Tilt-to-length noise subtraction with pointing jitters from closed-loop dynamics for TianQin

TL;DR

This work tackles tilt-to-length (TTL) noise in TianQin by leveraging closed-loop drag-free and pointing control (DFPC) simulations to generate realistic jitter and test TTL coefficient calibration via null TDI channels. It finds that a single-MOSA rotation combined with high-frequency data in the band $0.1$–$1$ Hz yields more accurate TTL coefficient estimates and TTL subtraction than symmetric MOSA rotation, and demonstrates that using a different null channel, such as $C_3^{14}$, further improves the estimation under correlated jitters. The authors also propose injecting artificial jitter maneuvers at 1 Hz and using MOSA modulation to enhance identifiability, showing potential to reduce residual TTL below the target $0.3$ pm/Hz^{1/2}$. These results inform pointing-control strategy and post-processing pipelines, enabling TianQin to meet TTL constraints essential for robust GW detection in its designed frequency band.

Abstract

TianQin is a proposed space-based mission for gravitational wave detection, employing a constellation of three drag-free satellites in high Earth orbits to form a laser interferometric observatory. A critical technical challenge is mitigating tilt-to-length (TTL) coupling noise, which is expected to be the third dominant noise source after laser frequency and clock noises. This noise is unavoidable in the presence of the residual angular movement of satellites, movable optical subassemblies (MOSAs), and test masses (TMs), and needs to be subtracted after reducing the first two types of noises using time-delay interferometry (TDI). Previous works have shown that TTL coupling coefficients can be estimated from the null TDI channel $ζ$ and used for noise subtraction in other combinations. However, it was found that correlated MOSA yaw jitters have a negative impact on the TTL calibration, and the effects of realistic residual angular jitters from drag-free and pointing control (DFPC) are yet to be investigated. In this paper, we use closed-loop DFPC simulations to generate more realistic jitters in the science mode and test TTL calibration capability. Our simulations reveal that rotating only one MOSA is more favorable, compared to symmetrically rotating two MOSAs, for enhancing the accuracy of TTL coefficient estimation, while employing only high-frequency data (0.1 - 1 Hz). Moreover, we propose two other methods to further improve estimation accuracy. Firstly, using different null channel combinations, such as $C_3^{14}$, enhances the least squares estimation accuracy even in the case of high correlations in MOSAs' yaw jitters. Secondly, injecting different sinusoidal artificial maneuvers to the six MOSAs also shows improvements. These methods can help TianQin to meet the 0.3 pm/Hz$^{1/2}$ requirement after the TTL noise subtraction.

Figures (11)

• Figure 1: In the context of TDI labelling conventions, the MOSA located on the left side of satellite $i$ is referred to as MOSA$i$, while the corresponding MOSA on the right side is represented as MOSA$i'$. The arm length opposite to satellite $i$ is denoted as $\text{L}_i$. Arm lengths oriented clockwise are indicated using a prime, $\text{L}_{i'}$, whereas those oriented counter-clockwise retain the designation $\text{L}_{i}$.
• Figure 2: The schematic diagram briefly illustrates the angular jitter between the coordinates within the constellation plane, where the angles $\psi_{OA_1}$ and $\psi_{OA_{1'}}$ is the MOSAs opening angle for compensation of the breathing angle. The true jitter in the DWS readout is represented by $\varphi_{DWS_1}$ and $\varphi_{DWS_{1'}}$. The satellite jitters, along with the two MOSAs, are denoted by $\varphi_S$, $\Delta\psi_1$, and $\Delta\psi_{1'}$.
• Figure 3: Time-domain jitter simulation diagrams under two different control strategies. The upper plot illustrates the symmetrical rotation of two MOSAs to compensate for breathing angles, whereas the lower plot demonstrates the rotation of a single MOSA, which exhibits relatively larger dynamic ranges.
• Figure 4: Illustrative diagram of the null TDI channel method for TTL noise subtraction. By employing the null channel method, we can directly estimate all 48 TTL coefficients, including the linear drifts. To verify the accuracy of the calibration coefficients, it is necessary to examine whether the residual noise remains below 0.3 pm/Hz$^{1/2}$ using the X, Y, Z combination.
• Figure 5: The ASD plots of the satellite’s three-axis jitter and MOSA yaw angle jitter under symmetric rotation mode (the upper plot), along with the two DWS readout signals (the lower plot). The true jitter data are multiplied by the coupling coefficients to simulate TTL noise in the TDI. The DWS readout data will subsequently be utilized for TTL noise estimation.