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

Abstract

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.

Figures (12)

• Figure 1: The diagram of the SSB frame. In the SSB frame, the $z$-axis is parallel to the orbital angular momentum of the Earth, while the $x$-axis points to the vernal equinox.
• Figure 2: Comparison of different GW sources. (a) shows BBH signals and sensitivity curves, where the vertical axis represents the dimensionless characteristic strain $\sqrt{fS_n(f)}$. The BBH curve is derived from Ref. LISA_noise and is intended solely for illustrative purposes. For luminosity distance, we set SBBH at $D_L=44.6$ Mpc and MBHB at $D_L=6.79$ Gpc. The three vertical dashed lines represent the transfer frequencies $f_*$ of the three space-based detectors. (b) displays SGWB signals and the corresponding sensitivity curves, where the vertical axis denotes the dimensionless energy density spectrum $\Omega(f)$. For visualization purposes, the peak amplitude of the PT signal is fixed to $\Omega_{\rm p} = 10^{-9}$, and the amplitude and reference frequency of the power-law signal are set to $\Omega_{\beta} = 10^{-8}$ and $f_{\rm ref} = 0.1\,\mathrm{mHz}$. (c) and (d) illustrate a simulated SGWB source configured as white noise with $\mathrm{PSD}=1$, shown in the frequency domain and time domain, respectively. Only tensor modes are displayed, and the same setup applies to the other polarizations.
• Figure 3: The constellation of space-based detector.
• Figure 4: Comparison of the noise PSD for LISA. (a) shows the instrumental noise and the confusion noise in the $X$ channel. The upper subpanel presents the noise PSD in the frequency domain, while the two lower subpanels illustrate the corresponding signals transformed into the time domain. (b) shows the noise PSD for different second-generation TDI combinations. Frequencies below 0.1 Hz are shown on a logarithmic scale. No TDI refers to the interference only between adjacent links, such as $\eta_{31}-\eta_{21}$. Both instrumental noise and confusion noise are included. All sensitivity curves and PSD in this paper are numerically simulated. For clarity and conciseness, median smoothing is used.
• Figure 5: Computation of the PLIS curve for an observation time of one year and $\mathrm{SNR}=1$ for LISA. The gray curves correspond to power-law SGWB spectra with different spectral indices with $\mathrm{SNR}=1$. The LISA's sensitivity curve is also shown for reference.