise,shot noise,clock noise and so on.The laser phase noise is the largest noise term,which is mainly eliminated by time delay interferometry.On the basis of time-delay interferometry,clock noise has aroused heated debate in academia and has been widely studied,but there is no simple result.In addition,different research groups have done some research on the transfer function,and the results have certain limitations,and also do not give a fully analytical result.Therefore,it is of great scientific significance to establish a perfectly analytical theoretical model for the sensitivity of space-based gravitational wave detector.This paper mainly focuses on studying the sensitivity of space-based gravitational wave detector and analyzing the detection ability of LISA and Tian Qin.The research contents include:(1)combined with the principle of eliminating the laser phase noise with the time delay interferometry,the influence of clock noise is analyzed systematically,the power spectral density of laser interferometric space gravitational wave detector noise is given,and the main noise is evaluated.The “sideband measurement technology” is used to eliminate clock noise and calculate the remaining clock noise to provide a theoretical reference for the analysis of the noise;(2)The two methods of encoding the gravitational wave signal into the detector(the responses of the detector to different polarization angles;the responses of the detector to the plus and cross polarizations of the gravitational wave)are summarized and compared,and the responses of the detector are analyzed by using these two methods respectively.Finally,the equivalence of their results is proved,and it provides the basis for us to use the second method(the responses of the detector to the plus and cross polarizations of the gravitational wave)to calculate the transfer function.(3)The transfer function of space-based gravitational wave detector is analyzed by expanding the research method of the “time delay interferometry” and a complete analytical expression of the transfer function is given by using the coordinate transformation and algorithm,which establishes a perfect theoretical model for space-based gravitational wave detector.The analysis plays an important guiding role in the evaluation of the detection capability of the instrument.In addition,based on the derived analytical expression,the detection capabilities of LISA and Tian Qin are analyzed.In general,we give the full analytical expression of the space sensitivity function.The result not only helps to clearly reflect the influence of various parameters in the experiment on the sensitivity of the detector,but also helps to compare the detection performance of different detectors,and provide a theoretical reference for the design of gravitational wave detection scheme in the future.