A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

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A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

Han, Xiaoqing / Tang, Wenlin / Peng, Xiaodong / Yang, Zhen

Abstract The Taiji project is a space gravitational wave detection mission consisting of three satellites that form a large equilateral triangle with a side length of approximately $3 \times 10^{9}$ m in heliocentric orbit. It may have the potential to detect gravitational waves below 0.1 mHz. Gravitational wave signals in the $μ$ Hz range have a strain sensitivity as large as $2.9 \times 10^{- 14}$ , or approximately $8.7 \times 10^{- 5}$ m variation in inter-satellite distance. However, inter-satellite distances are affected by the celestial bodies in the solar system, introducing changes that may reach magnitudes of $3 \times 10^{7}$ m; thus, the effect of celestial bodies on these distances may exceed the gravitational signals below 0.1 mHz. Therefore, it is necessary to accurately estimate the effect of the gravity of celestial bodies below 0.1 mHz. In this study, based on the inter-satellite distances in the Taiji mission, a window function design method is proposed and a six-term cosine window function is designed. It has a high decay rate of $h^{- 12}$ and a good peak sidelobe level of −88 dB. It improves the attenuation of spectral leakage while maintaining an acceptable minimum number of signal periods, which is beneficial for signals where it is difficult to obtain more periods, such as for the Taiji mission. Based on the analytical results of the states of satellites in cases when the satellites move only in the gravitational field of the Sun, the ability of the new window function is validated.