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Detection of the stochastic gravitational wave background with the space-borne gravitational-wave detector network

Jun Cheng, En-Kun Li, Jianwei Mei

TL;DR

This work develops a Bayesian cross-correlation framework for stochastic gravitational-wave background detection using two space-based detectors (TianQin and LISA) and time-varying overlap reduction functions. By segmenting data to handle orbital motion and computing the ORFs numerically, the authors demonstrate improved parameter estimation and detection limits for isotropic SGWB models (power-law, flat, and single-peak) within a three-month observation. The TianQin–LISA network yields notably tighter constraints on spectral parameters and achieves detectable amplitudes down to $\Omega_{\rm PL}=6.0\times10^{-13}$, $\Omega_{\rm Flat}=2.0\times10^{-12}$, and $\Omega_{\rm SP}=1.2\times10^{-12}$, outperforming a single detector. The study highlights the value of detector networks for SGWB science in the mHz band and points to future extensions incorporating full A,E,T channels and astrophysical foregrounds.

Abstract

The stochastic gravitational wave background (SGWB) is one of the main detection targets for future millihertz space-borne gravitational-wave observatories such as the \ac{LISA}, TianQin, and Taiji. For a single LISA-like detector, a null-channel method was developed to identify the SGWB by integrating data from the A and E channels with a noise-only T channel. However, the noise monitoring channel will not be available if one of the laser interferometer arms fails. By combining these detectors, it will be possible to build detector networks to search for SGWB via cross-correlation analysis.In this work, we developed a Bayesian data analysis method based on \ac{TDI} Michelson-type channel. We then investigate the detectability of the TianQin-LISA detector network for various isotropic SGWB. Assuming a three-month observation, the TianQin-LISA detector network could be able to confidently detect SGWB with energy density as low as $Ω_{\rm PL} = 6.0 \times 10^{-13}$, $Ω_{\rm Flat} = 2.0 \times 10^{-12}$ and $Ω_{\rm SP} = 1.2 \times 10^{-12}$ for power-law, flat and single-peak models, respectively.

Detection of the stochastic gravitational wave background with the space-borne gravitational-wave detector network

TL;DR

This work develops a Bayesian cross-correlation framework for stochastic gravitational-wave background detection using two space-based detectors (TianQin and LISA) and time-varying overlap reduction functions. By segmenting data to handle orbital motion and computing the ORFs numerically, the authors demonstrate improved parameter estimation and detection limits for isotropic SGWB models (power-law, flat, and single-peak) within a three-month observation. The TianQin–LISA network yields notably tighter constraints on spectral parameters and achieves detectable amplitudes down to , , and , outperforming a single detector. The study highlights the value of detector networks for SGWB science in the mHz band and points to future extensions incorporating full A,E,T channels and astrophysical foregrounds.

Abstract

The stochastic gravitational wave background (SGWB) is one of the main detection targets for future millihertz space-borne gravitational-wave observatories such as the \ac{LISA}, TianQin, and Taiji. For a single LISA-like detector, a null-channel method was developed to identify the SGWB by integrating data from the A and E channels with a noise-only T channel. However, the noise monitoring channel will not be available if one of the laser interferometer arms fails. By combining these detectors, it will be possible to build detector networks to search for SGWB via cross-correlation analysis.In this work, we developed a Bayesian data analysis method based on \ac{TDI} Michelson-type channel. We then investigate the detectability of the TianQin-LISA detector network for various isotropic SGWB. Assuming a three-month observation, the TianQin-LISA detector network could be able to confidently detect SGWB with energy density as low as , and for power-law, flat and single-peak models, respectively.
Paper Structure (16 sections, 24 equations, 10 figures, 2 tables)

This paper contains 16 sections, 24 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Description of the SGWB
  3. Detector Network
  4. Orbital characteristics
  5. Noise model
  6. Search method
  7. Correlation analysis
  8. Overlap reduction function
  9. Likelihood
  10. Detection results
  11. Parameter estimation
  12. Astrophysical origin
  13. Cosmological origin
  14. Detection limit
  15. Summary and discussion
  16. ...and 1 more sections

Figures (10)

  • Figure 1: Illustration of the TianQin-LISA detector network. TianQin is expected to operate in a geocentric orbit, whereas LISA is designed to orbit the Sun, trailing $20^\circ$ behind the Earth.
  • Figure 2: Schematic diagram of the TDI-1.5 generation Michelson-type X channel.
  • Figure 3: The TDI-1.5 generation Michelson-X channel noise PSD from different space-based GW detectors.
  • Figure 4: The overlap reduction function as a function of time in X channel, which shows the detector network's correlated responses to the SGWB at $t = 0$, $t = 1$ day, and $t = 4$ day. The upper panel illustrates the real parts, while the lower panel represents the imaginary parts.
  • Figure 5: Corner plot for the data = noise + a power-law spectrum case for TianQin-LISA detector network. The black vertical dashed lines represent the injection values of the SGWB and instrument noise parameters, while the vertical shaded region on the posterior distribution denote 68% credible region, the contour lines denote [68%, 95%] credible regions.
  • ...and 5 more figures