Fundamentals of the orbit and response for TianQin

TL;DR

This paper provides analytical orbit expressions and response models for TianQin, a space-based gravitational wave detector, enabling improved science objectives analysis and data interpretation.

Contribution

It introduces analytic orbit formulas and a comprehensive detector response model for TianQin, facilitating accurate science studies and detector optimization.

Findings

Derived leading-order orbit coordinates in heliocentric-ecliptic system.

Developed a full-range gravitational wave response model for TianQin.

Generated a realistic sensitivity curve and applied it to a white-dwarf binary.

Abstract

TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz -- 1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately $1.7 \times 10^{5} ~\rm{km}$. The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit and the response of the detector. In this paper, we provide the analytic expressions for the coordinates of the orbit for each spacecraft in the heliocentric-ecliptic coordinate system to the leading orders. This enables a sufficiently accurate study of science objectives and data analysis, and serves as a first step to further orbit design and optimization. We calculate the response of a single Michelson detector to plane gravitational waves in arbitrary waveform which is valid in the full range of the sensitive frequencies. It is then used to generate the more realistic sensitivity curve of TianQin. We apply this model on a reference white-dwarf binary as a proof of principle.