Constraints and detection capabilities of GW polarizations with space-based detectors in different TDI combinations

TDI is essential in space-based GW detectors, effectively reducing laser noise and improving detection precision. Space-based GW detectors provide a unique opportunity to probe GW polarizations, including possible additional modes that may signal deviations from general relativity and alternative gravity theories. In this study, we examine the impacts of second-generation TDI combinations on GW polarization detection by simulating LISA, Taiji, and TianQin, including realistic orbital effects such as link length and angle variations. Detector performance is assessed using sensitivity and power-law integrated curves, as well as the SNR of BBHs and phase transitions (PTs). For massive BBHs, the A and E channels typically offer the best sensitivity, while the X channel in TianQin is most effective for detecting additional polarizations. For stellar-mass BBHs, the $α$ channel provides the highest SNR for vector modes in LISA and Taiji specifically for lower-mass systems, while the A and E channels are optimal for higher masses or other polarizations. For PT signals, the X channel generally delivers the optimal performance, except in the low-peak-frequency regime below 1 mHz, where the U channel in TianQin becomes more sensitive. When considering additional polarizations, the X channel emerges as the most robust choice for TianQin, in contrast to LISA and Taiji, where the A and E channels provide strong capabilities for GW polarization tests. This distinction between LISA, Taiji, and TianQin represents a key result of the present work and has not been explicitly emphasized in previous studies. Our findings emphasize the importance of selecting high-sensitivity TDI combinations to enhance detection capabilities across different polarizations, deepening our insight into GW sources and the fundamental nature of spacetime.

💡 Research Summary

This paper investigates how second‑generation time‑delay interferometry (TDI) combinations affect the detection of gravitational‑wave (GW) polarizations in three planned space‑based detectors: LISA, Taiji, and TianQin. The authors model realistic orbital dynamics, including time‑varying arm lengths and angles, and construct nine commonly used TDI channels (A, E, α, β, γ, X, Y, Z, U) for each mission. Noise contributions from laser frequency fluctuations, acceleration, optical path, and clock noise are combined to produce a total one‑sided power spectral density (PSD) for each channel.

GW signals are generated for six possible polarizations (two tensor +, ×; two vector X, Y; two scalar B, L). Tensor waveforms are taken from the SEOBNRv4 model, while non‑tensorial modes are added using the parameterized post‑Einsteinian (ppE) framework, with amplitude parameters α_V, α_B, α_L scaling with chirp mass, distance, and inclination. Three source classes are considered: massive black‑hole binaries (MBHBs) with 90‑day observation windows, stellar‑mass black‑hole binaries (SBBHs) observed for one year up to 1 Hz, and stochastic backgrounds representing first‑order phase‑transition (PT) signals with a fixed peak amplitude Ω_p = 10⁻⁹ and peak frequency in the 10⁻⁴–10⁻² Hz range. A flat‑spectrum stochastic GW background (white noise) is also injected to compute power‑law integrated (PLI) sensitivity curves.

The authors convert channel PSDs into characteristic strain h_c(f) = √