Earth–lunar thermal effect on the temperature stability of TianQin telescope and the suppression methods

TianQin is a geocentric space-based gravitational wave detection mission, it will confront a more complex and variable orbital thermal environment compared to heliocentric orbit missions like LISA. As one of the core payloads in TianQin, the telescope requires stringent temperature stability. Furthermore, the telescope operates as an open system directly exposed to the external environment. Besides the solar thermal irradiation, the earth and lunar heat irradiation exist in the TianQin orbit, and may enter the telescope during the observation period. Up to now, the effect of earth–lunar heat flux on the temperature stability of the TianQin telescope has not been addressed. In this article, an innovative algorithm is proposed for accelerating the Gebhart factors calculation, and the detailed evaluation from the direct earth and lunar heat flux to the telescope’s temperature stability has been accomplished. Our findings reveal that the temperature stability of the telescope’s secondary mirror closely approaches the level of total TianQin requirement (about 2 mK/$\sqrt{\mathrm{Hz}}$@0.1 mHz and 5$\mu$K/$\sqrt{\mathrm{Hz}}$@2 mHz) in the absence of a baffle, especially in proximity to frequencies of the 0.1 mHz and 2 mHz. To suppress the heat flux influence, we researched the effect of the geometry and surface thermo-optical property of the baffle on the temperature stability of the telescope. A bunched entrance baffle is optimized by Linear Programming analysis based on the smallest laser aperture and baffle geometric size constraint and then achieved temperature stability of about 0.3 mK/$\sqrt{\mathrm{Hz}}$ @0.1 mHz for the secondary mirror. In addition, An empirical formula derived from conic curve analysis is utilized to guide the iterative optimization of vanes. Subsequent implementation of vanes within the baffle serves to further suppress the earth and lunar heat flux disturbances, leading to an improved temperature stability of about 0.04 mK/$\sqrt{\mathrm{Hz}}$ @0.1 mHz and 0.7 $\mu K\sqrt{\mathrm{Hz}}$ @2 mHz, one order of magnitude below the TianQin total requirement. The methods and results can also provide enlightenment for other similar space missions.